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University Microfilms 300 North Zeeb Road Ann Arbor, Michigan 48106 A Xerox Education Company 73-4638 MUELLER, James William, 1941IHE USE OF SAMPLING IN ARCHAEOLOGICAL SURVEY. The University of Arizona, Ph.D., 1972 Anthropology University Microfilms, A XEROX Company, Ann Arbor, Michigan THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED. THE USE OF SAMPLING IN ARCHAEOLOGICAL SURVEY by James William Mueller A Dissertation Submitted to the Faculty of the DEPARTMENT OF ANTHROPOLOGY In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY In the Graduate College THE UNIVERSITY OF ARIZONA 19 7 2 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE I hereby recommend that this dissertation prepared under my direction by James William Mueller entitled THE USE OF SAMPLING IN ARCHAEOLOGICAL SURVEY be accepted as fulfilling the dissertation requirement of the degree of Doctor of Philosophy UJ * hwAAi/u— Dissertation Direc^pr Date' After inspection of the final copy of the dissertation, the follov/ing members of the Final Examination Committee concur in its approval and recommend its acceptance:"" T~(«I ? £ . .KcleU " ?/¥ /7> This approval and acceptance is contingent on the candidate's adequate performance and defense of this dissertation at the final oral examination. The inclusion of this sheet bound into the library copy of the dissertation is evidence of satisfactory performance at the final examination. PLEASE NOTE: Some pages may have indistinct, print. Filmed as received. U n i v e r s i t y M i c r o f i l m s , A Xerox Education Company STATMENT BY AUTHOR This requirements is deposited rowers under dissertation has been submitted in partial fulfillment of for an advanced degree at The University of Arizona and in the University Library to be made available to bor rules of the Library, Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or re production of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the in terests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED: PREFACE The inspiration for this dissertation came from Professor Stuart Struever's seminar in Archaeological Research Methods at North western University in the spring of 1969. As I recall now, the ques tion under discussion concerned a comparison of a site inventory based on farmers's reports to an archaeologist's inventory of sites based on an intensive, continuous survey of the same area. T quickly realized that the continuous, intensive survey that I had participated in during the previous summer on the Paria Plateau was quite amenable to an ex periment concerning the above sampling question. This rapidly-fermenting idea assumed an additional meaning in light of the increasing schism between the "new" and the "traditional" brands of archaeology of the late 1960's. Some programmatic state ments by the "new" archaeologists advocated the use of sampling. I thought that an empirically-based sampling experiment would shed some light, rather than heat, on the mushrooming controversy. This experi ment would constitute one criterion for accepting or rejecting the "new programmatic dogma." At any rate, if I may use an overused word, the relevancy of this experiment motivated me to consummate it. Some data verification and preliminary processing occurred while I was at the Museum of Northern Arizona in the spring and summer of 1970, with the valued assistance of Dr. Alexander J. Lindsay, Jr., Curator of Anthropology. I began to work full-time with the data in January 1971. Conversations with many friends influenced me; fellow graduate iii iv students, Meade Kemrer and Donald Graybill, listened and offered sug gestions. Among the faculty, Drs. William Robinson and Jeffrey Dean at the Laboratory of Tree-Ring Research continually reinforced me by indicating a need for this kind of project. Dialogues with Professor Alan Humphrey, statistical consultant to the Department of Anthropology, forced me to be more rigorous than I might have been otherwise. Mr. David Asche of the University of Michigan provided useful statistical guidance for many long nights during the 1971 field season at the Koster project in southern Illinois. Larry Manire and Philip Strongin, computer consultants to the Department of Anthropology, were the leg men itfho did all the technical work that I could not do. They worked many long hours with me and with my long, inscrutable letters from Massachusetts trying to derive computer samples. My debt to Larry particularly is very great. My dissertation committee at The University of Arizona gave me "free reins to do my own thing." Specifically, Dr. William A. Longacre, my chairman, accepted the idea and thankfully forbade com promises as I began to feel the pressure of completion. Dr. T. Patrick Culbert saw some usefulness to this project back in 1969 and en couraged me to abandon other proposed topics in favor of this one. The lucid intellect of Dr. Raymond H. Thompson was a model that I constantly tried to emulate. Drs. Culbert and Thompson, playing the role of the devil's advocate, forced me to be very explicit and to direct the study towards a more general audience than the sampling specialists whom I was addressing. As a result, the revising of the V dissertation became as valuable a learning experience as the initial writing. I would also like to thank the entire committee for their diligent work "above and beyond the call of duty" that allowed me to complete the revisions and the defense in a single visit to Tucson from Massachusetts. Dr. Thompson, from an administrative viewpoint, was particularly instrumental in permitting me to complete these final degree requirements. The final tyoing \<ras done by Mrs. Hazel Gillie in her typi cally meticulous manner. Special thanks to her for performing the liaison with Mrs. Kozan in my absence. Mrs. Irene Corsini typed most of the tables and non-textual materials in draft form. The illustra tions testify to the already-established competence of Gayle Hartmann. Dr. Getty and the secretaries at the Department of Anthropology — Mrs. Vearl Ferdon, Harriett Martin, and Dorothy Caranchini — cooper ated wonderfully to assist in the success of my visit in August, 1972. Another bouquet of appreciation goes to Bridgewater State College where I was allowed the freedom to complete the project during my first year of teaching. My friendship with Mr. Jaime Calderon in the Department of Sociology developed from a common interest and mutual intelligibility in sampling questions. The greatest sacrifices were made by my wife who endured my leave of absence from life during this past academic year. The largest bouquet goes to Sandi. TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS ix LIST OF TABLES x ABSTRACT xiii 1. THE THEORETICAL FRAMEWORK 1 Introduction Background Purpose General Outline The Sampling Concept The Meaning of the Concept Approaches to Sampling Archaeological Survey Types of Survey The Question of VIeighted Results Spatial Units Summary 2. THE PARIA PLATEAU SURVEY .. » 1 1 3 3 U 5> 6 0 8 10 12 13 1U Synopsis Methods Objectives Strategy Tactics Tasks Dissertation Research Site Classification and Community Plan Culture History Environmental and Settlement Patterns The Inter-plateau Locale The Detrital Locale The Mesa Locale The Rim Locale The Big Ridge Locale , The Northern Locale ..... The Sand Hill Locale The Valley Locale Temporal Aspects of Locale Occupation vi D-i 16 18 18 19 21 23 2k 27 32 33 3£ 36 37 38 39 39 UO lj.1 vii TABLE OF CONTENTS--Continued Page Material Culture h3 Ii3 52 62 The Ceramics Lithic Artifacts Conclusions . THE DESIGN OF THE EXPERIMENT The Experimental Approach An Overview of Sampling Concepts and Definitions The Sample The Sampling Process The Sampling Scheme The Sampling Fraction The Size of the Sampling Unit The Sampling Repetition The Selection of Samples Sampling Schemes Sampling Unit . A Quantitative Evaluation of the Validity of Conclusions Based on Sampling Levels of Measurement 65 65 67 68 71 71 72 73 7h 7h . 75 76 99 103 10h Statistical Indices 10B Economy Summary 112 116 . THE RESULTS OF THE EXPERIMEMT 118 Summary Statistics 118 Sampling Scheme Expected Results 120 120 Economy Chi-square Analysis Summary Minor Schemes VECT Sampling Sampling Unit Sampling Fraction Repetition Descriptive Variable Conclusions Summary ... 121 125 127 128 133 136 139 Ili5 l!iS> 150 152 viii TABLE OF CONTENTS—Continued Page $. THE CONCLUSIONS OF THE EXPERIMENT An Appraisal of the Experiment Research Methods Archaeology and Sampling Theory 15U 1 l£U l£6 Archaeological Survey as the Cluster Sampling Techmoue Miscellaneous Sampling Conclusions Pragmatic Archaeological Considerations Sampling Scheme Sampling Fraction Sampling Unit Repetition Variable Guidelines for Implementing a Sampling Program . . Suggestions for Future Research .. Experimental Research Field Research Back to the Starting Line 1^6 161 16)4 16U 170 170 170 171 171 173 173 175 176 APPENDIX A: SAMPLING SUMMARY 178 APPENDIX B: FINANCIAL AND STATISTICAL DATA 183 APPENDIX C: THE EXPERIMENTAL DATA 185 LIST OF REFERENCES 199 LIST OF ILLUSTRATIONS Figure 1. The location of the Paria Plateau and of geographical landmarks 2. The location of the eight environmental locales in the survey area ix LIST OF TABLES Table Page 1. Site density and frequency of site form by locale .... 25 2. Temporal analysis of the nucleational ratio 31 3. Temporal analysis of locale occupation Ii2 U. Ceramic summary UU 5. Site fx-equencies cross-tabulated by locale and unpainted ceramics U7 6. Site frequencies cross-tabulated by locale and painted ceramics U8 7. Temporal analysis of unpainted ceramics 50 8. Temporal analysis of painted ceramics £1 9. Summary of catalogued and stone-catalogued artifacts . . 53 10. The provenience of temporally diagnostic lithic artifacts by locale 55 11. Cross-tabulation of subsistence activities by locale .. 58 12. Cross-tabulation of subsistence activities by site type . 59 13. Temporal analysis of subsistence activities 60 Hi. The STRAT DIS sampling fractions 83 15. The STRAT PRO sampling fractions 86 16. The stages of CLUS sampling . 88 17. Summary of the VECT STRAT and the VECT SUP schemes ... 95 18. List of variables and values 19. Schedule of variable survey costs 105 * 115 20. The average economy and rank order of sampling schemes . 122 x xi LIST OF TABLES—-Continued Table Page 21. Ranking of sampling schemes by percentage of signifi cant variables 123 22. A comparison of the CLUS SIM and CLUS SYS schemes by sampling .fraction 129 23. A comparison of the two and three-stage variants of CLUS SIM 131 2k* The relationship between second- and third-stage selection of CLUS SIM sampling 132 2 T h e economy and rank order o f CLUS SIM 13U 26. Analysis of sampling unit by economy and chi-square analyse.s 136 27. Tabulation of significant variables by sampling fraction II4.O 28. The number of exceptions to the expected chi-square pattern tabulated by sampling fraction Ilj2 29. Tabulation of exceptions to the expected pattern of economy lUi 30. The most satisfactory repetition IJ46 31. The frequency of significantly different occurrences of the six archaeological variables Ih7 32. A secondary chi-square test of the validity of locales . 1^9 33. SIM QSEC 186 3h. SIM SEC 187 35. SYS QSEC 188 36. SYS SEC 189 37. THU SYS QSEC 190 38. TRU SYS SEC 191 LIST OF TABLES—Continued Table Page 39. STRAT DIS SIM 192 UO. STRAT DIS SYS 193 Ul. STRAT PRO SIM 19U k2. STRAT PRO SYS . 195 ii3* Manually selected samples ............... 196 ABSTRACT This dissertation attempts to fill a void in the literature concerning probabilistic sampling in archaeological survey. The methods and results of the Paria Plateau Survey which provides the empirical base for remedying the above problem are presented. The experiment itself evaluates four major sampling factors — scheme, fraction, unit, and repetition as well as the archaeological variables. The experiment compares 326 simulated, sampling-based surveys to a known, empirically-derived population of U38 sites in or near the Paria Plateau in north central Arizona. Chi-square, economy, Spear man coefficient, and percentages are the statistics used to summarize and test the results. Sampling produces results that do not differ significantly from the population and is, therefore, regarded as a useful tool in archaeological survey. The hypothetical sample that would best predict the population is the second repetition of a siinple cluster scheme at the O.U sampling fraction using the section as sampling unit. The lithic function variable among five others is also the best population predictor. General guidelines concerning the usefulness of each scheme, as well as a field tactic for mini mizing sampling costs, are presented. The similarity between archae ological survey and the cluster sampling technique raises serious doubts concerning the validity of confidence limits in statistical inference. xiii CHAPTER 1 THE THEORETICAL FRAMEWORK A general outline of and justification for this study, as well as a discussion of the major related concepts, are presented in this chapter. Introduction Background Carl Lloyd supervised an archaeological survey of the area adjacent to the Ackmen pueblo in southwestern Colorado in 1937 in order to supplement the data recovered from the excavation of the famous pueblo. Sixty-six quarter-sections (each equivalent to a l/lj sq. mi. area) that measured 1/2 mile on each side were intensively surveyed by a large crew. Members of the crew were stationed 100 feet apart along the l/2 mile, width of the quarter-section, and the entire crew walked across the 1/2 mile length of the quarter-section. Froic each section consisting of four quarter sections, two diagonal quarter sections were selected for investigation. Lloyd assumed that the 66 surveyed quarter-sections represented at least a 33 square mile area near the ruin. He was not certain that the above methods would produce a contribution to the archaeology of the area and stated the uncertainty as follows: 1 2 Given a discontinuous intensive archaeological survey of a region, what contributions can be made to the archaeology of that region bv means of an analysis of the data thus ob tained? (Lloyd 1938: 282). He did not explicitly answer that question during the course of his report. However, I believe that his answer was implicitly positive, that is, the kind of survey he performed did produce a meaningful contribution to the archaeology of the Ackmen-Lowry regionc Other archaeologists have probably at;keel and will continue to ask Lloyd's question concerning the validity of conclusions based on a survey of less than 100 percent of an area. Most archaeologists cannot survey an entire area, but are forced to observe only a part of the whole area under investigation. Limited time and funds fre quently prevent the attaining of the ideal of 100 percent investiga tion, The question of which parts of an area to select for investi gation when the entire area cannot be covered is a common, but crucial, problem in archaeological survey. Despite the commonality of this question, a minimum of atten tion has been devoted to it. In many papers in which sampling is discussed (Vescelius I960; Rootenberg 196b; Binford I96L1; Ruppe 1966; Hill 1968; Longacre 1968; Redman and Watson 1970; Binford and others 1970) the methodological question as stated by Lloyd is overlooked. In fact, the general use of sampling in archaeological survey is also usually overlooked. These various authors have assumed on faith alone that sophisticated sampling will produce results that are representa tive of the population to be investigated. Perhaps, this inferential leap has been demonstrated for other kinds of data, but it appears 3 that it is time for an empirical test of sampling dogma in the face of archaeological survey data. Purpose The purpose of this study is to. answer empirically Lloyd's methodological question and to suggest guidelines for selecting which parts of a larger area should be surveyed. The problem is discussed in this study on the basis of a maximum of evidence derived from archae ological survey and with a minimum of polemics. I would hope that this empirical approach will avoid the unquestioned application and "cook book" use of statistical theory which has not been tested archaeologically. This study is actually an empirical test of statistical theory using archaeological survey data. General Outline The empirical basis of the study is an actual survey"-, the 1967-68 Paria Plateau survey. Each quarter-section within the sur veyed area of the Paria Plateau was investigated intensively in a manner similar to that of the Ackmen-Lowry survey (see Methods section in Chapter 2). The total frequencies of sites and artifacts recovered during the Paria Plateau survey represent the ideal of 100 percent coverage. In order to answer Lloyd's question, I have performed on paper 326 surveys that simulate various ways of selecting parts of the survey area. The assumption underlying these "paper" surveys is that each survey would have been performed with the same intensity and completeness of coverage as the real Paria Plateau survey in 1967 and 1968. (Additional controls that are described in Chapters 2 and 3 have been instituted to insure complete and equally intensive cover age.) Each "paper" survey is thus a small-scale version of the real Paria survey and closely resembles Lloyd's discontinuous intensive survey. For each of the 326 surveys, frequencies of sites and arti facts are tabulated in the same manner as for the real 100 percent survey. The frequencies for each of the partial surveys are compared to those of the actual survey in order to evaluate the contribution of each discontinuous survey to the archaeology of a region. The frequencies of each simulated survey are ranked among themselves in order to determine which of the partial surveys produces conclusions that most closely approximate the conclusions derived from the ideal 100 percent survey. The standard of evaluation in all cases is the actual Paria Plateau survey. The Sampling Concept Most scholars throughout the history of American archaeology have used sampling in both the survey and excavation phases of field work. Some archaeologists have knowingly applied sampling ideas, while others have unconsciously been sampling sites and survey areas. The concept, sampling, has been bandied about by different archaeolo gists in ways that have neither been completely clear nor consistent. In this section, I try to summarize and clarify the various meanings and usages of the concept. 5 The Meaning of the Concept The most common meaning is negative and implies that there is less than 100 percent recovery of data from any given research unit. A research unit is a spatial unit that is being investigated archaeologically (for example, a mesa, the area of red-on-buff ceramics, a site). In order to determine if recovery is complete, the boundaries of the research unit must be defined and data must be collected from every spatial subdivision of the entire research unit. I think that it is commonly, and at least implicitly agreed, that sampling occurs when the two preceding conditions have not been fulfilled. The kinds of data collected from each subdivision of a research unit vary with the research objective, the recovery technology avail able, the archaeological budget, and the archaeologist in charge. For example, pollen data were not collected 30 years ago in the South west because pollen was not considered necessary for culturehistorical research objectives. If other kinds of data relevant to culture history were collected from each excavation and all spatial subdivisions of a hypothetical site were excavated, then this site would be considered completely excavated and not sampled at all. Therefore, the distinction between sampling and complete investigation is determined by the collection of data from each spatial subdivision of a research unit. The kind of data collected is not crucial to whether a research unit was sampled or completely investigated. There is probably less agreement concerning the positive con notations of the sampling concept. Which spatial subdivisions of the 6 research units are selected for either excavation or intensive survey? What are the criteria for selecting these subdivisions? There appear to be three approaches to answering both of these questions: (l) archaeological, (2) statistical, and (3) archaeo-statistical. Each of these is discussed in turn. Approaches to Sampling The Archaeological Approach, This approach utilizes known archaeological (or archaeological-related) evidence to indicate which unknown subdivisions should be investigated. The research objectives determine which subdivisions are selected for further survey or exca vation. For example, if an archaeologist were interested in finding surface indications of devices for controlling water run-off, he would survey hillsides and slopes that drain areas of moderately high pre cipitation, An archaeologist interested in the beginnings of agricul ture in the Southwest would probably excavate the part of the site containing Basketmaker materials, rather than the Tsegi phase com ponent. Despite the presence of problem orientation, there are in reality probably as many solutions to selecting subdivisions as there are practicing field archaeologists. A second characteristic of this approach is that the sampling is usually restricted to the \xnsophisticated simple random method. This feature distinguishes this archaeological approach from the other two approaches. This approach has been used implicitly for a long period of time in American archaeology. Recently, the approach has been criti cized for being intuitive, inductive, and unstated (Binford 1961±). 7 Of the three criticisms, the enduring one will probably be the latter — the failure to state the sampling criteria and the research objec tives in the published monograph. Readers are not altogether clear as to why a particular area within the research unit was surveyed or a particular part of the site was excavated. Thompson's0-956) suggestion that the background and competence of the field archaeologist should be used to evaluate an archaeological project must be followed when the methods, sampling criteria, and research objectives are not ex plicitly stated. This failure to be explicit is undoubtedly a reflection of the period in American archaeology when all archaeolo gists knew each other personally and were able to discuss these method ological topics on a face-to-face basis. The Statistical Approach. This approach is an alternative answer to the question of which criteria to use to select certain sub divisions for investigation. This approach entails adherence to one of the many statistically-valid methods of recovering data from less than 100 percent of the research unit. These sampling methods are much more sophisticated than the simple random method of the archae ological approach. Stratified and systematic sampling are two such sophisticated methods, and each one, as well as others, will be fully described in Chapter 3. The particular sampling approach that is employed depends on the archaeological problem, the research objective, and other factors. It is quite easy to misuse this approach by blindly following sampling theory in a "cookbook" manner. 8 The Archaeo-statistical Approach. The ideal solution to the problem of selecting criteria and subdivisions is a combination of the archaeological and statistical approaches. This combination allows one to modify statistically-valid sampling methods because of archae ological or archaeologically-related data. This approach avoids the "cookbook" criticism that is frequently directed at archaeologists who employ a strictly statistical approach. One must have a working familiarity with the data before subjecting it to sampling or statisti cal procedures. This approach differs from the archaeological approach in that the latter includes less sophisticated sampling procedures. Archaeological Survey Types of Survey Dichotomous Classification. It was, and occasionally still is, common for archaeologists to describe survey as either intensive or extensive. Lloyd's (1938: 282) description illustrates this polar ization: A reconnaissance survey is a random (?) sampling of sites in an area, as opposed to an intensive survey, which stresses a thorough examination of an area. An intensive survey is an attempt to investigate every piece of terrain within a fairly small research area, such as a narrow river valley. On the other hand, an extensive survey (which Lloyd equates with a reconnaissance) deals with an area that is so large that it generally cannot be completely surveyed except as part of a very long-term, planned project. However, Lloyd incorrectly states that sites are sampled within a research area. What is really being sampled are 9 spatial subdivisions of the research area; this important point wi11 be discussed in subsequent chapters. Relativistic Classification. Recently, the dichotomous atti tude has been partially replaced by a more relativistic problemoriented approach. Hole and Heizer (1969s 127) exhibit this rela tivism: The kind of survey he /the archaeologist^ will make, as well as where he -will make it, depends on the kind of information he wants to obtain. Ruppe's classification of survey recognizes the variation that exists in survey strategies. His four partially overlapping types are based on the research objectives. Type I (which corresponds to an extensive survey in the earlier dichotomous classification) is, one that endeavors to secure a catalog of sites . . . /and is often described as a7 . . . "reconnaissance" or "ex ploration . . (Euppe 1966: 31h). Using this type of survey, the inventory of sites obtained is not com plete, and many unrecorded sites probably exist within the survey area. Type II survey, is the brief survey conducted in conjunction with a specific program of excavation (Ruppe 1966: 31$)* Additional chronological data and a larger artifact yield are gathered to supplement the excavated yield. Type III survey is the problemoriented survey which is designed to solve a particular problem such as Gladwin and Gladwin's (1935) survey to trace the areal limits of the Hohokam culture. Type IV (which corresponds to the intensive survey in the dichotomous conception) results in a complete inventory of sites in which all sites in the surveyed area are recorded. 10 Relationship to Sampling. The degree to which sampling tech niques are applicable varies with the type of survey and the size of the survey area. The excavation adjunct survey (Type II) is probably least amenable to sampling because the survey area is small enough so that all parts of it can be intensively surveyed. The problem-oriented and intensive surveys (Types HI and IV respectively) may include areas larger than the Type II survey, and sampling appears potentially pro ductive. The extensive survey (Type I) is most amenable to sampling because of the great size of the survey area and of the likelihood for environmental stratification. Some prior knowledge, acquired through library research and field work is essential to the application of sampling to any type of survey. The Question of Weighted Results Lloyd's project is an exemplary Type IV survey since every site in all 66 quarter-sections was recorded. The Paria survey approached the completeness of the Ackmen-Lowry project, and all sites varying in size from isolated hearths and cists to large pueblos were recorded. Because of the completeness and the relatively unbiased recording of all classes of sites, the data derived from the Paria project provide a good empirical base for examining the question of weighted results. Any project that does not produce a 100 percent inventory of all sites is likely to produce a biased or weighted sample that does not accurately reflect the true population of sites in the survey area. 11 This statement is equally true of the archaeological, statistical, and the combined archaeo-statistical approaches. The Archaeological Approach. The tendency to record spec tacular sites is well known in archaeological survey. (This tendency may or may not be a bias depending on the objectives of the survey.) If there is a tendency to record more spectacular architectural sites than the less spectacular, non-architectural sites, this tendency should be stated and corrected. Phillips, Ford and Griffin (I95l: Ul) in their Type I survey noted their predilection thusly: It is inevitable, therefore, that our sample is weighted somewhat on the side of larger and more conspicuous sites. Their weighted sample was probably caused by the use of motorized vehicles and of existing roads for travel within the survey area. This mode of travel undoubtedly prevented the observation of most small sites that were not located close to roads. The Statistical Approach. Some archaeologists have assumed that the statistical approach will automatically produce unbiased results. Ruppe's comment is one example: The above-mentioned surveys /Phillips, Ford and Griffin 1951; Hanson 1957? arc sampling techniques by nature, but a glance at the repox-ts will show that they do not conform to the rules for statistical sampling and the sample can not represent the universe (Rnpne 1966: 3'lh). It is likely that the statistical approach will also provide weighted results, but this possibility has yet to empirically be tested. Until the statistical approach is tested, it must also be regarded as a potentially biased approach. The advantage of the statistical approach is that it allov:s a precise quantification of 12 the degree to which the sample is weighted. This study also attempts to determine the degree of bias produced by various sampling methods. Spatial Units The dimension of space is quite, important in archaeological survey, and the archaeologist frequently works with vase spatial units. Willey and Phillips (1958: 18-21) have ranked archaeological divisions of space in increasing order of size — site, locality, region, subarea, and area. The area, the largest spatial unit, "corresponds roughly to the culture area of the ethnographer" (Willey and Phillips 1958s 20), and is exemplified by the North American Southwest. The next smallest units within the Southwest area are three subareas — the Colorado Plateau, the central mountains of New Mexico and Arizona, and the basin-and-range deserts. A region is determined partially by the historical accident of exploration and research and by environmental similarity (for example, the Glades region of Florida). The Paria Plateau and its western drainages share both defining character istics of a region — general environmental similarity and the his torical accident of having been investigated as part of the same project in the late 1960's. Secondly, the Paria Plateau appears to be the next smallest spatial unit within the Colorado Plateau subarea. For both of these reasons, the Paria Plateau Survey area is considered a region as defined by Willey and Phillips. The term, survey a;rea, has been used relatively commonly in archaeology, but appears to me to be somewhat vague. The vagueness derives from the fact that an entire area cannot always be completely surveyed. The term should be reserved to refer to the entire research area that an archaeologist claims to be investigating — for example, west-central New Mexico and east-central Arizona for Danson's (1957) survey. I would suggest. the term surveyed area to denote those parts of the survey area that were actually investigated. The 66 quarter- sections that Lloyd investigated constitute the surveyed area, while the total 33 square mile area to which he extrapolated comprises the survey area. These terms are used in these respective senses through out the remainder of this study. Summary The fact that some survey areas cannot be completely investi gated has created a multi-faceted problem in archaeology. One facet of the problem is the inferential leap from data collected by a partial survey to conclusions concerning the entire survey area, A second facet is the question of weighted results when sample-surveying a given research area. Archaeologists have not addressed themselves to either facet of this problem. This study is an attempt to resolve the problem by empirically testing each of the three approaches to sampling. Data recovered in the course of the 100 percent Paria Plateau survey is the standard by which 326 simulated sampling surveys are evaluated. CHAPTER 2 THE PARIA PLATEAU SURVEY The Paria Plateau survey was conducted on and adjacent to the Paria Plateau in Coconino County in north-central Arizona by personnel of the Museum of Northern Arizona during the summers of 1967 and 1968. All of the surveyed area is located in the Arizona Strip District of northern Arizona, although unsurveyed portions of the Paria Plateau extend into southern Utah. The Plateau is situated approximately midway between Pa^e, Arizona, on the east and Kanab, Utah on the west (Fig. 1). The familiar Vermillion Cliffs seen from U.S. 89 enroute to the North Rim of the Grand Canyon form the southern escarpment of the Plateau. The western boundary of the surveyed area is formed by Coyote and House Rock valleys, which also separate the Kaibab and the Paria plateaus. The Paria River forms the northeastern boundary of the Paria Plateau making it a naturally-bounded region within the Colorado Plateau subarea. Synopsis A total of £00 new sites was recorded during the survey, 108 in 1967 and 392 in 1968. Because of the exclusion of two historic sites recorded in 1967, the research universe consists of U98 sites. Historic sites were not recorded in 1968, and the exclusion of the two historic sites, NA 9639 and NA 96h2, is one attempt to standardize 1U LEGEND [or Tank Wash ;fch i cnk WGsh le Formation 0 5 mi. KAIBA3 PLATEAU Mo:;iccn Sink Corral Voiley V UTAH Konsb 85 emmet Buffalo Rcnch ARi/LONA Figure 1. The location of the Paria Plateau and of geographical landmarks. H 16 the data between the two years. At multi-component sites, the historic data have been excluded, while the prehistoric components are part of the research universe. The descriptive, as opposed to the later experimental, section of the study is based on these U98 newly recorded sites (Haskell 1967 J Mueller and others 1968). A total of 101 United States Geological Survey sections and quarter-section markers was found during the Paria Plateau survey (see below, "Objectives"). This total constitutes 32 percent of the 320 markers within the 8£-l/li square-mile surveyed area. Nine percent of all possible markers were found during the survey of the western drainages of the Paria, while hk percent were found on the Plateau itself. The surveyed area encompasses 85-lA square miles, representing 2li percent of the surface area of the proposed project. In 1967, 2h square miles were surveyed in the western drainages, House Rock and Coyote Valleys. (An additional 25-l/U square miles located on certain parts of the Paria and Kaibab plateaus adjacent to the western drain ages, have not been surveyed.) Nineteen percent, or 61-l/U square miles of the Plateau itself, was investigated in 1968. Although the Paria River Canyon was surveyed in 1967, the newly-recorded sites are not included because of the physical separation of the Canyon from the areas surveyed in 1967 and 1968. Methods A section frequently entitled "Methods" or occasionally "Pro cedures" constitutes part of most survey reports encountered in my archaeological experience. The contents of these sections varies and includes such diverse topics as field logistics of very large projects to descriptions of sherd collecting at a site. For clarification I shall use the following categories to describe the operation of the survey: (l) objectives, (2) strategy, (3) tactics, and (U) tasks. These operations are explicitly described so that the project can be reasonably evaluated and criticized. I would hope others will find this outline useful in planning and describing archaeological surveys. Rouse (195>3, 1968) has also used three of the preceding four terms to describe the organization of research. He uses objective ". .. t o refer to the end-product of any particular segment in the procedure of culture-historical research" (Rouse 19!?3: £7), and this definition corresponds to my use of the term. Regarding other levels, I use strategy to refer to major programs that aid the archaeologist in accomplishing his objective, while minor programs are considered to constitute tactics. I see strategies and tactics as different levels of technological, conceptual, and organizational tools that lead the archaeologist to the objective. However, Rouse's definition appears to differ from mine as this quote illustrates: The term strategy may be defined as the logical arrangement of research objectives, whereas the term tactics refers to the modified sequence of objectives that one must design in order to meet the particular conditions one encounters in a research project (Rouse 1968: 3, his emphasis). Rouse considers strategy and tactics as networks and chains of objec tives, which leaves his research plan without goal-direction at the very top. He seems to believe this lacuna are higher order research goals: also by implying that there 18 However, we are trying to build up a picture from archaeolo gical remains of what life and events were like during pre historic times (Rouse 1968; 3). If one accepts this quotation as the general goal of research that determines strategies and tactics, then the two conceptual plans for the organization of research differ very little. Objectives The Bureau of Land Management sponsored the survey as one part of a multi-component, long-term planning project designed to evaluate and utilize the resources of part of the Arizona Strip in an optimal manner. The Paria Plateau survey was generally intended to evaluate only the archaeological resources and several specific objectives were outlined by the Bureau to attain this goal. The primary objective was to obtain a complete inventory of all sites in the survey areaj there fore, the project corresponds to Ruppe's (1966) Type IV survey. The secondary goal was to locate and to plot the position of section markers and quarter-sections markers established by the United States Geological Survey. Other objectives that comprised the contractual agreement between the Bureau and the Museum were performed as part of the normal survey tasks or during the laboratory phase of the project (see below, "Tasks")* Strategy The Bureau's general plan was to survey as much of the Strip District as possible within budgetary limitations determined by Con gressional appropriation and Department of the Interior policy. The 19 Bureau implemented this general plan and established the surveystrategy by subdividing the Paria Plateau part of the Arizona Strip District into numbered priority areas, probably expressing proximity to the nearest paved access route, U.S. 89. The number of the area indicated the Bureau's priority for collecting archaeological infor mation j the low number priority areas were those to be surveyed first. Each priority area usually consists of nine sections (three miles on a side) within the township-range system, although the vagaries of terrain resulted in priority areas of other dimensions. The areas with the highest priority are located in the western and southern parts of the survey area, while the northern and eastern areas have lower priority. The 1967 survey was consequently begun in House Rock Valley (priority area 1) and covered Coyote Valley (priority area 2-Ua), terminating in area $ on the southwestern part of the Plateau. The 1968 survey was devoted entirely to priority areas five through ten in the southwestern quarter of the Plateau. Tactics The Paria Plateau survey was primarily a pedestrian survey, although vehicles were used in certain areas. Priority area 5 was one area in which motorized survey was used in 1967, and was resurveyed on foot in 1968. One hundred sites were recorded during the 1968 pedestrian effort. A second instance of motorized survey occurred in selected parts of the sage brush lowlands in Pinnacle and Corral Valleys of the Plateau. Initial foot survey did not result in the 20 discovery of any sites. Consequently vehicles were used to drive to suspected site locations which were then surveyed by foot. The 1967 survey generally was carried out by two people al though the number varied between one and. three at different times of the field season. All workers, regardless of the number, participated as a single team under the general supervision of John Haskell. During the first week of the field season, Alexander J. Lindsay trained the members in general survey methods in accordance with the Museum's system of recording data. The 1968 survey consisted of an average of five people who were supervised and trained by J. Richard Ambler during June and supervised by me during July. Crew members who walked the sandy and irregular terrain at similar speeds worked together as two-man teams. Three such teams were in operation for most of the season. Inter personal compatibility became an overriding factor in partner selection toward the end of the field season. The normal pattern of two-man teams was not followed during the initial training period and during the last week of the season when vehicular trouble and the arrival of two additional survey members from the Museum disrupted the normal survey tactics. Each survey team generally walked not more than a mile in a cardinal direction between natural or cultural boundaries (such as an arroyo, a section line, or a jeep trail). The team then swung around 180 degrees and returned in a parallel direction adjacent to the first swathe. A half-mile front was covered in this manner by three or four swathes with team members walking 5>0 to l£0 yards apart. 21 This general tactic was modified when the terrain or observed site distribution warranted. A team was assigned to one area until it was completed in order to minimize omission or duplication of any part of the assigned area. The areas worked by survey teams were between two and nine miles distant from each other. Tasks Field. Each member of the survey was responsible for observing an area on both sides of his general walking path; the size of the area was determined by the distance between the two partners. For example, with partners walking 100 yards apart, each person was responsible for an area $0 yards on either sidej the resulting surveyed area for that team was a 200-yard wide swathe. Alternately, one member was respon sible for the swathe adjacent to the one he had previously surveyed in order to minimize duplication or omission of any part of the survey area. Upon encountering a site or a United States Geological Survey marker, one member signaled (by voice or whistle) for his partner to join him at the site or at the suspected area so that the proper re cording tasks could be undertaken. The procedure for recording a site were the following standard survey tasks: making a surface collection, completing the Museum's site survey card, photography of the surface remains, and plotting the location on maps and aerial photographs. The surface collection consisted of chipped stone and some ground stone artifacts, as well as potsherds. However, manos, metates, and other large stone artifacts were sometimes stone catalogued in the field and were left at the site. The ceramic collection was a grab sample that was weighted heavily in favor of painted sherds in order to solve archaeographic questions of a temporal-spatial nature. The surface collection from each site was bagged separately as a distinct provenience unit identified by a field number prefaced by the initials PP3. The field supervisor verified the labeling at the conclusion of each day and processed the collections for weekly shipping by bus to the Museum in Flagstaff. On the site survey card, locational, cul tural, and environmental information was recorded, and a roughlyscaled sketch map of surface remains was drawn. Site photography normally consisted of two black and white snapshots taken with a 2 - l / k x 2-l/U camera. A "mug board" containing the field number of the site was included in the photography to distinguish the many similar photo graphs. The location of the site or of the United States Geological Survey markers was plotted on one-inch-to-the-mile United States Geo logical Survey quadrangle sheet (15 minute series) and an acetate overlays for four-inch-to-the-mile aerial photographs supplied by the Bureau. The field maps were given to the field supervisor who tran scribed the plots from the team's field maps to a master plotting map at the conclusion of each day's survey. Laboratory. Artifacts were washed and catalogued in the labo ratory in Flagstaff by Museum personnel during and after the field phase of the project. Upon returning from the field, each member of the survey crew performed one step of the over-all analytical process, e.g., environmental descriptions, sherd and lithic classification, and 23 site typology. Sherds were tabulated by named type and by site in accordance with the Museum's type collection and published descrip tions (Colton 1952, 1955)• The classification of ground and chipped stone artifacts conformed primarily to Woodbury's (195U) and Haury's (1950) schemes respectively. Sites were classified in accordance with several specific criteria of surface remains. Other tasks in cluded cataloging stone artifacts and photographs, map plotting, assignment of permanent site numbers in the Museum, Bureau of Land Management, and Arizona quadrangle system, and drafting the report with its included illustrations. Most of the tasks and the first draft of the report were completed during August; the final report was completed in December. Dissertation Research For purposes of this dissertation, I performed additional analyses to make the data from the two seasons comparable and also verified some of the original analyses for completeness and accuracy. I classified the 1967 sites on the basis of site form (pueblo, sherd scatter, etc.) and verified the correctness of the 1968 classification, making several revisions. I defined and spatially delimited the en vironmental locales of the 1967 survey area. The boundaries of the 1968 locales and sublocales were verified by specifically assigning each quarter-section to a particular locale or sublocale. The above revisions supercede the same analysis summarized in the manuscripts (Haskell 19675 Mueller and others 1968) on file at the Museum of Northern Arizona. I also classified the 1967 projectile points into 2U temporal stages as had been done for the points recovered during the 1968 season. Frequency tabulations of catalogued and stone catalogued artifacts from 1967 were obtained to make the data comparable to the 1968 season. Except for the revisions and additions, this dissertation depends on the empirical base created by the collecting, processing, and recording of descriptive data during the field and laboratory phases of the 1967 and 1968 Paria Plateau survey. Site Classification and Community Plan The sites recorded during the Paria Plateau survey can be clas sified into two general classes, architectural and non-architecturalj each of which may be subdivided into numerous categories. Architectural sites include pueblos, pithouses, and modified rockshelters. Non- architectural sites consist of sherd, lithic, and sherd-lithic scatters as well as petrograph sites and isolated features. Pueblo sites, which appear to be only one-storied units from surface indications, are the most common site form (Table 1). The pueblos in the western drainages of the Plateau appear to be built in different stylesj those pueblos on or near the Paria are constructed in courses of Navajo sandstone slabs, while the pueblos nearer to the Kaibab Plateau are built of limestone boulders irregularly placed in a cyclopean style. More than two-thirds of the pueblos are small units consisting of one to five rooms. Medium pueblos (six to 15 rooms) and large pueblos occur less frequently. Floor plan varies with the size of the pueblo. Small pueblos are usually linear, while medium pueblos are either rectangular or curvilinear. Large pueblos are either *•3 O c»P H CO p 3 O. w H t-J 2! P3<5 o 4 M el H s' CD CD <<4 4 3 W H* CD CO P> TO PTO CD o CD <+ Hc+ P> H M 3 c+ CD 4 1 H J» ciCD fo tr1 o fU H U> Sherd o CD £ NO VA VjJ O H \n VjJ vo M O \+> (-> Lithic no ro H ro vo H ro -J O 97 1—1 NO Petrograph a> Isolated features V Modified Rockshelters ro OO Pithouses co VO ON Small Pueblos VA ro NO Medium Pueblos l-< (-> VjJ .er v»> • oo vn CD H er n Large Pueblos O 1. 11 H 1. 7 OO f=- H i—1 n 2. 11 U> • 02 vn • ON 6. 3 82 • CX> Sherd-Lithic 66 Kti N> 61 11 32 ON VA w 21 22 £T ro NO a? co t-J 11 (=- fr- —J ON ro c- W 93 ON —a hJ NO UT. vn. 00 U> \A ro ro H -O Total Density per square mile 26 C-, U-, or L-shaped. Pueblos occasionally include other structures or features such as adjacent pithouses, possible kival, cists, or firepits. Circular rooms, tentatively designated as kivas, are located adjacent to some medium and large pueblos, but are not found isolated. Trash areas are normally found east of pueblos of all sizes, although the position varies slightly from northeast to southeast. areas generally consist of ceramic and lithic debris. These trash Except for small pueblos, sherd scatters are the most frequently encountered site. Pithouses are the third most common category of site. For the purposes of this study, pithouses that occur with pueblos are con sidered in the appropriate pueblo category. Pithouses were distin guished from storage cists on the basis of surface remains by the size of the circle of upright stone slabs. Large circles between 2.£ m. and U.5 m. were classified as pithouses while smaller circles were recorded as storage cists. Pithouse sites may additionally contain isolated features and artifactual scatters. The plan views of pit- houses ranges from ovoid and circular to square and rectangular. The building stones are slabs of Navajo sandstone. Isolated features including cists, hearths, and windbreaks constitute about five percent of the sites. Cists were thought to be smaller in surface area than pithouses; and hence, the subjective, unquantified criterion of size served to distinguish these structures from the similar surface remains of pithouses. (The excavation of NA 10,U69 raised serious doubts concerning the validity of this classificatory criterion. On the basis of surface remains the site was classified as a pithouse, but excavation revealed it to be a storage cist.) Hearths, usually quadrilateral or pentagonal in plan view, are the smallest (usually less than 0.£ m. along any single dimension) variety of isolated features constructed from vertical slabs. Wind break sites consist of a three-sided outline of limestone boulders that appear to form the base for a perishable superstructure. They differ from pithouses because they are not sub-surface structures and are not built of vertical slabs. Lithic sites, combined sherd-lithic scatters, modified rock shelters, and petrographs comprise the remaining sites which occur in very low frequencies. Modified rockshelter sites consist of an amor phous structure built in a natural rockshelter or against a rock out crop. Rockshelter sites consisting of recognizable structures were classified as small pueblos. Utilized rockshelters where only arti- factual debris was found on the surface are considered as sherd or lithic scatters. Culture History The surveyed area appears to have been occupied from Archaic through Pueblo times. The evidence for an Archaic occupation — Pinto, Axnargosa-like, and San Pedro projectile points — is found at sites associated with the later Anasazi ceramic tradition. None of these earlier points were found at any of the five lithic sites. These "stylistically" earlier points may be explained by the re-utilization of these points or by stylistic persistence into Puebloan times on the Plateau. It is interesting to note that although no single-component 28 Basketmaker II sites were found, two points representing this period were discovered at two sites of later occupation. The ceramic continuum from Basketmaker III to early Pueblo III is represented by Ulii datable, ceramic sites. (See "Material Culture" below for the ceramic basis of these and the following time periods.) The Basketmaker Ill-Pueblo I transitional period occurs at 27 sites (or 6.5 percent); two of these are single-component sites. The Basketmaker III period is not distinguishable on the basis of ceramics alone from the Pueblo I sites. The densest occupation was a Pueblo II manifestation that prob ably occurred during the 11th and 12th centuries on the Plateau. Two hundred and eighteen sites (52.7 percent) date to earlier Pueblo II times, while 366 sites (88.U percent) contain a later Pueblo II com ponent. The trend for the increasing number of sites through time culminates in the later Pueblo II period. Possible working hypotheses for this trend include population increase, movement of people onto the Plateau, and a new fragmentation of social groups to exploit the environment in a more efficient manner. One hundred and eighty sites (U3.5 percent) represent the later Pueblo II-III transitional period. This decline apparently marks the first time in 7,000 years of occu pation that the number of sites of a given time period has decreased. The occupation of the Paria seems to have been terminated abruptly by ca. A.D. 1200. The architectural evidence may conflict with the ceramic data during the later parts of the Paria sequence. Eight large pueblos 29 containing more than 1$ rooms and plazas or courtyards are of a ques tionable nature; their floor plan indicates a Pueblo III manifestation, although the ceramics are the same diagnostic types found on smaller, single component Pueblo II sites. Fifteen additional sites on which pueblos were built appear to have been occupied initially during Pueblo II times and, later, in early Pueblo III times. At this point in the history of research on the Plateau, it appears that the con struction and occupation of large plaza- or courtyard-oriented pueblos may be a Pueblo II, as well as a Pueblo III phenomenon. If the larger pueblos date to the Pueblo II period, their even distribution through out the densely-occupied Big Ridge locale may represent a ceremonial center for the surrounding populations residing in smaller pueblos (Longacre 1966). Alternatively the large pueblos may be a Pueblo III manifestation, possibly representing a point of aggregation for the adjacent inhabitants that previously lived in smaller pueblos. The use of pithouses does not appear to be a dwelling practice restricted to the early part of the Paria occupation. Although there are no single component Basketmaker-Pueblo I pithouse sites, three pithouse villages are multi-component and were first utilized during this early period. Twenty-nine pithouses were first occupied during Pueblo II times; the remaining, dated pithouse sites were occupied during both Pueblo II and early Pueblo III times. Thus, pithouse occupation seems to continue into Puebloan times and is not restricted to the Basketmaker period. In this way the Paria culture history con forms to the general, Western Anasazi pattern. 30 Eight sites date only to the transitional late Pueblo II-early Pueblo III period. The presence of Flagstaff and Toquerville Blackon-white, as well as Tusayan Black-on-red and Polychrome and Tsegi Orange indicates the presence of part of a Pueblo III component that is so poorly known in the Western Anasazi area. Additionally, 172 sites that were first utilized during earlier times were also occupied in early Pueblo III. However, the absence of black-on-white pottery with predominantly more black paint than white paint (so called "negative" black-on-white, for example, Tusayan, Wuptaki, or Betatakin Black-on-white) and of the "white line" polychromes testifies to the absence of a classical, Pueblo III, Tsegi phase occupation in the Paria survey area. The terminal date of the Paria occupation appears to be before the beginning date of these classical Pueblo III ceramics at ca. A.D. 1210. The presence of "prehistoric Hopi" on the Plateau sometime after A.D. 1300 is indicated by Jeddito Black-on-yellow and Plain sherds. A division of sites into two major categories: (l) architec tural sites including pueblos, pithouses, and modified rockshelters, and (2) non-architectural sites consisting of sherd, lithic, sherd and lithic, isolated features, and petrograph sites, suggests an interesting temporal change (Table 2). The ratio of architectural to non-architectural sites increases through time. This evidence suggests an increasing localization of activities involving only ceramics and lithics artifacts in the area of permanent structures in later Pueblo II and early Pueblo III times. Perhaps this phenomenon is a part of 31 Table 2. Temporal analysis of the nucleational ratio. Time Periods Type of Site BM III PI Early PII Late PII PII Early PHI Architec tural 88 Oil .88:1 2.U-.1 NonArchitectural Total *Total 3:1 35 15 98 * Only single component sites are included 123 the nucleation trend that culminates in the large, late Pueblo III sites in other areas of the Southwest, If so, perhaps this ratio of residential to non-residential sites can serve as an operational quantification of this nucleational process. The explanation for the abrupt termination of this incomplete nucleational process on the Paria at about A.D. 1200 remains unclear at present. Environmental and Settlement Patterns Although there are presently no permanently flowing streams in the survey area, the general south to north seasonal drainage pattern conforms to the topography of the Plateau. The highest point in the survey area is at the top of the Vermillion Cliffs on the south rim, the elevation decreasing continually as one proceeds northward. Corral Valley drains the west-central part of the Plateau and is a tributary of Coyote Wash that flows to the north collecting runoff from the northeastern part of the Kaibab Plateau and the northwestern part of the Paria Plateau. The drainage system of House Rock Wash includes the southwestern and southeastern parts of the Paria and the Kaibab Plateaus respectively. House Rock Wash which generally flows in a northwest to a southeast direction, empties into the Colorado River south of the Vermillion Cliffs. The survey area includes two major biological zones and eight principal variants. The Plateau's western drainages, consisting of House Rock and Coyote valleys, are part of the Great Basin biome ~ the dominant flora being sagebrush. Most of the Paria Plateau is part of the Upper Sonoran life zone that is typically dominated by pirion and juniper trees. The variants of the two major zones can be dis tinguished on geomorphological and botanical criteria and will be referred to as locales. The prehistoric settlement varies slightly in each locale, which constitutes a framework for describing the vari ation in settlement. The eight locales are the Inter-plateau drainage, the Detrital slope, the Mesa, the Rim, the Valley, the Big Ridge, the Northern, and the Sand Hill locales (Fig. 2). (Since the locales are distinguished on the basis of my observations of the contemporary en vironment, no implications of prehistoric adaptation are intended. Excavational data such as pollen information, dendrochronological specimens, and micro-faunal remains as well as qualified biological assistance, would be essential to an environmental approach.) The Inter-plateau Locale This locale includes relatively flat land and, at an elevation between 5100 and 6000 feet, is the lowest locale in the survey area. The locale resembles the Great Basin biome that is typically character ized by sage brush, rabbit brush, and other xerophytic scrub vegeta tion. The locale is divided into two sub-locales: (l) the wider House Rock lowlands, and (2) the Coyote Valley located to the north. The two sub-locales are separated by an east and west ridge (elevation being 6000 feet). The drainage gradient of the House Rock Valley is 120 feet per mile, while the gradient of Coyote Wash is approximately 82 feet per mile. The site density for the Inter-plateau locale is 3.8 sites per square mile, a relatively low average for the entire survey area LEGEND l.iier— plateau Locale ¥7''A Rim Locale £ 5 5 Mesa Locale L| 1 Unsurveycd KA1BA3 PLATEAU '• Valley mi. Figure 2. The location of the eight environmental locales in the survey areas. 5 mi. (Table l)• The greater number of sites in House Rock sub-locale may be associated with the relative number of springs. There is only one extant spring in Coyote Valley, while there are five active springs in House Rock Valley. Sites occur more frequently in the northern part of Coyote Valley, where the spring is located, than in the south ern part. In House Rock Valley, sites tend to occur more frequently in the north-central area where the Valley begins to widen and on the Paria side of House Rock Wash where the springs are currently located. Small pueblos are the most common site form, but occur more frequently in the House Rock than in the Coyote sub-locale. Pithouses constitute the second most frequently occurring class in Coyote Valley. The Detrital Locale Located between the lower Inter-plateau and the higher Mesa locales (except in the area of the Vermillion Cliffs), the Detrital locale consists of both talus and alluvial fans derived from the erosion of adjacent parts of the Kaibab and Paria plateaus. The elevational increase between the high and low points is 1100 feet (from £200 to 63OO feet) in the Coyote drainage and 700 feet (from 5500 to 6200 feet) in House Rock Valley. The vegetation is not as diagnostic as the geomorphology and varies from steeply sloping areas with only scattered grasses to heavily forested areas with juniper and pinon trees on alluvial fans. This locale can be divided into three sub-locales: (l) the Paria, and (2) Kaibab sides of the Coyote drain age, and (3) the Paria side of House Rock Valley. (The Kaibab side of the House Rock Wash is not in the surveyed area.) The over-all site density for the Detrital locales is 3 J* sites per square mile, the lowest density of all locales. Fifteen of the 16 sites in this locale occur in the Paria sub-locales, while one site was found in the single quarter-section of the Kaibab sub-locale that was intensively surveyed. Small pueblos are again the most common site form. The Mesa Locale This locale consists of the relatively flat areas that are located adjacent or close to the Detrital locale on the Paria Plateau. Above the Vermillion Cliffs, this locale is separated from the Detrital locale by the intervening Rim locale. The land is very gently rolling, although it gradually slopes upward to the south. The vegetation is moderately dense, consisting of typically Upper Sonoran flora, a dominance of pinon and juniper trees, as well as an undergrowth of sage and grasses. The mesa locale is divided into the Coyote and House Rock sub-locales, depending on proximity to either of the two drain ages; the former lies north of Corral Valley, while the latter lies south. Five quarter-sections of this locale lie within the survey area on the Kaibab Plateau, but have been excluded from this analysis since they were not surveyed. Unsurveyed parts of this locale on the Paria have also been eliminated from the spatial universe. Site density for the entire locale is a very high 11.1 sites per square mile (Table 1). The density in the House Rock sub-locale is dramatically greater than that of Coyote Valley sub-locale. Small 37 pueblos and sherd scatters rank in that order as the most common site classes. The Rim Locale The rim lies along the extreme southern and southeastern edges of the Paria Plateau above the Vermillion Cliffs and is one-quarter to one-half mile wide. The boundary between this and other locales is vague, since the diagnostic features are not ubiquitous, and several criteria must be used. The relative openness and sparceness of trees differentiates the rim from adjacent locales in some places, whereas in other places, the dominance of pinon, as opposed to juniper, trees is a useful criterion. A diagnostic floral feature is occasional stands of prickly pear cactus; the presence of active sand dunes serves as a geomorphological diagnostic. The elevation varies 700 feet between 6I|00 and 7100 feet. As might be expected, the topography varies from gently rolling to irregular terrain. The site density for the Rim locale is moderately high — 7.1 sites per square mile (Table l). Two clusters of sites in the areas of Sand Hill Crack and of VABM 7097 occur near possible descent routes off the Plateau to the base of the Vermillion Cliffs. Jacob Pool, Emmett Spring, and one other unnamed spring, as well as the claybearing Chinle Formation are located at the base of the Cliffs in the area of Sand Hill Crack. In the area below VABM 7097, the Chinle Formation is the only known natural resource that the prehistoric natives would have been able to exploit. The relative location of the site clusters in the Rim locale and of the natural resources below the Cliffs indicate that these descent routes may have been used prehistorically. Two other site clusters occur in areas where descent is not possible; thus, site location in the rim seems to be effected by factors in addition to ease of descent. Sites located southeast of Sand Hill Crack do not cluster in space as obviously as the three other groups. The frequency of occurrence of site classes represents a rever sal of the pattern found in other locales; in the rim, nonarchitectural sites, primarily sherd scatters, are more common than other classes. Three of the four clusters mentioned in the preceding paragraph each contain at least one pueblo surrounded by two to seven non-architectural sites and, in one case, by an isolated cist. The Big Ridge Locale This locale lies on the Paria Plateau west of Pinnacle Valley and southeast of Corral Valley, Other boundaries of this centrally located locale are the Northern and Valley locales on the north and the Rim and Sand Hill locales on the south. It is characterized by a heavily dissected and irregular topography produced by the south to north drainage from the high ground at the rim. Badger Tank and Moquitch Tank Washes are the two named, intermittent drainages. The vegetation of the Big Ridge is denser than any other locale and pre dominantly consists of juniper and pinon trees. Big Ridge is the most densely occupied locale within the survey area (Table 1). Sites predictably occur on high ground such as knolls and ridges and also tend to cluster along the ridges overlooking the two principal washes. Small pueblos are the most frequent kind of site, while pithouses and sherd scatters are the second most common site classes. The Northern Locale Extending beyond the survey area, lying east of Corral Valley and north of the Big Ridge, is the Northern locale. The elevation is between 6300 and 6800 feet. The vegetation is typically Upper Sonoran except for the virtual absence of sage brush which is replaced by gamma grass. Pinon and juniper trees are less frequent and more dis persed than in adjacent locales. The flat topography together with the dispersed trees and dominance of grasses, give the locale the appearance of a tree-savanah region. The site density is a moderate 3.8 sites per square mile (Table 1). Small pueblos are by far the most frequently occurring class of sites. The Sand Hill Locale The Sand Hill locale is situated between Pinnacle Valley on the north and the rim locale on the south, extending beyond the south eastern limits of the survey area. It is relatively flat and occurs at elevations between 6600 and 7000 feet. The locale is moderately forested with pinon and juniper trees. Moderately occupied (5.6 sites per square mile, Table 1) the Sand Hill locale conforms to the general pattern of more architectural sites, particularly small pueblos, than non-architectural sites. The Valley Locale This locale consists of three sub-locales — the valley floor and fringe, as well as the surrounding ridge — that are found in Corral and Pinnacle valleys. The over-all site density for this locale is a low 3.6 sites per square mile (Table l), and the relative occurrence of site classes in the entire locale conforms to the pattern for most other locales. One notable fact is the relatively common occurrence of pueblos (especially medium pueblos) in Corral Valley in contrast to their relative dearth in Pinnacle Valley. The prehistoric utilization of the two valleys differed; Corral Valley seems to have been used primarily for residence, while Pinnacle Valley may have been the location of temporary camps. The flat valley floor resembles the Great Basin biome of the Inter-plateau locales and is similarly dominated by sage brush and salt brush and lacking trees. Three sites are found in this sub- locale, and, since the area seems to be a likely area for floodwater farming, additional sites may have been concealed by post-occupation aggradation. The density is O.U sites per sauare mile. The second sub-locale is the valley fringe which consists of the land between the lower valley floor and the higher ridges. The topography varies from the mildly sloping fringe of Corral Valley to the steeply-sloping alluvial fans and detrital slopes of the western parts of Pinnacle Valley. The vegetation also varies from moderately dense cover of pinon and juniper trees to grass areas. The over-all site density for the fringe is 3#£ sites per square mile, while the Ill corresponding figures for the Pinnacle and Corral Valley fringes is 2.5 and U.6 respectively. Small pueblos constitute 50 percent of the sites in Corral Valley, while in Pinnacle Valley sherd scatters com prise the same percentage of sites. The ridge sub-locale, the third natural unit in the Valley locale, is the high ground surrounding the valley floor and fringe. The ridges geomorphologically and botanically resembles the adjacent Mesa, Northern, and Big Ridge locales. It is considered part of the Valley locale because it overlooks the valleys, a factor that may have determined site location. The western and northern ridges of Pinnacle Valley, as well as parts of the northern ridge of Corral Valley are, beyond the survey area and are not included in this analysis. Site density for the sub-locale is 7.U sites per square mile; the density on Corral Valley ridge slightly exceeds both the sub-locale average and the Pinnacle Valley density. The frequency of medium and large pueblos on the Corral Valley ridge contrasts sharply with their absence on the Pinnacle Ridge. Temporal Aspects of Locale Occupation The .Northern locale is the only one that was not occupied during each of the four ceramically dated periods (Table 3). Only the Inter-plateau locale exhibits a pattern of an increasing percentage of sites from early to late. The occupation of all other locales varies irregularly through time. U2 Table 3. Temporal analysis of locale occupation. Locale ~! 0) r5 Pn 1 h Time Period CO + H HJ 3 «H la® S 8 T3 *H ft; . K <u C <1) ja «h 'id o -rj W _ 0) S CO H njo Basketmaker III7.U 3.7 7.U 1U.8 51.8 11.1 Early Pueblo II 10.1 0.5 7.8 6.L 39.1 20.6 Later Pueblo II ia.s 1.9 7.1 9.0 36.9 Pueblo IIPueblo III 18.3 3.3 9.U U.U 37.2 Pueblo I 3.7 27 9.6 7.8 218 16.1 7.9 6.6 366 12.8 7.2 7.2 180 U3 Material Culture The Ceramics Ceramic collections totaling 18, 326 potsherds (Table U) were obtained from the surfaces of U70 of the U98 sites. Fifty-six sites do not contain painted pottery types, making a net total of UlU ceramic sites containing temporally-diagnostic pottery suitable for chrono logical analysis. Three main ceramic groups and two subdivisions were formulated to classify the sites chronologically. The earliest group includes the Basketmaker IH-Pueblo I period, roughly conforming to the interval from the 6th to the 9th centuries after Christ when Lino Gray and Black-on-gray, as well as Kana-a Black-on-white, were the dominant decorative styles. The second group is the Pueblo II manifestation and includes two subdivisions: (1) an earlier Pueblo II period, which is represented by Black Mesa Black-on-white, Deadmans Black-on-red, and Middleton Red, and (2) a later Pueblo II period which is mainly represented by Sosi and Dogoszhi Black-on-white although other types (Medicine, Middleton and Tusayan Black-on-reds, as well as Citadel, Cameron, Nonkoweap and Middle Polychromes) were also found. The third ceramic group is transitional and includes later portions of Pueblo II and early Pueblo IIIj ceramically it is represented by Flagstaff Black-on-white, Tusayan Polychrome, and Toquerville Black-on-white. The Black Mesa, Sosi, Dogoszhi, and Flagstaff design styles found on Virgin White Ware were assigned to the same period as their homologs in the Tusayan White Ware. The results of this chronological analysis Table U. Ceramic Designation Tusayan White Ware Kayenta Series Kana-a B/w Black Mesa B/w Sosi B/w Dogoszhi B/w Flagstaff B/w Virgin Series St. George B/g North Creek B/g Sosi style Dogoszhi style Flagstaff style Hurricane B/g Black Mesa style Sosi style Dogoszhi style Flagstaff style St. George Fugative Red Shinarump White Ware Virgin B/w Black Mesa style Sosi style Dogoszhi style Flagstaff style Toquerville B/w Shinarump white Tusayan Gray Ware Virgin Series North Creek Gray North Creek Corrugated Washington Corrugated Coconino Gray (tooled) Tsegi Series Lino Gray Lino B/g Kana-a Gray Coconino Gray Honani Tooled Tusayan Corrugated Shinarump Gray Ware Shinarump Brown Shinarump Corrugated Ceramic summary. 1967 Total Sherds Percent U5 5U 19 0.8 1.0 T 1968 Total Sherds Percent 31U 1 U88 1530 £62 1U5 1.3 56 h2 3 82 9 U8 20 6 2 99 115 33U 172 7 37 0.8 0.9 7.6 1.U T T 1611 3882 70 12.7 30.6 0.6 36 3 2 2 T T T T T 0.5 1U.0 3 2h 227 7k U.O 1.3 20 T 51 397 183 0.9 7.0 3.3 U6 0.8 T 2h 1388 8hh 1179 1 2U.6 15.0 20.9 T h 59 1777 18U 251 3.3 U.5 k.h 1.1 T T T T T T 0.6 T T T T T 2h 73 2.5 T 3.9 12.1 Table lj. Ceramic summary—Continued Ceramic Designation 1967 Total Sherds Percent 1968 Total Sherds Percent Logendale Gray Ware Logendale Gray Moapa Gray Ware Boulder Gray San Juan Red Ware Deadman B/r Middleton B/r Middleton Red Tsegi Orange Ware Black Mesa Series Tsegi Orange Medicine B/r Tusayan B/r Cameron Poly. Citadel Poly. Tusayan Poly. Little Colorado Series Middleton Red Deadmans B/r Deadmans B/r (WAF) Middleton B/r Nakoweap/Middleton Poly. Jeddito Yellow Ware Jeddito Series Jeddity B/y Awatovi Yellow Ware Jeddito Plain Unidentified Total 2 3(?) hi 26 h3 153 26 3U T 1 T 0.8 0.8 2.7 96 37 20 lilO 1.1 0.5 0.6 h 17 a T 0.7 0.5 227 118 2^2 56UO U.5 98.2* T T T T T 1.8 0.9 32 h T T 318 72 2.5 0.6 12 T 1 12 T T 12686 96.!^ * T signifies a trace percentage which is less than 26 sherds for the 1967 season and less than 57 sherds for 1968. The percentages do not total to 100 percent because of the traces. U6 of pottery have been presented earlier (see "Culture History" in this chapter)• In order to analyze the ceramic traditions in the surveyed area, I classified the pottery taxa into Virgin and Kayenta groups and then subdivided each into painted and unpainted sub-groups. Unpainted Kayenta pottery consists of the Tsegi Series of Tusayan Gray Ware. Unpainted Virgin pottery consists of the following formal categories: (l) Tusayan Gray Ware, Virgin Series; (2) Shinarump Gray Ware; and (3) Moapa Gray Ware. category. Table Li lists the named types included within each Painted Kayenta pottery consists of the following taxa: (1) Tusayan White Ware, Kayenta Series; and (2) Tsegi Orange Ware, Black Mesa and Little Colorado Series. two named groups: Painted Virgin pottery" includes (1) Tusayan White Ware, Virgin Series; and (2) Shinarump White Ware. The results of this classification are summar ized in Tables £ and 6. An overwhelming majority (83.1 percent) of sites contain only Virgin unpainted pottery (Table !?). Kayenta unpainted ceramics do not occur in isolation without its Virgin homolog. The pattern for unpainted pottery is not repeated for painted potsherds; the majority (55*2 percent) of sites contain both Virgin and Kayenta painted pottery (Table 6). At the remaining sites, Kayenta white wares were found more commonly than Virgin white wares. The Paria population was dif ferentially following each ceramic tradition in the production of painted and unpainted vessels. These potters slightly favored the Kayenta tradition for painted vessels and overwhelmingly preferred U7 Table Site frequencies cross-tabulated by locale and unpainted ceramics. Locale Unpainted Ceramic Tradition VirginNo Virgin Kayenta Kayenta Collection Total 2 66 1 16 h 1 36 32 6 3 hi 1^1 26 17 19U Valley 69 6 U 79 Northern 30 5 3 38 Sand Hill 2U h Total klh S3 Inter-plateau 62 Detrital 15 Mesa 31 Rim Big Ridge 2 28 31 It98 U8 Table 6. Site frequencies cross-tabulated by locale and painted ceramics. Locale Inter-plateau Decorated Ceramic Tradition VirginNo Virgin Kayenta Kayenta Collection 17 Total Sites U3 6 66 Detrital 5 1 7 3 16 Mesa 3 U 27 2 36 Rim 1 17 16 7 Ul 12 U9 105 28 19U Valley 3 21 U3 12 79 Northern 1 12 18 7 38 9 16 3 28 113 275 68 h9& Big Ridge Sand Hill Total h2 the Virgin tradition for unpainted vessels. Therefore, it can be said that this conclusion represents a clear illustration of prehistoric potters selectively borrowing ceramic aspects from two adjacent cul tural traditions. One alternative explanation is a movement of two groups of people, each practicing either the Virgin or the Kayenta ceramic craft, onto the Paria Plateau. This explanation is less parsamonious and less probable because the population expansion on the Paria Plateau appears to be an internal growth just as the entire Southwestern Pueblo II expansion is an in-site growth. The Inter-plateau and the Detrital locales in the valley between the Kaibab and the Paria plateaus are the only areas where this pattern of Kayenta dominance of painted pottery is not found. This distributional data may be explained by differences in pottery analysts, since the ceramic analysis of the non-conforming locales was done in 1967, while the remaining locales were analyzed by a different classi fier in 1968. On the other hand, the dominance of Virgin pottery may suggest a trade route through a natural corridor by which the Paria population exchanged painted pottery with the northern and eastern Virgin population. A consistent classification of the pottery from both 1967 and 1968 by a single observer is a precondition to further discussion. The temporal analysis of ceramic traditions (Tables 7 and 8) suggest several interesting generalizations. Regarding unpainted ceramics, the period between Pueblo I and Pueblo II seems to represent 5o Table 7. Temporal analysis of unpainted ceramics. Virgin Kayenta VirginKayenta No Collection Total Sites Basketmaker III Pueblo I 18.6 81.5 Early Pueblo II 87.3 12.U Later Pueblo II 87.6 12.6 366 Pueblo II Pueblo III 87.3 12.7 180 The figures above are expressed as percentages. 27 .5 218 51 Table 8. Temporal analysis of painted ceramics. Virgin Kayenta VirginKayenta No Collection Total Sites 1U.8 Hi.8 66.7 3.7 27 Early Pueblo II 1.8 16.5 81.U 0.5 218 Later Pueblo II 7.1 22.2 70.U 0.5 366 Pueblo II Pueblo III 0.9 10.0 89.1 Basketmaker III Pueblo I The above entries are expressed as percentages. 180 a time of change. At this time, the Paria potters, who had been over whelmingly participating in both the Virgin and the Kayenta ceramic traditions, abandoned the dual tradition and borrowed more heavily from the Virgin tradition alone. A different and equivocal pattern emerges for the painted tradition (Table 8); an extreme diversity in percentages for each ceramic category is obvious. Most of the dis junctions occur at the more recent end of the time scale in the later Pueblo II and the transitional Pueblo II-Pueblo III periods. Late Pueblo II time is an exception to the constant decrease in the Virgin tradition and to the constant increase in the combined traditions. The transitional Pueblo II-Pueblo III period represents a decrease in the frequency of the Kayenta sites from the constant increase through earlier times. Potters in the area north and west of Corral Valley frequently made pottery with a red paste that differs dramatically from the white gray paste found in all other surveyed areas of the Plateau. These potters undoubtedly used a local clay source and did not utilize the clays in the Chinle Formation at the base of the Vermillion Cliffs. Lithic Artifacts The lithic collection (Table 9) represents a fairly complete range of tool types. The most common raw materials were chert for chipped stone artifacts and quartsitic sandstone for ground stone tools. Agate, chalcedony, quartsite, and river cobbles were also used other crytocrystalline minerals were found less frequently. None of the crytocrystalline raw materials occur indigenously on the Paria 53 Table 9. Summary of catalogued and stone-catalogued artifacts. Artifact I. 10 6 27 2 k$ luli 2.7 12.0 .9 99 25 28 WuO ll.l 12.5 1 T T U.U Chipped Stone Artifacts Projectile Points Scrapers Knives Drills Planes Gravers Knife-Scrapers Knife-Gravers Knife-Choppers Knife-Points Chopper-Scraper Graver-Scraper Saw-Scraper Chopper-Hammersto ne Core III. Percentage Ground Stone Artifacts Metate Bedrock Mortar Manos Maul II. Number 1 10 2 1 1 1 1 1 1 2 1 175 .9 T T T T T T .9 T Other Material Polishing Stones Hammerstones T » 0.$% or less. 2 3 5 1.0 Plateau. The most convenient sources are the Kaibab Plateau, the Chinle formation at the base of the Vermillion Cliffs, and gravel alluviums in the Colorado River to the south. Therefore, the Paria populations were undoubtedly engaged in either (l) direct exploitation by quarrying toolstones from these sources, or (2) indirect exploita tion by trading with groups occupying those three areas. There is no reason to expect that each resource area was exploited in the same mannerj therefore, a combination of the above two alternatives is ex pected to be the most probable explanation. Sixty-eight sites contain morphologically diagnostic projectile points (as well as a San Pedro knife form). (5U.U percent) contain San Pedro points. The majority of sites At 13 sites, Pinto points were found, while Amargosa II (11 sites) and Easketmaker II (seven sites) points were less common. Table 10 analyzes the occurrence of each type of lithic artifact by locale. It must be remembered that either pottery or some form of masonry architecture are found at these same sites. Therefore, it is not possible to date the initial occupa tion of a locale by the presence of a diagnostic lithic artifact. Of five lithic sites, none contain projectile points that could be iden tified as named types. Four of these sites are located in the Rim locale. On the western ridges adjacent to both Corral and Pinnacle valleys, there are numerous scatterings of lithic debris that are not sufficiently concentrated to be recorded as sites. This light, but uniform, scatter was not noted elsewhere on the Paria Plateau. 55 Table 10. The provenience of temporally diagnostic lithic artifacts by locale. Locale PintoAmargosa I Diagnostic Artifacts* San Pedro Desert Amargosa II Mesa X X Sand Hill X X Inter-Plateau BasketMaker X X X X Detrital X Rim X X X X Big Ridge X X X X Valley X X X X Northern X X X X * "X" indicates the presence of one or more named artifacts. 56 Activities related to the production and use of stone tools may have occurred at non-residential sites in the ridge sub-locale more fre quently than elsewhere in the survey area. At other areas, these same lithic-related activities may have been performed at residential sites with architecture# The sites containing stone artifacts have also been classified into gross categories related to subsistence activities. I think that subsistence activities can be subdivided into procuring and processing tasks. The former includes tools such as projectile points and hoes that are useful in the initial acquisition of a dietary item. The latter category consists of those activities related to the preparation of the raw product for ingestion. Each activity can be cross- classified by the nature of the raw product being acquired and pre pared, i.e., whether the dietary item is floral (vegetative) or faunal (meat). Thus, there are four basic kinds of subsistence activities: (l) procuring animal products (e.g., projectile points, atl-atl weights, "net sinkers"), (2) procuring vegetable products (e.g., hoes, digging stick weights), (3) processing animal products (e.g., scrapers, gravers), and (U) processing vegetable products (e.g., manos, metates, mortars, pestles). I am assuming that the primary use of scrapers and gravers is for meat processing and leatherworkingj the prehistoric use of these artifacts for woodworking is considered far less common. Some tools such as choppers cannot fit into these neat pigeonholes and are regarded as multi-purpose tools. Some sites would contain both procuring and processing tools; hence, these sites are also S7 tallied as multi-purpose sites. This simple classification only- accounts for subsistence-related artifacts. Therefore, tools that were used in non-subsistence tasks (such as floor polishing stones) and tools to make subsistence tools (i.e., secondary tools such as pecking stones to shape manos or metates and "antler wrenches" to straighten arrowshafts), as well as the ubiquitous undeterminable artifacts are included in the miscellaneous category. Suggested im provements for this trial classification are welcome. The results of this analysis cross-tabulated by locale, site type, and time are presented in Tables 11, 12, and 13. The most obvious of all patterns in Table 11 is the absence of sites concerned only with vegetable procurement. In other words, isolated hoes and digging stick weights were not found on the surface; the reason for the conspicuous absence of this artifact class is not clear. It may be that gathering of vegetable products was an unimportant activity or that horticultural plots were maintained close to residential sites. It is possible that these artifacts had been surface collected by other people prior to the survey. A second pattern is that, in all locales, artifacts related to meat procurement and processing were found at more sites than artifacts related to vegetable procurement and processing. Thirdly, in all locales except the Valley, sites related to procuring are more fre quent than processing-related sites. Fourthly, the frequencies of multi-purpose sites in the Mesa locale is higher than would be expected on the proportional basis of included surface area. The explanation 58 Table 11. Cross-tabulation of subsistence activities by locale. Subsistence Activity* Locale Inter-Plateau Procurement Vege table Meat 17 Processing Vege table Meat 3 MultiPurpose Misc. 5 1 2 i 1 2 Detrital U Rim 9 2 l u Mesa 11 6 2 10 1 Big Ridge 25 11 5 8 1 Valley- 15 6 9 3 Northern 9 1 h 2 Sand Hill 7 6 97 35 Total 6 27 35 6 * The number of sites with at least one subsistence-related artifact 59 Table 12. Cross-tabulation of subsistence activities by site type. Subsistence Activity Site Form Sherd Procurement Vege Meat table 16 Lithic Sherd and Lithic Multi purpose Misc. 5 6 1 2 1 Processing Vege Meat table 9 1 3 3 h 3 1 1 Petrograph Isolated Features Modified Rockshelter 1 Pithouse 12 1 2 k 1 Small Pueblo 32 10 9 13 3 Medium Pueblo 1h 9 h 6 Large Pueblo 10 k 2 1 1 97 35 27 35 6 Total 60 Table 13. Temporal analysis of subsistence activities. Subsistence Activity Procurement VegeMeat table Basketmaker III Pueblo I Sk.S Processing Vege table Meat Multi purpose Total Sites 9.1 18.2 18.2 11 Early Pueblo II 149.6 2U.8 12.8 12.8 109 Later Pueblo II 1*9.1* 19.1* 13.5 17.6 170 Pueblo II Pueblo III U7.2 19.6 13.8 19.6 87 The above entries are expressed as percentases. of this is unclear. The frequencies for other locales in all lithic- based categories conforms intuitively to proportional surface areas. Two generalizations are possible regarding Table 12. First, there appear to be no pure meat-procuring loci (i.e., no "kill" sites) among the lithic sites. There are, however, two pure meat-processing sites (i.e., "butchering" sites) and two multi-purpose sites. Meat- procuring seems to have occurred at all other site classes where other subsistence activities were also executed. Secondly, it also appears that modified rockshelters and petrographs were not related to sub sistence activities that involved the use of stone tools. Two patterns result from a chronological analysis of subsis tence activities (Table 13). First, there is a slight, but continual, decrease in meat procurement activities. Secondly, three subsistence changes occurred at the time between the Pueblo I and Pueblo II periods. These subsistence changes may be related to the slight climatic shift that occurred at A.D. 1000 in the Anasazi area (Schoenwetter and Dittert 1968). Two subsistence changes involved a large decrease in the number of sites where activities involving vegetable processing and multi-purpose stone tools were performed. The most obvious change is the nearly three-fold increase in sites where meat processing or butchering was completed. This change is unexpected and unexplainable in the light of the slight decrease in meat procurement sites through time. Conclusions Aikens has advanced several generalizations regarding the cul ture history of northern Arizona and southern Utah. He suggests that .. the Virgin and Kayenta traditions came to be separate sociocultural populations by approximately A.D. 900" (Aikens 1966: %$). After this time, the previously uniform ceramic and architectural traditions that constitute the empirical basis of Aikens' generaliza tion begin to separate into noticeably different traditions. The Paria Plateau is on the southeastern extreme of the Virgin area where it borders with the Kayenta area. The evidence suggests that Aikens' postulated divergence did not occur in the survey area; rather, it appears that the Paria population selectively borrowed certain ceramic and architectural traits from each of the Virgin and Kayenta traditions. This borrowing of both kinds of traits continues from the beginning of the ceramic continuum in late Basketmaker times to the apparent abandonment of the Paria at ca. A.D. 1200. The Plateau thus seems to be a suitable region where a well-designed excavation program can continue to illuminate the processes of prehistoric cul ture contact from an archaeological perspective. Secondly, Aikens describes the Pueblo II expansion as an in situ process and rejects the hypothesis of a migration of people. During this internal expansion, Aikens postulates a change in settle ment pattern. The lowland valley occupation of Formative Southwestern times changes to highland occupation of the later Florescent times (Daifuku 1952). The evidence indicates that this settlement shift did not occur on the Paria. There is no tendency for the earlier Basketmaker Ill-Pueblo I sites to be located in the Inter-plateau locale or the valley floor sub-locale. The highest terrain in the survey area is the Rim locale; the highest percentage of sites in the rim occurs during the earliest time period. Thus, the settlement changes postulated by Aikens do not occur in the survey areas. How ever, there is a very real Pueblo II expansion that occurs at about A.D. 1000. Three additional patterns that derive from the survey data can be used to formulate working field hypotheses. Pithouse residence tends to be a late Pueblo phenomenonj this form of architecture occurs less frequently in the Basketmaker Ill-Pueblo I period. Large courtyard- or plaza-oriented pueblos of the kind associated with the Tsegi phase, Pueblo III period may be a Pueblo II phenomenon in the survey are. Finally, Corral Valley may have been a location for permanent residence, while Pinnacle Valley appears to contain temporary camps. There are also several disjunctive points when radical changes in ceramic tradition or adaptation occurred in the culture history of the Plateau. Two such changes occurred during the transition from Pueblo I to Pueblo II: (l) a change from a combined unpainted ceramic tradition (consisting of both Virgin- and Kayenta-associated ceramics) to the Virgin unpainted tradition, and (2) a dramatic increase in the number of meat-processing sites during this period. The latter shift represents the most important change in all kinds of subsistence activities during Basketmaker and Puebloan times. Several changes also occurred during the late Pueblo II and early Pueblo III periods. The strongest pattern is a possible aggre gation of people, represented by the increasing nucleational index and by a decrease in the number of sites. Changes in the decorated ceramic tradition are less dramatic, and exceptions are found during the later Pueblo II and early Pueblo HI period. These changes are not as strong as shifts at other times, but suggest that changes in non-material aspects of culture may have been concurrent. CHAPTER 3 THE DESIGN OF THE EXPERIMENT The Experimental Approach The remainder of this study is designed to determine which parts of a hypothetical region that is archaeologically unknown must be surveyed in order to derive valid conclusions concerning the entire region. This sampling problem can be fruitfully approached by performing an experiment with the data recovered during the Paria Plateau survey. An experiment is necessary because the stated purpose of this study is to refine sampling methods in an empirical, instead of a polemical, manner. Therefore, a maximum of data that can be handled properly under the correct theoretical conditions can be used to answer questions concerning the sampling methodology of archaeolo gical survey. Secondly, I consider this study experimental in an innovative sensej to my knowledge, the kind of data processing that will be described in this chapter has not been previously attempted. The data from the Paria Plateau are quite useful for this pur pose for four reasons: (l) the unbiased observation and thorough methods of the survey, (2) the refined spatial controls made possible by locating the U.S.G.S. markers, (3) the large number of sites re corded, and (U) the maintaining of financial records. The Paria data survey comes closer than most other projects to achieving a 100 percent 65 site recovery rate. Therefore, the Paria data, as the standard of comparison for the simulated surveys, comes as near as possible to representing a true and complete population of sites that archaeolo gists are attempting to measure by sampling spatial subdivisions of the survey area. The location of U.S.G.S. markers helps to insure that sites are plotted on maps as near as possible to their true location on the ground. Precise location is necessary because the experiment will involve spatial subdivisions smaller than quartersections j the chances for error increase as the size of the spatial subdivision decreases. The use of four-inch-to-the-mile aerial photo graphs also helps to insure precise site plotting. The large site in ventory also makes statistical manipulations more valid because of the high site and artifact frequencies. The maintaining of financial records allows for real-world, dollar-and-cents estimates of survey costs. For these four reasons, as well as for the two experimental reasons, an experiment with the Paria Plateau survey data is likely to produce more light than heat concerning the topic of archaeologi cal survey sampling. The processing of the large amounts of data necessary for the experimental approach was accomplished with the aid of a main program, SAMPLE, and an auxilliary, but independent program, PUN. Both were written in Fortran IV for the Computer Data Corporation 6U00 computer at The University of Arizona. SAMPLE included both specially-prepared subroutines (QSEC, SEC, TSYSS, TSYSQ, STRAT 1-U, CLUSTER, CK, STAT, and CHI) which are described in the appropriate section of this chapter and system subroutines. The latter performed the arithmetic calculations when called by the specially-prepared subroutines. The system subroutines include BDS, SQRT, SYSTEM, RANF, GETBA, INPUTC, KODER, KRAKER, OUTRJTC, and S10$. The statistical formulas used in deriving the computer-generated samples are given in Appendix A. The experiment is methodological in nature — that is, the objective of the experiment is to assess the sampling methods that are available for use by archaeologists. It must be remembered that sampling, like a trowel or a bulldozer, is an archaeological tool, a means to an end. The experiment is not substantitive in nature and the results do not involve culture history or cultural adaptation. An Overview of Sampling Statistical textbooks unanimously agree that there are three decisions to be made concerning the employment of sampling. These decisions refer to the choice of a particular technique, scheme, and sample size. There are two additional kinds of decisions that I would like to investigate since they are peculiar to archaeology. The fourth decision is the size of the sampling unit, a problem that is particularly important in archaeology. The final decision concerns which repetition of the sampling program is the most predictive of the research area. This aspect of the problem is not discussed in sampling textbooks, but I will investigate it because it is a common question asked by archaeologists. In this section, sampling concepts will be defined and each decision of the sampling process will be 68 generally described; detailed mechanics of sample selection will be presented in subsequent sections of this chapter. Another common tenet of sampling is that the nature of the re search and of the data will influence each decision. In this study, I hope to determine which decision will produce the most valid results for the data and the research objectives of archaeological survey. The essential precondition to any sampling design is a knowl edge of the boundaries of the research universe and a list of all the equally-sized spatial subdivisions within the research universe. This precondition forces an archaeologist to be more explicit and rigorous than if he had used an archaeological approach to sampling. Deriving a list of spatial subdivisions can be difficult in areas vrhere the U.S.G.S. or a similar organization has not mapped and gridded the survey area. Concepts and Definitions Until this point, such terms as research unit, area, or uni verse that are familiar to most archaeologists have been used to describe the purpose and theoretical framework of this study. It is now appropriate to adopt and use the technical vocabulary of sampling theory so that future discussion can be meaningful. Therefore, in this section, sampling concepts will be defined in terms that I hope are familiar to most archaeologists. The Element and the Population. The most important concepts are probably the element and the population. Kish defines population as ". . . the aggregate of elements," and goes on to define elements as 69 . . . the units for which information is sought; they are the individuals, the elementary units comprising the popu lation about which inferences are to be drawn. They are the units of analysis, and their nature is determined by the survey objectives (Kish 196£: 67, Kish's emphasis). The population roughly corresponds to the sum total of each of the classes of various artifacts or of sites in a research unit or area. There are as many different kinds of populations as there are classes of data to be gathered within a research area. The objective of the sampling process is to make an accurate inference of character istics of each kind of population. On the other hand, the explanation of the inferred population and of the relationships among the various populations is the over-all goal of archaeological research. Two sampling specialists, Kish and Cochran, distinguish be tween two kinds of populations — ". .. the population to be sampled (the sampled population) . . . and the population about which infor mation is wanted (the target population)" (Cochran 1963: 6). The sampled population corresponds to what I have defined as the surveyed area, while the target population is the survey area. At this level, both kinds of populations are spatial in nature. Cochran states that the target and sampled populations should correspond, and when this is not possible, the conclusion only applies to the sampled population unless other information is available. Kish recognized that this kind of correspondence is frequently an unachievable ideal and that 'nonresponses' and 'noncoverage' are the causes of lack of correspondence. Kish (196^: 7) goes on to claim that the sampled population "... may be difficult to describe exactly and it is easier to write about the defined target population." 70 A possible confusion between research universe and the statis tical concept of universe should be avoided. The two phrases are con fused because the research universe is actually misnamed. It is an aggregate of spatial or cultural elements and, therefore, is actually a population in sampling terms. Research universe is an archaeolo gical term that is synonomous with research unit or area, as well as survey area. The use of the latter terms to replace research universe would avoid all confusion. On the other hand, sampling specialists suggest that a universe is a high order unit that stands behind a population and is not at all synonomous with a population. A uni verse "... denotes a hypothetical infinite set of elements generated by a theoretical model .. . such as the endless tossing of a perfect coin" (Kish 1965: 7). This definition does not at all describe the archaeological use of the term. Research universe should bo dropped as an archaeological term, because of its confusion with the statis tical meaning. The Sampling Unit. All elements can be totaled to obtain a population; alternatively, they can also be subtotaled to derive an intermediary unit, the sampling unit. Sampling units can then be totaled to obtain the population. Therefore, there are two ways of describing the population ~ in terms of elements or of sampling units. Cochran notes the relationship between sampling units and population succinctly: These units /sampling units7 must cover the whole of the population and they must not overlap in the sense that every element of the population belongs to one and only one /sampling7 unit (Cochran 1963: 7). Just as a sampling unit must include every element, each of which can belong to one and only one sampling unit, the population must include every sampling unit, each of which can belong to one and only one population. Each concept, sampling unit and population, displays the characteristic of being non-overlapping and completely inclusive. The list of all sampling units (or of elements in some cases) in a population is called a frame. The Sample For purposes of this study, a sample is considered to be a group of spatial units chosen according to one of the four aspects of the sampling process — scheme, fraction, unit, or repetition. For example, the first repetition of the scheme with the quarter-section as sampling unit at the 0.1 fraction constitutes a single group of quarter-sections. Changing only the fraction to 0.5 would produce another group of quarter-sections. Two samples have been generated in this way by the change of only one aspect. The Sampling Process Regarding the first decision, there are two general techniques — element and cluster sampling. The former technique occurs when the frame (that is, the list of elements to be sampled) consists of the elements to be observed and measured. For an example, an archae ologist who wants to measure 70 attributes per lithic artifact and has excavated a larger number of artifacts than can be analyzed may chooseto list all artifacts and then select x number for analysis. 72 This situation is element sampling because the elements (that is, the artifacts) to be measured are listed individually and comprise the frame. The alternative technique is cluster sampling in which the frame consists of a list of groups (or clusters) of elements that will be observed. The frame in this case is not a list of elements but is a list of larger and more inclusive entities called clusters. To continue the previous example, the archaeologist may not choose to list individual lithic specimens, but instead may list excavation units (either cultural or arbitrary). The frame consists of excava tion units, each of which includes clusters of lithic artifacts. When an excavation unit is selected for analysis according to one of the schemes to be described in this chapter, all elements (that is, all lithic artifacts) are observed and analyzed. It is possible to sub- sample within a cluster, and this alternative will be described in this chapter. The Sampling Scheme The second level of decision-making involves the choice of a sampling scheme. A scheme is a more particular and detailed method than the concept of sampling technique. Most of the schemes familiar to archaeologists are forms of the element sampling technique, in cluding simple random, systematic, and stratified sampling. These three schemes may be combined and recombined with each other to pro duce a large number of possible variants of the three basic schemes. Each of these schemes and their variants will be described in turn in this chapter. If the cluster technique is chosen at the first level of decision-making, two sets of alternatives are available at the second level. The first set of alternatives involves combining the cluster technique with one or more of the preceding element schemes — simple random, systematic, or stratified. The resulting combination is also referred to as a scheme. The second set of alternatives refers to the number of stages of sampling and results in variants of the related techniques and schemes. A stage of cluster sampling refers to the number of times a cluster can be subdivided above the level of ele ments. There are single-stage and multi-stage (including two-, three-, and four-stage) variants. The multi-stage variant is also referred to as nested cluster sampling because, in the case of two-stage cluster sampling, elements are included within, or "nested" inside of, subclusters which in turn are "nested" within clusters. All of the possible cluster schemes and variants will be described more completely in the appropriate section of this chapter. The Sampling Fraction The third level of decision-making in sampling concerns the choice of sample size. How many elements must be drawn from a given frame in order to achieve valid conclusions concerning the research universe? The sample size is frequently expressed as a fraction (or percentage) of the number of elements on the frame. Therefore, I will refer to this level of decision-making as the sampling fraction. One 7U "cookbook" rule of thumb is that for research units consisting of more than 300 elements, a ten percent sample is necessary. For smaller research units, a %0 percent sample is necessary to accurately describe the research universe. This one particular rule seems suspicious to me because of the discontinuity between a ten percent and a 50 percent sample for research units respectively consisting of 300 and 299 ele ments. Therefore, it seems appropriate to evaluate the effect of sample size on the validity of the conclusions. The Size of the Sampling Unit The choice of size of the sampling unit is the fourth level of decision-making and is rarely discussed in sampling textbooks. The concept refers to the size of the units that comprise the frame and is particularly important in archaeology since the spatial subdivisions of a research unit vary in size from investigator to investigator. The following question illustrates the problem to be resolved: "Will the same results be obtained when a sampling frame consists of sec tions as opposed to one consisting of quarter-sections?" This concept is different than the concept of sampling fraction; the sampling fraction refers to the number of units to be sampled, while the con cept of size refers to the amount of space enclosed by a sampling unit. The Sampling Repetition The particular repetition is the fifth and final level of decision-making, the idea derived from a conversation with Alexander Lindsay. A repetition can be conceived as a lottery in which a set of successive draws out of a barrel are made in order to determine one winning number. In archaeological survey sampling, a set of successive draws are made to supply enough sampling units (that is, quartersections) to constitute a sampling fraction of £0 nercent. I think it is commonly assumed that the first repetition produces results that are as valid as the second or nth set of drawings. In the long run when a large number of drawings are made, the laws of chance probably make the assumption true. However, in the short run, when the number of draws is small, there may be quite a discrepancy between the first and nth draws. This possibility will be evaluated. Repetition should not be confused with the term sample as de fined earlier in this section. A repetition is a repeated drawing when the remaining three aspects of the sampling process are held constant. A sample is a new drawing when at least one of the four aspects changes. There are no more than three repetitions of any particular sampling scheme, fraction, and unit. There are 326 samples that are generated by many combinations of the four aspects of the sampling process. The three repetitions of the simple random scheme with the section as sampling unit at a fraction of 0.5, for example, constitute three of the 326 samples. The Selection of Samples Sampling technique will not be discussed in this section be cause the decision at this level is usually implicit. That is, the choice between cluster sampling and element sampling is usually made 76 as if it were at the level of sampling scheme. When I manuallyselected cluster samples, I was unknowingly working at the level of sampling scheme. However, the distinction between cluster and ele ment sampling is an important theoretical point that will have sig nificant ramifications in Chapter 5. It should be recalled that samples are being chosen for simulated surveys that are being performed only on paper for purposes of this experiment. Sampling Schemes A description of the sampling schemes and their respective advantages is impossible without a background concerning the alterna tive aspects of the sampling process to be tested. These alternatives will be summarily presented at this point and described in detail in the appropriate succeeding subsection. All one-tenth sampling frac tions between 0.10 and 0.90 will be tested for most schemes in this experiment. Three kinds of sampling units will be evaluated ~ the complete section (one sq. mi.), the quarter-section, and the rec tangular sampling unit. The latter unit measures one-hale mile in length by one-sixteenth mile (or 330 ft.) in width. The first three repetitions for most sampling schemes and fractions were tested. The computer-generated schemes (SIM, SYS, TRU SYS, and all four STRAT schemes) are symbolically summarized in Appendix A in a manner that may be helpful to some readers. Simple Random Sampling. The primary characteristic of this scheme is that each sampling unit on the frame has an equal probability of being selected for survey. This precondition is a simple concept but is difficult to implement in social science and in the archaeolo gical approach to sampling. Blalock describes the situation very well: "It is sometimes erroneously thought that any 'hit or miss' method of sampling will yield a random sample. This is far from the case. Such methods almost invariably lead to a biased sample because of the human element involved" (Blalock I960: 393). The ideal way to insure equal probability is to assign each sampling unit a number based on its position on the frame and then to select digits from a table of random numbers. Units are selected for survey when their assigned position number corresponds to the selected random digits. Choosing random digits from a properly mixed and randomized barrel or hat is also a satisfactory way of insuring equal probability of selection. The procedure for selecting simple random samples involved assigning random numbers to the sampling units (quarter-sections and sections) and then choosing certain units with the aid of a Pseudo Random Digit Generator affiliated with the Computer Data Corporation Fortran Compiler. To assign random numbers, an ordered list of all units was manually compiled. The order of the list was constant by township from north to south within each range. For example, all sections within the h2N township lines always preceded those within the UlN lines which preceded UON, etc., within range 3S. This same procedure was followed for ranees UE and £E. Within each township, the U.S.G.S. section numbers (1 to 36) determined the order of the sampling units. Within each section, quarter-sections were listed in an arbitrary clockwise order: northeast, southeast, southwest, and northwest. When the sampling units were so listed, each unit was numbered sequentially beginning with "1." From this numbered and ordered list of sampling units, the Pseudo Random Digit Generator selected the proper number of units in accordance with the sampling fraction. The subroutine CK insured that no unit was included twice within a given sample producing a "sampling without replacement" scheme. The code word SIM designates samples that were chosen on this simple random basis. The ordered list of sampling units was restricted when SIM was used in conjunction with another scheme. Under these conditions the simple random procedure only partially determined the composition of the over-all sample. Systematic Sampling. This scheme is a means of choosing sampling units at regular intervals from a frame. The first unit to be selected is determined by drawing a digit(s) from a table of random numbers. Succeeding units are chosen thereafter at regular intervals, the size of which varies with the sampling fraction. In effect, a random starting point from where a sampler would begin to count i units down the list is selected. The i.th unit is included in the sample. The second and subsequent steps involve counting down i units from the previous unit, including that unit in sample, and stopping when the end of the list is reached. 79 The frame for the systematic scheme was the same frame as was used for SIM. The number of units selected by this method depended on the sampling fraction. The first sampling unit to be included was determined by a random draw between 1 and the inverse of the sampling fraction for the 0.1 to O.h fractions. The interval, i, between selected sampling units for these fractions was determined by the inverse of the sampling fraction with the result truncated to the nearest complete integer. For the fractions 0.5 to 0.9, the upper limit of this random starting point for quarter-sections was restricted in accordance with this schedule: 0.5-172; 0.6-137; 0.7-103$ 0.8-69; and 0.9-35. For these sampling fractions, every sampling unit (i.e., an interval of 1) beginning with the randomly selected unit was chosen. For example, 170 quarter-sections could be properly included in the 0.5 sample if any random starting point between and including 1 and 172 were selected. Subroutine TSYSQ executed this procedure, and the code word TRU SYS identifies this scheme. This same procedure was also followed when sections were used as the sampling units. The schedule for the upper limit of the starting points was 0.5-36; 0.6-29; 0.7-22; 0.8-15; and 0.9-8. For example, if the eighth section on the ordered list were randomly chosen as the starting point, the next 63 sections (terminating with the last or 70th section) would be included in the 0.9 sample. Sub routine TSYSS performed this part of the experiment. When combined with other schemes, the basic technique of sub dividing an ordered list and selecting units in the same position was followed. However, the list of sampling units was modified in these situations so that the number of units and the size of each group was reduced. A variant of the systematic scheme that is identified as SYS was also tested, despite the fact that it does not conform to the ideal theory of the systematic scheme. It was tested because it was a standard and consistent way of deriving samples for all fractions from 0.1 to 0.9. The TRU SYS scheme was not truly standard and sys tematic because the "system" changed (as described in the two pre ceding paragraphs) for different sampling fractions. SYS differs from TRU SYS in that the first unit to be selected by the former scheme is determined arbitrarily, not randomly as with TRU SYS. A second difference is that the interval between selected units was also arbitrarily fixed. To select units according to SYS, the frame was subdivided into groups of 10 units each. Unit(s) in the same position(s) from one to 10 were selected depending on the sampling fraction and the repetition. For example, for the first repetition of 0.1 fraction the 1st, 11th, 21st ... 3Ulst quartersections were drawn. The 11th unit is in effect, the first unit of the second group of 10 quarter-sections. For the 0.7 fraction, the lst-7th, llth~17th ... 331st-337th, and the 3blst (the first unit in the next group of 10 units) were chosen for the first repetition. This procedure was executed by a specially prepared subroutine (SYSTEM). This procedure was executed by subroutines QSEC and SBC for sampling units of quarter-sections and sections respectively. 81 Stratified Sampling. This scheme is a means of employing the archeo-statistical approach to sampling. The research unit is sub divided, or stratified, on the basis of some prior knowledge, into various groups called clusters. The purpose of stratification is to insure that sampling units are selected from each stratum, and, there fore, that the full variability that exists within a survey area is expressed in the sample. The criteria for stratification may be archaeological (in other words, cultural) or environmental, but, in any case, should be related to the research objective(s). The precise effect of the data used for stratification on obtaining the full variation of the research unit is not clear at this time. Each unit of the research area should be assigned to one and only one stratum. The number of units in each stratum may vary or may be constant. When the number of units is constant from stratum to stratum within one research area, the probability that one unit in any stratum will be selected is also constant, When the number of units per stratum varies, the probability of selection for any one element will vary from stratum to stratum. The environmental locales described in Chapter 2 constitute the strata of this sampling scheme. The frames used for two previous schemes were modified in two ways. First, quarter-sections are the only sampling units. Sections were not used as sampling units since they frequently could not be assigned to a single locale. Secondly, units in the same stratum were grouped together, constituting a newlyordered list. Within each stratum, the township, section, quartersection, range order used for the two previous schemes was followed, as were the principles of the SIM and SYS. These principles, as well as those of disproportional and proportional approaches to be described in the following sub-sections, determined the number and composition of sampling units in each stratum. The disproportional stratified scheme is characterized by un equal sampling fractions among the various strata of the total popu lation (Blalock I960: 399). This general statement was ooerationalized in the following way to achieve experimental consistency: the total number of quarter-sections to be drawn from a particular strata was obtained by dividing the total number of quarter-sections in the over-all sample by eight, which is the number of strata in the spatial universe. In the case of the 0.3 fraction, the 102 quarter-sections in the over-all sample was divided by eight to obtain 12.7!? units (rounded to 13) from each strata sub-sample. This resulted in choosing the same number of quarter-sections from each stratum. The particular quarter-sections that are drawn are determined either by the simple random or the systematic technique. When combined with SIM, this technique is indicated by the code word STRA.T DIS SIM. When combined with SYS, the code word is STRAT DIS SYS. Continuing the 0.3 example, every fifth quarter-section would be drawn; the digit, £, represents the universe of the strata samDling fraction (or the inverse of 0.19 which equals 13 units divided by 69 units in that locale). The strata sampling fractions generally are unequal because of the variation in the surface area of different strata (Table ll;.) However, the sampling fractions for strata 1 and 5> (the Inter-plateau Table 11*. The STRA.T DIS sampling fractions Over-all Sample Sampling Fraction No, of 1/1* s. No. of lA s. 1 2 /"69 19 Strata Sampling Fraction 3 li 5 6 7 8 Best Real Best Real (1) (2) (3) (U) (5) .09 .09 32 32 1* .06 .21 .31 .17 .06 .13 Per Stratum 13 23 69 88 1*0 20J (6) (7) (8) (9) (10) (li) (12) (13) (11*) .56 .19 .15 .32 .65 .85 17 .25 .89 1.0 .71* .25 .19 *2 .85 .81 157 21 .30 1.0 1.0 .91 .30 .2U .53 1.0 .76 208 179 26 .38 1.0 1.0 1.0 .38 .30 .65 1.0 .70 .57 21*0 195 30 .U3 1.0 1.0 1.0 .1x3 .3U .75 1.0 .66 .62 272 211 3k .1*9 1.0 1.0 1.0 .U9 .39 .85 .61 .89 .67 301* 227 38 .55 1.0 1.0 1.0 .55 .U3 .95 1.0 .21 .21 72 72 9 .31 .31 101* 101* 13 .1*0 .39 136 132 .1*9 .1*6 168 .61 .53 .70 .1 l.o • o J VC .19 .68 1.0 OOo 9 .59 • .1*8 .69 .39 .13 .10 .22 .1*5 • .27 .ou .57 and the Big Ridge locales, lit-7^ square miles each) and strata 2 and 8 (Detrital U.75, and Sand Hill, £.0) are exactly or approximately equal. There appears to be no way to resolve this discrepancy without dis turbing the experimental consistency. The strata sampling fractions are calculated by dividing the number of quarter-sections to be drawn from each stratum (Table Hi, left of center) by the total number of quarter-sections in the sample (indicated in brackets under the appropriate stratum). The ideal sampling fractions (integral multiples of 0.1) are not attainable for two reasons. First, the arbitrary number of quarter-sections drawn from each locale does not match the ideal number of quarter-sections. For the 0.1 fraction, 3U quarter-sections are ideal, but 32 was the best possible approximation because of the arbitrary rule of choosing four units from each of eight locales. Secondly, the best possible approxi•niation (and the ideal) could not be attained for fractions greater than 0.31 because some locales have fewer than the arbitrary number of quarter-sections per locale. For example, the ideal 0.5 fraction could not be attained because strata 2, 3> and 8 had less than the arbitrary 21 units, making a total of 177 quarter-sections in a sample with a real sampling fraction of 0.U6. Stratified proportional sampling, on the other hand, is designed to insure that the strata sampling fractions aporoach equality (Blalock I960: 399, hOl). This was easily achieved by multiplying the over-all sampling fraction by the number of quartersections in each locale. Products involving decimals were rounded to the nearest integer, since partial quarter-sections could not be used. The particular units chosen were determined by either the simple random (STMT PRO SIM) or systematic STRAT PRO SYS) technique. Table l£ (STRAT PRO) shows that the range of strata fractions in the rows is more equal than that in Table 11* (STRAT DIS). For example, the range for the O.U fraction of STR1T PRO is 0.11, while the similar figure for STRAT DIS is 0.81. In Table 1^, the numbers in the rows opposite each over-all sampling fraction represent the number of quarter-sections selected from each stratum. When this number is divided by the total number of quarter-sections in a stratum (the numbers in brackets), the stratum sampling fraction is obtained and is listed in the row below the over-all sampling fraction. Cluster Sampling. This is a means of employing the statisti cal approach to sampling in which the research universe is divided into entities called clusters. The clusters are formed on the basis of the township-range system, rather than the cultural or environ mental criteria of the stratified scheme. The cluster scheme is effec tive because the selected sampling units are located close together in a group (that is, they are clustered), rather than being dispersed widely throughout the survey area. The clustering phenomenon reduces the cost of survey since travel and locating time are saved. Each cluster should be so formed so as to represent all of the variability in the survey area; a cluster in effect is a small-scale replica of the research unit. Some clusters are divided directly into sampling 86 Table 15. Over-all Sampling Fraction .1 .2 .3 .h .5 .6 .7 .8 .9 The STHAT PRO sampling fractions. Strata 5 6 1 2 3 U 7 /£>9 19 13 23 69 88 1*0 7 2 1 2 7 9 h .10 .11 .08 .09 .10 .10 Hi a 2 U Hi 18 .20 .21 .15 .17 .20 .20 21 6 3 6 21 27 .31 .32 .23 .26 .31 .31 28 8 h 8 28 36 .111 .U2 .31 .35 .U1 .m 35 10 5 10 35 H5 .51 .53 .38 .U3 .51 .51 U2 12 6 12 U2 5U .61 .63 .U6 .52 .61 .61 k9 Hi 7 Hi U9 63 .71 .7U •5U .61 .71 .72 56 16 8 16 56 72 .81 .8U .62 .70 .81 .82 63 18 9 18 63 81 .92 .95 .69 .78 .92 .92 .1 8 .2 ~~8~ 20_7 2 .1 U .2 16 .U 20 .5 214 .6 28 .7 32 .8 36 .9 8 .03 16 .06 2h 12 .3 Range .3 8 .k 10 .5 12 .6 lli .7 16 .8 18 .9 .09 32 .11 Uo .15 U8 .17 56 .20 6U .22 72 .26 units (single-stage) or into sub-clusters (two-stage) which are also divided again before getting to the level of sampling units (threestage). Like the stratified scheme, cluster sampling is supposed to be a more efficient means of sampling that either SIM, SYS, or TRU SYS, Therefore, it should be possible to either (l) derive more valid results for the same cost as the other schemes, or (2) to decrease survey costs in order to obtain results similar to SIM or SYS. These theoretical suppositions will be evaluated in this experiment. The two- and three-stage variants of the CLUS SIM and CLUS SYS schemes will be evaluated. There are three possible stages of selection: (1) the cluster, (2) the section, and (3) the quartersection (Table 16). For the quarter-section stage, all four sampling units in each cluster are eligible for selection. The section and quarter-section stages are employed for the two-stage variant, while all stages are used for three-stage cluster sampling. Adopting a sampling usage of the term, I define a cluster as a spatial subdivi sion of the survey area that consists of portions of township(s) that are physically grouped together in either the general shape of a rectangle or a square. The criteria for forming clusters included spatial contiguity and the inclusion of similar numbers of sections. The section and quarter-section stages refer to the same spatial units used elsewhere in this study. Only those sections that contain four completely surveyed quarter-sections are included in the second level. The entire selection process for both schemes and variants was manu ally performed. 88 Table 16. The stages of CLUS sampling. Cluster Stage Cluster Number Township Range Section Stage Section Numbers No. of Sections UlN, 3E 1U, 23, 2U, 26 UON, 3E 2, 11, 3U 39N, 3E 3, 10, 15, 23 11 2 UON, UE, W-l/2 19-21, 28-33 9 3 UON, UE, E-1/2 22-27, 3U-36 9 U 39N, UE, W-l/2 U-9, 16-21 12 5 39N, UE, E-1/2 1-3, 10-15, 22-2U 12 6 39N, $E, N-l/2 U-9, 16-18 9 7 39N, 5E, S-l/2 19-21, 28-30, 32, 33 8 1 70 89 In the two-stage variant, selection at the section and quartersection levels is made, while there is no selection at the cluster level since all seven clusters are included. The nomenclature of the two-stage samples follows this four-part format: (l) name of scheme which is always cluster (abbreviated as CLUS); (2) kind of variant for choosing the quarter-section which is either simple random (SIM) or systematic (SYS); (3) number of sections selected from each of the seven clusters; separated by a comma from (b), the number of quartersections included from each section. For example, CLUS SIM 5,3 indi cates that for the cluster scheme three quarter-sections were randomly selected from each of five sections in all seven clusters. For the CLUS SIM schemes, sections and quarter-sections are generally selected randomly (by drawing from a table of random digits). For each CLUS SYS sample, the same quarter-section in each section of all clusters was always selected on a random basis. For example, in the case of CLUS SYS 12,2 — random digits three and four representing the south west and northwest quarter-sections were drawn, and only those two units from each section were included in the sample. The three-stage variant included selection of sampling units at the cluster, section, and quarter-section levels. The selection process at the cluster and section levels was manipulated in order to obtain sampling fractions that approached the ideal sampling fractions of unitary tenths. Quarter-sections were consistently selected in accordance with the sample name. The nomenclature of the three-stage • variant follows this four-part seouence: (l) over-all sampling fraction, (2) name of scheme, (3) name of variant, and (U) the mean sampling fraction within each section. For example, l/lO CLUS SYS l/3 indicates that every third quarter-section starting with the third was systematically drawn to yield a cluster sample with an over-all sampling fraction of 0,1. In this sample, the sections that were selected were listed sequentially by section numbers; the four quartersections in those sections were also listed sequentially by number, one to four. The digit one, represented the northeast quarter-section, while two indicated the southeast unit; three and four respectively symbolized the southwest and northwest quarter-sections. Selecting every third quarter-section meant that only the underlined units in the following sequence were drawn: 1, 2, 3, U (comprising the first section); 1, 2, 3> U (the second section); 1, 2, *3, it (the third section); 1, 2, 3> U (the fourth section, marking the beginning of another complete cycle). So the southwest quarter-sections of the first and last sections were drawn, while the southeast quartersection was drawn respectively from the second section; two quartersections — the northeast and the southwest ~ were selected from the third section. For thel/LO CLUS SYS l/U sample, every fourth quartersection was drawn beginning with the third one — the digit, three, being randomly drawn; thus, the overlined units in the above illus tration would be included in the sample. In the case of the b/lO CLUS SB! l/2 sample, two of the four quarter-sections in a section were randomly drawn. The draw for each section was independently per formed so that only by chance do several sections include the same numbered quarter-section* 91 A known omission from the experiment is the failure to correct for clusters of unequal size. The clusters differed by as many as four sections which means a maximum difference of 16 third-stage, quarter-section units. The effect of these disparities are unknown, but corrective factors should be introduced (Kish 1965: 182-216). Vector Sampling. This scheme which has been rarely used in archaeological survey may be compared to the path of a single billiard ball haphazardly shot around a billiard table. The survey area is analagous to the table, while the path of the ball across the table and rebounding from the cushions simulates the path of the archae ological survey. The path is continuous and sequential in opposition to the discrete nature of samples using the section and quarter-section as sampling units. In billiards, it is common to begin by placing the cue ball on the white spotj however, in vector survey, the be ginning point should be randomly determined. The scheme is called vector sampling (and codified as VECT) because the path of this fictive billiard ball and of a vector survey has the properties of a vector-magnitude and direction. Spitzer (196U) calls this scheme random walk, VECT differs from other schemes in two ways. First, a rec tangular sampling unit, as opposed to the square section and quartersection of other schemes, is employed. The size of the rectangle is one-half mile in length by one-sixteenth mile in width (or 3.0 ft.). The width was chosen for two reasons: (l) as a simulation of the maximum width that one surveyor can observe under ideal terrain 92 conditions, and (2) as the minimum width that can be accurately drawn and read on a one-inch-to-the-mile map. This sampling unit is identi fied as RECT. The second difference is that the sampling units are linked together along their longest dimension (the one-hale mile length) and the path of the vector is continuous. Thus, the starting point of one vector is the terminating point of the previous vector. When a hypothetical survey team encounters the southern border of the research area, the path of the next vector is limited to a northerly azimuth between 270-360 and 0-90 degrees. A border of the survey area may also be encountered before the full magnitude of a vector has been surveyed. In these cases, the magnitude of the abbreviated survey path is recorded and a new vector must be started. The location of the first vector was determined randomly. I have chosen a starting point on the perimeter of the survey in this manner: (1) symbolize the four cardinal corners of a research unit by the digits one to four, and (2) randomly select one digit to represent the corner that will be the starting point of the first vector. In some cases, there were several starting points at each cardinal corner due to the irregular shape of a locale. In these cases, I quickly and arbitrarily choose that single point which either (l) represented the more "accurate" position with respect to my knowledge of the survey area, or (2) avoided confining a vector to a small, "unescapable" corner of the entire locale. I am confi dent that this starting procedure can be improved since the total decisions were neither consistent nor unbiased. For irregularly shaped survey areas, it is possible to draw a random digit representing an azimuth direction east of north. The starting point of the survey is the point where the azimuth intersects the outer border of the survey area. This case is more general and could be applied to square or rectangular survey areas. It is also possible to begin in the interior of the survey area. To accomplish this alternative, one of the above methods (either the actual cardinal corner or the programmatic azimuth method) is performed and then one vector is laid out, so that the starting point is in the interior. It is unknown whether a starting point on the outer point of a survey area will produce results that are different from a starting point within a survey area. The magnitude and direction of the vector is determined by chance, that is, by making a set of two separate drawings from a table of random digits. The first draw, a two-digit number from 01 to 10, represents the magnitude of the vector as a multiple of 0.5 mile units. The second draw, a three-digit number from 001 to 360, determines the number of degrees east of north. For example, one would walk a dis tance of miles observing a width of 330 feet along an azimuth of 171° east of north if the random digits 07 and 171 were drawn. Another set of two random draws would determine the magnitude and direction of the second vector path. This process was terminated when the appropriate sampling fraction was attained. The selection of units included in the VEGT scheme was performed manually, and the results were tabulated by the computer program. Two variants of the vector scheme were employed for this ex periment: stratified and supra-stratified vector sampling. For the first means of stratification (abbreviated as VECT STRAT), the eight environmental locales were used as strata (as was done for the four STRAT schemes discussed above. The number of sampling units chosen for investigation was calculated similar to the method described above for the STRAT schemes. The sampling unit is a rectangular strip en compassing an area of l/32nd of a square mile. The total number of sampling units in one stratum was obtained by multiplying the number of quarter-sections by eight, which is the number of l/32nd square mile units in one quarter-section. This product was multiplied by the sampling fraction to obtain the number of sampling units. For example, stratum 1 (the Inter-plateau locale) includes 69 quartersections or 552 (69 times 8) rectangular sampling units; only 110,U (552 times the sampling fraction of 0.2) sampling units were included in 0.2 sample. Those 110.lt units comprise 3.U5 square miles (110.I* divided by 32), or 20 percent of the surface area of the 17.25 square mile locale (see Table 17). In order to attain this sampling frac tion, an archaeological surveyor would have to walk a straight line distance of approximately 56 miles. It is not necessary in this case to round the product, for example, 110.lj, to a whole integer since it is possible to investigate only O.U of a 0.5 mile length (or 0.2 mile). For the supra-stratified vector sampling (codified as VECT SUP), the spatial universe was divided into two parts — the western drainage and the Paria Plateau. The western drainage supra-stratum Table 17. Summary of the VECT STRAT and the VECT SUP schemes. Stratum 0.2 VECT STRAT Total Selected Sampling Units Sampling Units 1 552 110.h 2 152 30.It 3 10U 20.8 U 18U 36.8 5 552 110.h 6 70U 1U0.8 7 320 6U.0 8 160 32.0 2,72b 5U5.6 Total Sampling Fraction SuperStratum VECT SUP Total Sampling Units Selected Sampling Units .092 drainage 768 71.7 1,960 180.3 2,728 252.0 768 Ui3.U 1,960 360.6 2,728 756.0 Plateau Total .18a drainage Plateau Total V5 vn. included 2h square miles encompassing all of strata 1 and 2 (the Interplateau and Detrital locales) and a small part of stratum 3 (the Mesa locale). The Plateau supra-stratum (61.2£ square miles) includes the remainder of stratum 3 and all of strata U through 8 (the Rim, Big Ridge, Valley, Northern, and Sand Hill locales). This means of stratification was performed because of the irregular shape of the survey area. Most of the space between the western limit of the Big Ridge locale and the eastern limit of the Detrital locale was not surveyed. Therefore, the only surveyed area that connects the western drainage with the Plateau is a 0.£ mile wide strip in Corral Valley. Because some difficulty in crossing the narrow connecting strip was anticipated, the two units were divided and treated as supra-strata. The supra-strata approach has the advantage of comparing the effect of the size of the strata to the vector stratified method, A problem with the VECT scheme concerns the intersection of vector paths. Archaeologically, a surveyor would be investigating the same terrain twice when his survey path crossed an earlier one. This duplication would have the effect of, (l) giving unequal cover age of the sampling units, and (2) of reducing the sampling fraction. When two vectors intersect at right angles, an area equal to l/2£6th square mile has been covered by the earlier path. Eight such inter sections would have the effect of eliminating one rectangular sampling unit from the strata sample. For example, if the 62 intersections in stratum 2 were all perpendicular (which they are not) the net effect would be to reduce the sampling fraction to 0.186 based on the survey 97 of only 102.65 sampling units including 7.75 that were surveyed twice. The effects are actually greater since there are more oblique inter sections, which encompass a greater area of duplication than per pendicular intersections. Grab Sampling. Two additional schemes that do not conform to statistically-valid rules of sampling are classified as "grab" samples and. will be evaluated in this experiment. Cochran, Mosteller and Tukey (195>Us 13) describe a grab sample as ". .. what you can get by grabbing a handful," with no conscious consideration of sampling theory. A motorized survey similar to that of Phillips, Ford, and Griffin (1951) as described in Chapter 1 is the first type of nonstatistical scheme to be evaluated, because it is so common in archae ology. Quarter-sections were used as sampling units and were selected in the sample because they include places where I expected to find prehistoric occupation. The four places of expected occupation that were investigated by the simulated survey include: (l) an area near the Vermillion Cliffs and the monoliths of Pinnacle Valley, where Pueblo III, cave, or rockshelter sites would be expectedj (2) quartersections adjacent to extant springs; (3) elevated terrain (Big Ridge and the Rim locales, as well as the high ground dividing Coyote from House Rock valleys) in anticipation of finding Puebloan sites in accordance with Aikens1 (1966) hypothesis; and (b) the Corral and Pinnacle Valley floors where lowland Basketmaker occupation was likely (Aikens 1966). In all cases, several alternative groups of quarter- sections satisfied these criteria. However, the dominant criterion of accessibility by motorized vehicle determined the final inclusion of quarter-sections. This scheme is symbolized as "GRAB." The second kind of non-statistical scheme is the right-of-way sample that is used prior to the imminent destruction of sites by the construction of public facilities. The rights-of-way that are laid out by the planning engineers of construction organizations do not conform to sampling theory. Neither are they totally random, as is generally thought. They tend to follow easily traverseable terrain and do not represent all environmental diversity within a naturallybounded region. In effect, the space included by a right-of-way is a biased representation of the spatial population. However, it may happen that the sites included in a right-of-way are representative of the population of sites in a region. This -possibility will be tested. In order to simulate this situation for urgent archaeology, I drew five rights-of-way that appeared to be likely routes for either pipeline, roads, or power lines. The 19-mile valley right-of-way (VAL R/w) connects Kanab, Utah, in the north to Buffalo Ranch south of the Vermillion Cliffs. The RIM R/VI (12.3 miles within the survey avea) links Buffalo Ranch to a cattle watering area near VABM 7097 by departing from the VAL R/W at the head of House Rock Valley and as cending the Plateau. Designed to connect Kanab (or points further north and west) with Page, Arizona, the SINK R/W is located in Coyote and Corral valleys and then continues east until it leaves the survey 99 area in the vicinity of Mexican Sink. This right-of-way is 19.2? miles long within the survey area. Two routes (SAND R/W 1 and 2) link Kanab with Sand Hill Crack, a possible descent route to U.S. 89, both de parting from the SINK R/W near the northeastern corner of the survey area. The 26.? mile SAND Rfid 1 proceeds through the easily traverseable lowlands of Pinnacle Valley, while the latter route follows a 2Umile, straight-line path across the most rugged terrain in the 1968 survey area. The path of each right-of-way usually was parallel and adjacent to existing dirt roads and trails. In all cases, the simu lated routes were as realistic as my experience in salvage archaeology permitted. The rights-of-way were 330 feet wide, which is within the range of the minimal 20 foot width of waterlines and the maximal 5>5>0 foot width of interstate highway rights-of-way. Sampling Unit Three spatial entities were tested to evaluate the effect of' the size of the sampling unit on the validity of the results. The most significant entities are the complete one square mile section (codified as SEC) and the quarter-section (symbolized as QSEC), both of which were used in conjunction with the SIM, TRU SYS, and SYS schemes. The R/W and VECT schemes used the rectangular sampling unit, while all remaining schemes used the quarter-section. The section and quarter-section were used for statistical and pragmatic reasons. First, each unit is uniformly sized with constant dimensions. This fact meant that every such unit on a frame had an equal probability of being selected. The second, and pragmatic, 100 reason resulted from the objective of the survey -- locating and plot ting the U.S.G.S. boundary markers. I was accustomed to thinking in terms of sections and quarter-sections, and it became "natural" to test them as sampling units. The justification for the RECT sampling unit is part of the previous discussion of VECT and R/V sampling in the preceding section. Sampling Fraction. One of the most perplexing questions in sampling practice and theory is "How many elements do I need?" This size of sample can generally be estimated by the use of statistical formulae and is determined by the desired accuracy of the results# This question is slightly easier for archaeological survey than for sociological survey because the spatial limits of the research unit can be determined in archaeology. The spatial limits of the Paria Plateau Survey can be expressed in terms of quarter-sections(3Ul), sections (280 complete sections), and rectangular units (2,728). Sample size can then be expressed as a fraction of this known popula tion; 3h quarter-sections can be more succinctly expressed as a 0.1 sampling fraction. So, the concept of sampling fraction is my short hand way of answering the question — "What size sample do I need?" One-tenth fractions 0.10 to 0.90 will be tested for some repe titions of many sampling schemes. The most outstanding exception was the VECT SUP scheme in which approximations of only the 0.1 and 0.2 fractions were tested. The actual fractions are respectively 0.092 and 0.18U, based on the 2f>2 and %0k units that were selected propor tionally to the surface area of each super-stratum. The strata 101 fractions for VECT STRA.T were exactly 0.1. No other fractions were tested with the VECT scheme. The sampling fraction for the two-stage cluster schemes varied between 0.02 for CLTJS Sffi 1,1 and 0.62 for CLUS SYS 12,3. The CLUS SIM 11, 1-3 samples exactly duplicated the ideal fractions of 0.20, 0.U0, and 0.60. Other samples exactly approximated the ideal frac tions were CLUS SIM 5, 1-3 (respectively 0.102, 0.205>, and 0.308) and CLUS SIM 10,1 with a fraction of 0.19. The three-stage CLUS schemes were only tested for fractions less than 0.7 because several clusters contained two few sections. The first repetition of all sampling fractions of the syste matic scheme includes an extra quarter-section, making the fractions slightly larger than the ideal, for example 0.103 instead of 0.1 and 0.5>02 instead of 0.5. This deviation occurs because the list of quarter-sections totals 3hlt resulting in a one-unit group instead of the standard group of ten units. Cochran states that the introduction of this "... disturbance into the theory of systematic sampling . . . is unlikely to be large even when n /the number of sampling units7 is small /less than 3>0J" (Cochran 1963; 207). The stratified disproportional schemes (both simple random and systematic) are another case in which the ideal fractions were not obtained. To attain the ideal fractions 0.1-0.3, it would have been necessary to subdivide quarter-sections to attain the perfect number (3U, 68, and 102) in the over-all sample. The remainder of the fractions do not attain the ideal simply because there are not 102 enough quarter-sections in certain strata to allow drawing the full number of units. Table 1h presents the actual sampling fractions and the actual number of quarter-sections. The VECT SUP, the SYS QSECT, and the SYS SECT schemes are characterized by an additive feature in selecting sampling units. The units in the 0.1 VECT SUP constitute the first half of the units of the 0.2 scheme. The second group of units in the 0.2 scheme were chosen independently. Also, for both SYS schemes, consecutive sampling fractions of the same repetition differ by only one sampling unit per ten-group units. For example, the h2N3E360l| quarter-section is added to the 0.3 sample to form the sample from the first ten-group unit of the first repetition of the 0,h sample. This addition is made for each of the ten-group units in the over-all sample. The sampling fraction for the five R/W samples are VAL R/VI ~ O.OlUj RIM RAJ 0.009;SINK R/W — O.Ollj; SATO R./W 1 — 0.019} SAIID R/W 2 ~ 0.018. These fractions result from the division of the number of 0.£ mile sampling units (which is twice the length of each right-of-way given in the sub-section "Grab Samples") by the 2,728 sampling units (eight sampling units per quarter-section multiplied by the total 3hl quarter-sections) in the survey area. The 3U quartersections in the GRAB sample results in an ideal sampling fraction of 0.1. Repetition. One question that plagued me as this project developed concerned the element of chance. Suppose that a SIM sample were drawn twice, and that the frequencies for site and artifact occurrence differed each time. This difference could be attributed 103 to the "luck of the draw." Putting luck aside, I wanted to know which draw would produce results similar to the population frequencies. Therefore, in this experiment three sets of draws are made for as many samples as possible. Each set of draws is called a repetition (abbreviated as REP) when the scheme, fraction, size of sampling; unit are held constant. Various repetitions of SYS for the same fraction differed byonly one or two sampling units as can be shown. REP 1 always included the first, 11th, 21st . . . 3hlst quarter-sections (or the first, 11th .. . 6lst sections when applicable). For the 0.1 fraction, these were the only units selected as part of the sample. For higher sampling fractions, e.g., 0.5, the first - fifth, 11th - l£th, etc. quarter-sections or sections were drawn. REP 2 was always initiated by the second, 12th, 22nd . . . 332nd units for the 0.1 fraction; for the 0.^ fraction, the second - sixth, 12th - 16th, etc., units con stituted the sample. REP 3 was started with the third unit on the list and the units were increased in a similar manner. The same procedures concerning repetitions were followed within each stratum for the simple random and systematic variants of both the stratified disproportional and proportional schemes, A Quantitative Evaluation of the Validity of Conclusions Based on Sampling The preceding section outlined the methods of selecting which spatial units were sampled for the simulated survey. Within the 3Ul quarter-sections and eight environmental locales, I488 sites, as well 10!i as ceramic, architectural, and lithic data, were recorded. The cost of performing each of the simulated surveys was calculated after the survey as part of the dissertation research. This information is expressed in terms of seven archaeological variables and one financial variable (Table 18). Six variables are nominal in nature, while the seventh archaeological variable and the single financial variable are on the interval scale. The frequencies for all variables, as well as the statistics to be described in this section, were tabulated for the population and for each of the 326 samples with the aid of specially-prepared subroutines STAT and CHI. Statistical indices based on these frequencies are the means to compare each of the 326 samples to the population so that the validity of conclusions based on sampling procedures may be evaluated. These indices, chi square and economy, will determine which particular sampling scheme, fraction, unit, and repetition is the most accurate and economical way of predicting the known population. Chi square statistically compares the accuracy of the sample vis a vis the popu lation. Economy measures the financial and statistical benefits of the samples. Levels of Measurement A brief discussion of the concept of levels of measurement is necessary in order to describe the nature of the variables that are to be tested by means of chi square and economy. This discussion will also be useful in assessing the experiment. 10$ Table 18. List of variables and values Variable Value Variable Value Locale Inter-plateau Unpainted ceramic tradition Virgin Detrital Kayenta Mesa Virgin-Kayenta Rim No collection Big Ridge Valley Northern Painted ceramic tradition Virgin Kayenta Sand Hill Virgin-Kayenta Site Type Sherd scatter No collection Lithic scatter Sherd-lithic scatter Stone Tool Meat procuring Petrograph Vegetable procuring Isolated feature Meat processing Modified rockshelter Vegetable processing Pithouse Multi-purpose Small pueblo Miscellaneous Medium pueblo Site density Continuously distributed Cost Continuously distributed Large pueblo Age Basketmaker IIIPueblo I Early Pueblo II Late Pueblo II Pueblo II Late Pueblo IIEarly Pueblo III 106 Statisticians commonly agree that there are three scales to be used to observe and measure elements in a population — the nominal, ordinal, and interval scales. The nominal scale, the simplest method, is a classification of those elements that are similar for at least a single characteristic into one group. The objective of the classi fication is to maximize the homogeneity within a group and to maximize the differences between groups. The group is identified by a con venient label that names the group but is not and cannot be subject to any statistical manipulations. The sorting of lithic debris into waste flakes and artifacts is an example. The ordinal scale arranges, or orders, the groups into a uni fied system on the basis of the degree to which they share a certain characteristic. Differences between groups can be expressed qualita tively, but not quantitatively. In other words, it is possible to say that one group or element possesses "more of" or "less of" a certain characteristic than another group. This scale is a higher level of measurement than the ordinal scale since all elements are classified into groups and then ordered. The classification of lithic waste into small (thinning and retouch flakes), medium (waste flakes) and large (cores) flakes is a hypothetical example of the ordinal level, using the characteristic of size to measure the waste debris. The nebulous archaeological term, non~quantitative data or variable, implies either the nominal or the ordinal scale. The expression, quantitative data or variable, in archaeology usually signifies the third level of measurement, the interval scale. 107 This scale, the highest level, measures intervals, or differences be tween elements based on the degree to which they possess a certain characteristic. This scale differs from the ordinal scale in that differences between the groups can be expressed quantitatively. To continue the lithic example, small flakes may represent the grouping one-five cm., while large flakes are greater than 20 cm., and medium flakes fall in between these two groups. One thinning flake may measure three cm. in length, and one waste flake may measure lit cm.; the difference between these two elements can be expressed as an inter val of 11 cm. The interval scale is what measurement commonly de notes. A ratio scale is a particular kind of interval scale in which the zero point is known (Blalock I960: 11-17). It should be remembered that these scales are means of classifying the various ways of measuring a variable or an element. The scales do not refer to the frequencies of occurrence of the elements. These scales are cumulative in the order of presentation from lowest to highestj the ordinal scale displays nominality as well as ordinality, while the interval scale is both nominal, ordinal, and interval in naturej and the ratio scale implies all four scales. The highest level of measurement of the variable being investigated should correspond to the level of measurement for which a particular statis tical test (such as chi square or a correlation coefficient) is intended. If this ideal is not possible, it is permissible to go down the scale of measurement but it is not permissible to go up the scale of measurement. For example, a variable on the ordinal scale can be 108 tested by an interval level statistic. On the other hand, an interval scale variable cannot be t ested with an ordinal scale statistic• One cannot use a test at a higher level of measurement than the variable. Statistical Indices Chi Square. Chi square is used to determine the accuracy of each sample as compared to the population. The chi-square test is a very general test which can be used whenever we wish to evaluate whether or not frequencies which have been eirroirically obtained differ significantly from those which would be expected under a certain set of theoretical assumptions (Blalock I960: 212). For purposes of this experiment, the "empirically obtained frequencies" are those which have been tabulated from the units sampled in each of the 326 simulated surveys. These frequencies will be referred to as the observed frequencies throughout the remainder of this experiment. The terms empirically derived, observed, and sample frequencies are synonomous, but will be referred to as observed frequencies. The "expected frequencies" are those represented by the population of 3Ul quarter-sections in the real 100 percent Paria Plateau Survey. This set of frequencies are synonomous with population frequencies, but will be referred to as expected frequencies. The terms observed and expected frequencies are adopted for use herein because they are com monly associated with chi square applications. If the observed fre quencies of more than one of the six nominal variables used in the chi square test differs significantly from the expected frequencies, that sample will not be considered an accurate predictor of the popu lation. An inaccurate population predictor signifies that the 109 conclusions based on that sample are not valid. On the other hand, a sample with one or fewer significant variables is considered to produce valid conclusions. The occurrence of one significant variable means that 16.7 percent of the variables for one sample appear in a significant state. This threshold point admittedly is an arbitrarycompromise between the alternative of zero variables which would have been too conservative and two significant variables (33*U percent) which would have been a very liberal threshold point. The chi souare calculation was performed mechanically with the aid of a specially prepared subroutine, CHI. Two sets of expected frequencies for all six variables were manually tabulated, mechanically verified, and stored on tape to be read into the urogram. Two sets were necessary because there are actually two sets of expected fre quencies — one based on the spatial population of quarter-sections and the second based on sections. The first set is based on the population of 1*88 sites and is used for all samples in which the sampling unit was either a quarter-section (except CLUS) or a rec tangular strip. These samples include SIM QSEC, SYS QSEC, all four STRAT samples, VECTOR, R/W, and GRAB. The second set of "read in" expected frequencies is based on U38 sites located in those 70 sections in which all four quarter-sections had been surveyed. The samples involved here are those in which the complete section is the sampling unit, for example, SIM SEC and SYS SEC, or in which a complete section is a necessary intermediary unit for choosing quarter-section, for example, all CHJS schemes. 110 The appropriate set of "read-in" expected frequencies consti tute part of the chi square test. The other part is composed of the observed frequencies which were tabulated by the subroutine CHI as the sampling units were being selected for each sample. The following formula was used for the chi square calculationsj where f is the observed frequencies, fe is the expected frequencies, N is the number of sampling units in the sample, and c is the correc tion factor. The correction factor in the above formula is necessary in order to make the observed and expected frequencies equal in accord ance with the strictures of chi square testing. In contingency applications of chi square, the expected and observed frequencies are always equal. I believe that this equalization is necessary for the experiment and verified this with Professor Alan Humphrey of the University of Arizona and Mr. David Asche of the University of Michi gan. Two alternative correction factors were possible: (1) a factor less than 1.0 which would proportionately reduce the exoected fre quencies to the number of observed frequencies, and (2) a factor greater than 1.0 which would proportionately increase the sum of observed frequencies to equal that of the expected frequencies. The former alternative was chosen because of the relationship between Ill sample size and the chi square value. For contingency problems, chi square values increase directly proportional to an increase in sample size when the cellular percentages remain constant. This means, in effect, than when samples are large we are saying very little when we have established a 'significant' relationship .... Significance can be obtained with a very strong relationship and very small samples or with a very weak relationship and large samples (Blalock 1960s 225, 227). Each of Blalock's suggested routes for achieving significance respec tively correspond to the alternative correction factors presented above. I prefer and have chosen the conservative approach of a correction factor less than 1.0. The correction factor was arrived at by dividing the sum of observed frequencies for each variable in one sample by the sum of expected frequencies for the same variable in the total population or, symbolically, Multiplying fe by the correction factor in the denominator of the chi square formula had the effect of reducing the sum of expected fre2 quencies before the division of fQ by fe was made for each value of the variable. The calculation of both x^ and the correction factor was executed by the CHI subroutine. The degree of freedom is always one less than the number of values for variable that is tested by chi square. The level of probability is 0.05, a conservative choice. 112 Economy Kish's (1965s 266) concept of economy is a real-world archae ological method of ranking samples and variables that are considered representative of the total population. The concept is based on two factors: the cost of performing a survey and the sample variance that is empirically obtained. An economical sample is one that either minimizes the cost per unit of variance or minimizes the variance per unit of cost. The economy of a single sample is the cost of sur vey divided by the variance; this index was calculated on an electric calculator. The concept of economy is operationalized for this experiment by using the variance in site density and actual costs of survey. Site density — the seventh, and the only interval level archaeological variable — was recorded as the number of sites per sampling unit. Subroutine STAT tabulated the results and calculated the site density and the variance in accordance with this general formula: N - 1 where N is the number of sampling units in a particular sample for which is calculated; x is the average site density for the sample; and x^ is the number of sites in each sampling unit. The variance for the VBCT and R/W samples was manually calculated following the above formula. The actual costs of performing the survey were calculated manually on the basis of financial data compiled during the 1968 1.13 survey (Appendix B). Expenses included in the calculations are the wage compensation for the surveyors, administrators, clerks, and sup porting laboratory technicians for the field and laboratory phases; the rental and use of vehicles, supplies and equipment for transpor tation to and at the survey areaj and, food for the surveyors for the field phase only. The wage compensation includes only the threemonth period of field work, analysis, and the rough drafting of a report. Additional time devoted to finalizing the report and other contributions were not included in the cost analysis. The expenses of survey consist of non-variable costs that were incurred regardless of sampling considerations and of variable costs that depend on the sampling unit, fraction, and scheme (Kish 1965: 263-265). Non-variable survey costs include the time and expense of preparing and loading equipment, travel to the survey area, establish ing the camp, and learning the road system. Five days were allowed for these activities, or a total of $685, based on a four-man crew at the empirically-derived rate of $3b.25 per man day. Also included in the non-variable costs would be the environmental familiarization necessary for forming locales and strata for the stratified scheme. This familiarization could be performed by one person designated as the project statistician while the remainder of the crew are estab lishing camp. The variable costs of performing survey depend on sampling considerations. The cost of surveying one quarter-section is $35 or $1U0 per section when sampling units are contiguous. The sampling units in the various schemes of this experiment are not always con tiguous; time would have to be spent searching for the U.S.G.S. markers in unknown parts of the Paria Plateau Survey area. The time devoted to this searching activity would increase as the sampling fraction decreased because, with smaller sampling fractions, the sampling units are more isolated. It was thought that such searching at the 0.1 sampling level would require the help of an extra surveyor for the two months of the field season (at a cost of about $U00). A close approximation to this anticipated increase can be attained by increasing the survey cost per quarter-section for each decrease in the sampling fraction as illustrated in Table 19. The net effect of this schedule is to add $51*0 to the total expenses for the 1968 proj ect. The costs for the third sampling unit, the rectangular strip, depend on which sampling scheme is used. When the VECT scheme is used, the cost is $U.50 per R03T, based on the fact that a strip is one-eighth of the surface area of a quarter-section. When this unit is used in conjunction with the R/W approach, the survey costs are $7.00 per RECT. The increased costs for the R/W approach are due to the increased subsistence costs of a motel-restaurant (as opposed to a camp) lifestyle. A second explanation for the increased cost is the necessity of covering the entire width of the strip completely. With the VECTOR scheme, the width of the strip is assumed to be 330 feet but the actual width varies with such factors as vegetation cover, geomorphology, and the competence of the observer. Additionally, 115 Table 19. Schedule of variable survey costs. Sampling Fraction Quarter-Section Section 1.0 $35.00 $11*0.00 0.9 35.25 lhl.OO 0.8 35.50 1U2.00 0.7 35.75 1L3.00 0.6 36.00 HiU.oo 0.5 36.25 1U5.00 o.U 36.50 1)46.00 0.3 36.75 1U7.00 0.2 37.00 U18.00 0.1 37.25 lii9.00 116 VECTOR sampling would lose its value if more than one walking of a strip were necessary as is frequently done in right-of-way survey. Summary The Paria Plateau survey data are particularly amenable to an experimental approach for testing sampling theory. The sampling pro cess is analytically subdivided into four aspects — sampling scheme, fraction, unit, and repetition. An evaluation of the validity of conclusions based on each of the four aspects and of sampling in general is the purpose of the experiment. The sampling scheme is a particular method of selecting sampling units,and the following schemes that occasionally include variants are evaluated: simple random, systematic, stratified, cluster, vector, motorized, and. rightof-way sampling. The sampling fraction is an expression of how many sampling units should be surveyed; all one-tenth fractions from 0.1 to 0.9 are tested. Three sizes of sampling unit constitute another part of sampling theory to be tested; these units are the section, the' quarter-section, and the rectangular unit. A repetition is a re peated drawing from a population when the above three aspects remain constant; three repetitions are tested. A total of 326 samples are generated by a combination of the four aspects of the sampling process. Data pertaining to eight vari ables are tabulated for each sample. Observed frequencies of six of the nominal archaeological variables are compared to the expected frequencies of the Paria Plateau population and a chi square is used 117 to determine if the two kinds of frequencies are significantly dif ferent at the 0.05level of probability. Samples with more than one significant variable are not considered to lead to valid conclusions concerning the population. The final two variables, both of which are interval in nature — variance in site density and actual cost are used to calculate the economy of each sample. Chi square and economy, as indices for evaluating the results of the experiment, compliment each other very well. Chi square is a qualitative, nominal level statistic that determines whether the empirical results differ significantly or non-significantly from the expected results. There is no middle groundj the answer is categori cal and dichotomous — significantly different and unacceptable or non-significantly different and acceptable. The result of the chi square analysis is a list of acceptable alternatives that differ nonsignificantly for each aspect of the sampling process. Economy compliments this analysis because its values are con tinuously distributed within certain limitations on an interval scale of measurement. Therefore, the advantage of economy is that it is a refined method of ranking those alternatives that are categorized by the chi square analysis to be acceptable. In a few words, chi square determines whether a sampling alternative is acceptable or not, and economy tells which alternative is better than others. CHAPTER U THE RESULTS OF THE EXPERIMENT The data that were generated by the methods described in Chapter 3 are summarized in this chapter in terms of the problem of the dissertation. The problem as stated by Lloyd concerns validity of the conclusions based on a discontinuous intensive survey. In this study, 326 discontinuous intensive surveys are simulated on paper, and the results are interpreted in terms of the four aspects of the sampling process — sampling scheme, fraction, unit, and repe tition# Which alternative of each aspect of the sampling process is more likely to produce valid conclusions? I hope that an empirically based answer to these questions will assist archaeologists who want to survey complete regions, but are forced to sample because of tem poral and financial limitations. Summary Statistics Chi square and economy are useful for evaluating each simu lated sample and for comparing each sanrole to the population. However, the experiment, as outlined in the previous chapter, generated 326 samples. For each sample, a chi square value for each of six vari ables and one number representing economy is calculated. Thus, the data used to answer the question of this study consist of 1,956 chi square values and 326 values of economy. In order to summarize these 118 119 indices, four kinds of quantitative devices are employed: (l) the percentage of significant variables derived from the chi square analy sis in a large group of samples; (2) the rank-order correlation co efficient derived from the index of economy and from the chi-square analyses; (3) direct controlled comparison of either (a) the number of significant variables per sample, or (b) the economy of the samples; and (U) the mean economy of a large group of samples. The percentage of the first method is calculated by dividing the number of significant variables by the total number of variables (which always equals 6 X the number of samples). Those samples that minimize the number of significant variables produce the most satis factory results, and hence, are considered the better predictors of the population. The rank-order correlation coefficient (also called the Spear man correlation coefficient) measures the degree to which two separate rankings of the same items agree with each other (Young and Veldman 1965). The coefficient, symbolized by R, can vary between positive and negative one, respectively representing complete agreement and disagreement between the two rankings (Moroney 1965>: 33^-335). The coefficient frequently compares rankings based on economy with an independent criterion that predicts the results. Controlled comparison is used vrhen the former two methods either conflict or produce unclear results. It is expressed in terms of the number of samples with less significant variables or a smaller index of economy than a sample that differs only by one other factor, 120 for example, sampling scheme, fraction, or unit. Such samples are considered to be the better predictor of the population. This method will be clarified by illustrating its usage in other parts of this chapter. Average (or mean) economy is the final method and is calculated in accordance with generally accepted formulas for the mean. CLUS samples have been excluded from all chi-square analyses and summaries because it is radically different from all other schemes. The implications of this difference are important in influencing sig nificant levels. As Blalock warns, the archaeologist "... should not make use of statistics such as chi-square unless the sampling specialist can help him introduce the appropriate correction factors" (Blalock I960: U09). These correction factors have not been used in the experiment and so the CLUS samples have been omitted. Sampling Scheme Expected Results For both chi square and economy it was expected that the most satisfactory results would be obtained by the use of the most complex scheme. Berry's (1962) experiment shows that sampling efficiency in creases as the complexity of the scheme increases. The three schemes tested by Berry, in decreasing order of efficiency and complexity, are stratified stytematic, stratified random, and simple random. Therefore, it was similarly expected that the most complex schemes, stratified and cluster sampling, would yield the most satis factory results in this experiment. The columns entitled "Complexity 121 Ranking" in Tables 20 and 21 list these expected rankings. The STRAT, VECT STRAT, and GRAB schemes are considered more complex than CLUS because an intimate familiarity with the environment is required for the former schemes while the cluster schemes can be designed from the existing township-range erid system. STRAT DIS is considered more complex than STRAT PRO because of the means of calculating the number of quarter-sections to be drawn. In all cases where SYS and SIM are combined with other schemes, the SYS version is more complex because of the additional calculations necessary to select starting points and intervals. The systematic schemes are simpler than the cluster scheme since the former only requires a comprehensive list of quarter-sections, not spatial subdivisions at the township and range level. TRU SYS is more complex than SYS because the latter scheme selects quarter-sections in the same position every time, rather than the randomized starting points of the TRUE SYS scheme. The VECT SUP scheme is essentially a random method in which sampling units are chosen by one more random draw than the SIM method. Therefore, VECT SUP is considered more complex than SIM. The SIM scheme begins from the same list of quarter-sections as SYS, but the former avoids the additional complexity of calculating starting points and intervals. The right-of-way method is the simplest since the archaeologist has little control over the included sampling units. Economy Table 20 presents the results of all schemes that employ only the quarter-section as the sampling unit. The GRAB scheme stands 122 Table 20. The average economy and rank order of sampling schemes. Sampling Scheme GRAB Average No. of Economy Samoles All Schemes Com Economy plexity Ranking Ranking Large Schemes* Com Economy plexity Ranking Rankin? 1*80.215 1 1 6 R/W 1,139.931 5 2 13 CLUS SYS 1,20^.715 6 3 7 CLUS SIM l,hU6.858 h2 h 8 1 5 STRAT DIS SIM 2,377.326 27 5 2 2 2 STRAT DIS SYS 2,U15.096 27 6 1 3 1 STRAT PRO SYS 2,581.673 27 7 3 h 3 SIM QSEG 2,59U.358 27 8 12 5 8 STRAT PRO SIM 2,629.185 27 9 U 6 U SYS QSEC 2,753.050 27 10 10 7 7 TRU SYS QSEC 2,965.3h3 27 11 9 8 6 VECT SUP U,95U.191 2 12 11 VECT STRAT 8,072.U93 1 13 5 $ * Five schemes with less than seven samples have been eliminated from the rho calculation. 123 Table 21. Ranking of sampling schemes by percentage of significant variables. Variables Total Significant Sampling Scheme No. VECT SUP 12 No. % All Schemes ChiComsquare plexity Ranking Ranking 1 9 Large Schemes* ChiComsquare plexity Ranking Ranking STRAT PRO SIM 162 2 1.2 2 h 1 U SYS QSEC 162 a 2.5 3 8 2 6 STRAT PRO SYS 162 5 3.1 h 3 3 3 SIM QSEC 162 9 5.5 5 10 U 7 30 3 10.0 6 11 162 27 16.7 7 1 5 1 GRAB 6 1 16.7 8 6 VECT STRAT 6 1 16.7 9 5 STRAT DIS SIM 162 30 18.5 10 2 6 2 TRU SYS QSEC 162 67 1*1.3 11 7 7 5 R/W STRAT DIS SYS * Four schemes with less than 31 variables each have been eliminated from the rho calculation. 12U alone as the most economical, while R/tf, CLUS SYS, and CLUS SIM form a secondary group. The third group is the largest, consisting of the four STRAT schemes, as well as SIM, SYS, and THIJ SYS. The VECT schemes constitute the fourth and least economical group. Both the most and least economical schemes include two few samples to make the conclusion unequivocably valid. However, the interesting suspicion that GRAB and TiA'b both of which are nonquantitative in nature, are the most economical methods remains a possibility. The two VECT schemes are least economical. VECT and R/VI are different methods that employ the same rectangular sampling unit. It would appear that the extreme difference in their respective economies is due to their being different schemes, rather than their having a similar sampling unit. Of all the schemes for which a large number of samples (at least 27) were generated, CLUS SIM is the most economical, while both SYS and TRU SYS are the least economical. Table 20 presents the observed rank based on the index of economy and complexity. The calculated rho—0.072-- is positive, but quite lower than expected, and suggests that the degree of complexity is a poor criterion for predicting the economy of sampling schemes. However, the Student's t-test—0.239—reveals that the differences between the two rankings are not significant for all the listed levels between 0.001 and 0.20 (Blalock I960: Uh2). This conflict can be re solved by eliminating the five schemes with fewer than 27 samples. The resulting rho—0.£h8, based on the revised rankings of large 12£ schemes indicates an improved correlation between economy and com plexity. Student's t-test cannot be applied to the Spearman coeffi cient in this case because fewer than ten items are ranked (Moroney 196^: 33?)• Therefore, there is a slight tendency to accept the existence of a relationship between the rankings based on economy and complexity. Chi-square Analysis Samples or groups of samples that have a percentage of sig nificant variables of 16.7 or less are considered as acceptable population predictors, producing valid conclusions in comparison to the population. An inspection of Table 21 shows that all the schemes except STRAT DIS SIM and TRU SYS QSEC produce valid conclusions. More than one-half of the schemes have a percentage of 10 percent or less. It appears that most of the schemes are useful sampling devices for predicting the population frequencies. The question then becomes: "Which scheme has the least number of significant variables?" The chi-square analysis shows that STRAT PRO SIM yields the most satisfactory results of all the completely tested schemes (i.e., those with a large number of included samples). On the other hand, another stratified scheme, STRAT DIS SIM, yields poor results. Others are listed in Table 21 by the percentage of variables that differ significantly from the population frequencies. The results can be divided into three groups: (l) those with a percentage of 7.5 or less, (2) those that vary between 10 and 16.7 percent of significant 126 variables, and (3) those with a percentage greater than 16.7 percent. SIM and SYS, as well as two variants of STRAT PRO, are included in the first group which produces the most valid conclusions. The second group is within the range of acceptability but has a lower recommenda tion than the first group. The third group is completely unacceptable. The inadequacy of TRU SYS QSEC is localized among the 0.3 to 0.5 fractions with US significant variables for three repetitions; the six other fractions contain only 19 significant variables. The same range of inadequate fractions for TRU SYS SEC includes 29 sig nificant variables as compared to 11; for the remaining six fractions. The 0.3 fraction corresponds to the point at which the range of acceptable starting points exceeds i which is the interval between selected sampling units. Using the 0.2 TRU SYS SEC scheme as an example, i = 5 beginning with one of the first five sections. How ever, for the 0.3 fraction, 1=3 beginning with one of the first ten sections. A starting point between one and seven requires an arti ficial stopping point of 21 sections. A random starting point between eight and ten means that 21 sections would be drawn without a stopping point. The range of acceptable starting points is greater than i because 0.3 has been obtained by rounding down the true fraction 0.33 to make i a complete integer. The terminating point for the inade quacy of the TRU SYS SEC is 0.5, the point at which the range of acceptable starting points (1-36) nearly equals the number of sections (35) in the sample. The meaning of this correspondence is not clear. 127 The SYS scheme (both QSEC and SEC) lacks randomized starting points and the group of inadequate population predictors. Therefore, it is certain that the inadequacy of the 0.3 to 0.5 fractions of THLJ SYS is associated with the relationship between i arid the range of acceptable starting points. The TRU SYS scheme, therefore, should probably not be used in archaeological survey particularly at the 0.3 to 0.5 fractions. It is possible that the sampling fractions of 0.25 and- 0.33, in which i becomes a complete integer may avert the poor predictive qualities of the 0.3 and O.U fractions. This possibility was not tested during the experiment. Summary Several features are common to the rankings based on economy (Table 20) and on the chi-square analysis (Table 21). First, a STRAT scheme is found highly ranked according to both indices. For economy, this scheme is STRAT DIS SIM, while STRAT PRO SIM is the best pre dictor (of the large samples) on the basis of percentage of signifi cant variables. Secondly, VECT STRAT and TRU SYS QSEG are at or near the bottom in both rankings. The complexity criterion agrees weakly with the ranking based on economy, as the rho of 0.5U8 (Table 20) indicates. Both coeffi cients, one based on all schemes and the other based on only those schemes with a large number of samples, are positive. The correspond ing coefficients for chi square are both negative (Table 21), one of which is a perfect negative correlation. The positive rank-order coefficients for economy indicates that it is a better index than the 128 percentage of significant variables based on chi square values. At least, the ranking of schemes based on economony more closely agrees with the expected ranking than does the ranking on the basis of chisquare analysis. It seems that the archaeostatistical index of economy conforms more closely to the expected ranking based on com plexity than does the purely statistical chi-square analysis. The cluster and stratified schemes that are highly ranked by the index of economy are considered to produce the most satisfactory results. Minor Schemes The schemes to be discussed in this section either contain too few samples for the above general analysis or exhibit some uncommon characteristics that warrant special discussion. GRAB Sampling. GRAB is not the best predictor when compared to only the 0.1 fraction. The chi-square analysis shows that GRAB exhibits 16.7 percent of significant variables while all other schemes employing the quarter-section sampling unit have a corresponding 12.2 . percent. This comparison weakens the suspicion that GRAB is highly economical. CIUS Sampling. Several generalizations concerning the CLUS schemes should be made because that part of the experiment is so radically different. First, CLUS SYS is more economical than CLUS SIM at the lower sampling fractions, while there is no clear pattern for higher fractions (Table 22). Except for the lower comparison of Table 22, the number of quarter-sections and the stage variant of each of the compared schemes are equal so the comparison is valid. Table 22. A comparison of the CLUS SIM and CLUS SYS schemes by sampling fraction. Sampling Scheme CLUS SIM Lower Sampling Fractions .10 .205 $587,978 (1/10 CLUS SIM lA) CLUS SYS $U05.717 (1/10 CLUS SYS lA) .1 CLUS SIM $731,696 (CLUS SIM 5,1) CLUS SYS $U57.67U (1/10 CLUS SYS 1/3) $1,61U.605 (CLUS SIM 12,1) $1,311;.261 (CLUS SYS 12,1) Higher Sampling Fractions .U10 .615 $1,857,967 (CLUS SIM 12,2) $1,1*51.178 (CLUS SYS 12,2) $2,6UIU323 (CLUS SIM 12,3) $3,105.U6l (CLUS SYS 12,3) 130 Comparative data for other sampling fractions was not generated during the experiment. Secondly, the two-stage CHJS SIM examples are slightly more economical than are the three-stage variants. The two-stage variant has a lower average economy than the three-stage variant (Table 23). This conclusion is supported by the 0.2 comparison which is the best comparison because the number of quarter-sections in each variant is equal. On the other hand, the controlled comparison between samples at approximately the same sampling fraction shows that there is no clear difference between the two variants. There are two cases in which each variant is more economical than its counterpart. The threestage variant has been manipulated to attain the appropriate over-all sampling fraction. However, the particular units chosen at each stage to attain the stage sampling fraction have been drawn from a table of random numbers. Thus, the manipulation has occurred in a random manner that does not bias the selection of units at any stage of the cluster process. (It is not possible to compare the same two variants for CLUS SYS because of the lack of equivalent samples.) Thirdly, for the 0.1 fraction, greatest economy is obtained by maximizing the number of sections (second-stage units) and by mini mizing the number of quarter-sections (third-stage units). Referring to Table 2k for an example it is more economical to draw one quartersection from each of four sections per cluster than to draw two quarter-sections from each of two sections per cluster. This general ization is referred to as the maximize-minimize principle in Table 2k• Table 23. A comparison of the two and three-stage variants of CLUS SIM CLUS Variant Two-Stage ca. 0.1 Economy n $731,696 (CLUS SIM Three-Stage $587,978 . 0.2 Economy n ca. 0.3 Economy n 35 $1,287,092 68 $1,1-27.505 105 5,1) (CLUS SIM 11,1) (CLUS SIM 3h $ 765.21*0 68 $2,290,030 102 5,3) ca. O.U Economy $2,532,882 165 (CLUS SIM Average Economy n $1,195,835 8,3) $2,792,618 170 $1,287,173 (1/10 CLUS SIM lA) (2/10 CLUS SIM l/2) (3/10 CIUS SIM l/2) (5/10 CLUS SIM 3A) 132 Table 21;. The relationship between second- and third-stage selection of CLUS SIM sampling. Approximate Sampling Fraction More Economical CLUS SIM Scheme Economy Less Economical CLUS SIM Scheme Economy No. of Sampling Units Maximize-minimize Principle 0.1 2,1 $ S22.7U6 1,2 $ 828.6U0 1U 0.1 3,1 387.203 1,3 9U7.997 21 0.1 M 368.991; 2,2 751.301; 28 0.1 3,2 617.011; 2,3 1,029.01*8 h2 6,1 1,01*1.1*35 & Minimize-maximize Principle 0.1 0.2 h,2 6ft.869 8,1 956.295 56 0.2 5,2 1,11*8.316 12,1 1,611*.605 70 0.2 U,3 1,093.095 6,2 1,711.659 8U 133 the only exception among four possible cases is the last example at the 0,1 level with U2 sampling units. This exception may be caused by the fourth generalization concerning CHJS SIM, Fourthly, for fractions greater than 0,1, the selection of six or more sections per first-stage cluster is less economical than choosing more third-stage units from a fewer number of second-stage sections. In other words, referring to Table 2kf it is more economi cal to choose two quarter-sections from each of four sections of every cluster than to choose one quarter-section from each of eight sections in every cluster. The CLUS SIM 6,1 scheme is a transitional case between the third and fourth principles and indicates that this minimize-maximize principle begins to be effective when the level of six sections per primary cluster is attained. Finally, the most economical CHJS SIM samples are generally those with lower sampling fractions (Table 25). The most notable exceptions are those samples (CLUS SIM k,2'f 1,2; l,3j and h,3) that conform to the third and fourth generalizations. VECT Sampling Several questionable generalizations concerning the VECT schemes are also apparent from a limited number of cases. First, the larger stratum, VEST SUP, is more economical than a smaller stratum, VECT STRAT at the only fraction (0.2) where both strata were tested. This suspicion was further tested by considering each stratum (i.e., locale) as a separate sample and calculating economy and for each stratum. This test indicated that greater economy is attained by 13U Table 25. The economy and rank order of CLUS SIM. Rank by Economy Rank by No. of Sampling Units No. of Sampling Units 368,99k 1 6.5 28 3,1 2,1 387.203 522.7146 2 U.5 2.5 21 1/10 CLUS SIM 1/jU 587.978 3,2 619,01b It,2 65U,868 U 5 6 5,1 2,2 731.696 751.301; 2/10 CLUS SIM 1/2 765.2U0 1,2 828.6I1O 1,3 UU7,997 8,1 CLUS SIN Scheme M Economy $ 3 1U 11 3U U2 114.5 56 7 8 9 6.5 35 28 9 10 11 19.5 68 2.5 1U 21 12 1U.5 2,3 956.295 1,029.0U8 13 11 56 U2 6,1 l,OUl.U35 1U 11 U2 U,3 1,093.095 15 23.5 8U 3,3 1,11^.797 16 17 63 5,2 10,1 I,lii8.3l6 21.5 18 70 1,190.751 17 18 65 9,1 1,280.152 16 62 11,1 1,287.092 19 20 19.5 68 7,1 1,316.596 21 13 5,3 U/10 CLUS SIM 1/2 1,1*27.505 22 27 U9 105 1,601.190 23 32.5 136 12,1 l,6lli.605 2I4. 21.5 70 7,2 1,63U.905 25 25 98 6,2 1,711.659 26 23.5 8U 6,3 l,857.9l»6 27 30 8 U.5 126 135 Table 25. The economy and rank order of CLUS SIM—Continued Rank by No. of Sampling Units No. of Sampling Units Economy Rank by Economy 12,2 SI,857.967 28 3k 1U0 8,2 10,2 1,98U.70U 28 1,987.55b 2,008.176 29 30 31 112 130 31 32.5 136 9,2 3/10 CLUS SIM 1/2 2,072.792 32 29 12U 2,290.030 33 26 102 7,3 2,U12.U89 3h 35 1U3 8,3 2,532.882 35 36 165 6/10 CLUS SIM 2,655.092 36 bo.5 20U 5/10 CLUS SIM 3A 2,792.618 37 37 170 1,1 2,81*0.090 38 1 7 10,3 3,03i|.659 39 39 195 11,3 3,080.966 bo Uo«5 201* 12,3 3,105.b6l hi U2 210 9,3 3,356.303 h2 30 186 CLUS SIM Scheme 11,2 R » 0.821 136 decreasing the area of the stratum from 22 square miles (the Valley locale or stratum 6) to 5.75 square miles (the Mesa locale or stratum U). When the stratum area is further decreased (to 5.0j U.75; and 3.25 square miles for the remaining strata) the economy varies greatly and in an irregular manner. These irregularities are manifested in the low rank-order coefficient of 0.197 between stratum area and stratum economy. (The number of significant variables per stratum sample varies irregularly and offers no relevant data.) A second suspicion is that the most economical sampling frac tion for the V3CT SUP scheme is less than 0.1. The trend is for the 0.1 VECT SUP scheme to be more economical than its 0.2 counterpart. (Both samples contain no significant variables, making the chi-square analysis meaningless for this problem.) This trend is quite tenta tive because the two samples are not independent. The 0.2 scheme consists of those rectangular sampling units in 0.1 VECT SUP as well as an additional 272.8 units selected in the same manner. Sampling Unit All sampling units except for the controlled comparison of the TRU SYS scheme exhibit a percentage of significant variables less than the predetermined threshold of 16.7. The conclusion from this data is that all three sampling units are acceptable means of producing valid results. The square mile section appears to be the sampling unit that produces more satisfactory results than either the quarter-section or 137 the rectangular unit# This conclusion was not expectedj however, there is some equivocal evidence# The index of economy suggests that greater economy is attained as larger sampling units are employed (Table 26). The converse, that greater economy is obtained by smaller sampling units, is inferred from the chi-square analysis. For both indices, the quarter-section test includes approximately 3X the number of section samples and.. UOK the number of rectangular samples. These conclusions are based on a comparison of all schemes, repetitions, and fractions in which the three sampling units were employed. The same conflicting conclusion is derived by making controlled comparison of pairs of similar schemes (SIM, SYS, and TRU SYS) that differ only by unit (Table 26). The analysis of Table 26 shows that the section produces a lower percentage of significant variables than the quarter-section for the TRU SYS technique. However, this scheme was unquestionably shown to be a poor population predictor (see Tables 20 and 21). Eliminating the TRU SYS scheme from the three paired comparisons (in the lower two rows of Table 26) produces the same con flict between the two indices# A second attempt to resolve the conflict favors the section as the most satisfactory unit. This method compares the economy and percentage of significant variables for each of the 81 pairs of samples that differ only by sampling unit. For example, the 0.1 fractions of the first repetition of both SIM QSEC and of SIM SEC are compared. In all cases, the sections are more economical than 138 Table 26. Analysis of sampling unit by economy and chi-square analyses. Sampling Unit Included Scheme(s) Average Economy No. of Samples Percentage of Significant Variables Complete Comparison SBC All $ 228.539 81 16.2 QSEC All 2,U71.317 237* 12.7 RECT All 2,956.316 8 8.3 Controlled Comparison QSEC SIM 2,59U.358 27 5.5 SEC SIM 216.317 27 9.9 QSEC SYS 2,753.050 27 2.5 SEC SYS 222.180 27 12.3 QSEC TRU SYS 2,965.3^3 27 Ul.3 SEC TRU SYS 2U7.H9 27 26.5 Average - QSEC SM^SYS 2,770.79k 81 16.k Average - SEG SIM,^SYS 228.539 81 16.2 Average - QSEC SIM, SYS 2,673.518 5U U.O 219.2i*9 5U 11.1 Average - SEC SIM, SYS * The U7 CLUS samples have been omitted from the Chi-square analysis, making the number of samples 190. 139 the quarter-section units. In only one third of the cases (27) there are more significant variables in quarter-section samples than in section samples. Of the remaining Sh cases, UO have the same number of significant variables; 12* favor the quarter-section. Thus, both indices show that the section produces more satisfactory results than the quarter-section. Sampling Fraction All sampling fractions exhibit less than 16.7 percent of sig nificant variables, implying that all fractions would produce valid results when the population could not be surveyed. It was expected that the chi-square analysis would produce a smooth gradient, while the index of economy was expected to behave irregularly. For the chi-square index, the number of significant variables was expected to decrease continually as the sampling frac tion increased from 0.1 to 0.9. Furthermore, it was anticipated that a quantum reduction in the number of significant variables between two . consecutive fractions would be found. The higher of the two fractions with the fewer number of significant variables would be the best population predicator among all fractions along the gradient. The index of economy is based on survey costs that increase directly as the sampling fraction increases and on statistical variance that could be predicated to behave irregularly. Therefore, it was anticipated that economy would generally increase in an irregular manner. The expected results of an over-all decrease in the number of significant variables was encountered as indicated in Table 27. Uto Table 27. Tabulation of significant variables by sampling fraction. Sampling Unit* OSEC RECT-ss* •p Sampling Fraction c (It to C a> •r) rH JO •H C no •H to cd k cd > •P C m <u H ,0 rH cd cd •P U O cd «h to [q O 0) •rl H •H Cd C bl: U •H cd Eh > co > m v H £> H cd cd *h •P u 0 cd EH > SEC . -P C cd to v a> *rl 1—I «H £> •H (d C tko u •rl Cd Summary m r—1 , S> rH ctJ cd -H •P U O cd H co > E > •P c cd to O 0) •H 1—1 CM ,Q •H cd C -H tlC F •H cd to > H m a> H . .O rH Cd cd «rl •P U O cd E-i fc» s> be cd •p c <D 0 S <D H (1. 0.1 3 36 1U 109 6 36 23 181 12.7 0.2 1 12 12 108 6 36 19 1*6 12.2 0.3 11 108 6 36 17 liiU 11.8 O.u 6 108 36 11 1M 7.6 0.5 7 108 36 12 UiU 8.3 0.6 10 108 36 15 lldi lO.li 0.7 6 108 36 9 litU 6.2 0.8 6 108 36 6 uu U.2 0.9 6 108 36 6 3 U.2 * Both TRU SYS schemes have been omitted from this analysis because of their inadequacy as population predictors. ** Sampling fractions greater than 0.2 were not tested in conjunction with the REDT sampling unit. ua However, the decrease was not continual, but was interrupted by an increase at the 0.5 and 0.6 fractions. The second expected result of a quantum decrease between two adjacent fractions was also observed. This situation occurred once between the 0.3 and O.h fractions and again between the 0.6 and 0.7 fractions (Table 27). The decrease at 0.7 is due to the unexpected and unexplained increase at 0.5 and 0.6. This quantum decrease is also obtained by looking for a gradient within each run where all nine fractions for each scheme and repetition are present (Table 28). The frequencies in the Total column of Table 28 represent the number of times at each fraction that the number of significant variables initially decreased to and re mained at zero for all higher fractions. For example, at the 0.1 and 0.2 fractions of SYS QSEC and STRAT PRO SIM, there was one variable that differed significantly from the population frequencies, while no significant variables were found at the 0.3 to 0.9 fractions. These two cases are represented opposite the 0.3 fraction by the frequency of two. Only those samples (the four STRAT schemes, as well as SIM, SYS, and TRU SYS with both SEC and QSEC) with all fractions from 0,1 to 0.9 are included. The 0.7 fraction is the point at which the number of significant variables decreases to zero most frequently. The next most frequent fractions are O.h, 0.8, and 0.9 with three zero points each. The expected general increase in economy from 0.1 to 0.9 was encountered in nine of the 30 runs produced by three repetitions of ten schemes. (Of the remaining 21 runs, lU have one decrease across ik2 Table 28. Sampling Fraction The number of exceptions to the expected chi-square pattern tabulated by sampling fraction. Sampling Unit QSEC SEC Total 0.2 1 1 0.3 2 2 o.k 3 3 0.5 0.6 0.7 1 1 2 6 3 3 1 2 3 11 8 19 U 0.8 0.9 Total 1U3 all sampling fractions, while six runs have two decreases and one run — the first repetition of STRAT PRO SYS — exhibits a very oscilla tory pattern with three decreases.) Additionally, there are 2h0 pairs of adjacent fractions in which the expected increase could have occurred. In 29 pairs (12.1 percent), this increase was not observed. These two summaries indicate the expected results of the index of economy were not encountered. The distribution by sampling fraction of these unexpected results is present in Table 29. Exceptions to the expected pattern are tallied in Table 29 opposite each sampling frac tion at which the decrease in economy occurs within one run, and each decrease is tallied for the proper fraction. The frequencies of ex ceptions can be classified into two groups: (l) those fractions (0.1 - O.U and 0.9) with two or fewer exceptions, and (2) those (0.£ - 0.8) with four or more exceptions. One must conclude that the 0.9 and 0.1 - O.U fractions conform closest to the expected pattern. The 0.7 and 0.8 fractions which are good predictors according to the chi-square analysis must be eliminated from consideration because of the analysis by economy. Because of the quantum decrease and the minimum at the O.U fraction among the low group, O.U is considered the best predictor. These data are relevant to two distinct questions: (l) is sampling useful to archaeology? and (2) given a positive response to the first question, which sampling fraction is the best predictor of ~the population? The fact that the best predictor on the basis of chi square and of economy is 0.9 suggests that sampling is not useful in lUi Table 29. Tabulation of exceptions to the expected pattern of economy. Sampling Fraction No. of Exceptions 0.2 1 0.3 1 O.U 1 0.5 5 0.6 8 0.7 6 0.8 h 0.9 2 29 ll£ archaeological survey. The use of such a high fraction does not save the archaeologist much time or money in investigating a prehistoric region. On the other hand, it can be argued that 0.9 can be dis counted because one would statistically expect high fractions to approximate closely the population. If this argument is accepted, then sampling can be considered useful in archaeological survey, the 0,k fraction can then be considered the best predictoro Repetition The percentage of significant variables is less than 16.7 percent for all repetitions, even though the first and third repeti tions are close to that threshhold. It appears again that all repe titions will produce valid results when sampling of a population is employed. The second repetition produces the most satisfactory results when the index of economy and the chi-square analysis are considered together. The index of economy indicates that there is only a very slight difference (of approximately $37.00 per unit of variance) be tween the second and third repetition (Table 30). The second repeti tion, however, is favored over the third by 2.5 percent on the basis of the chi-square analysis. Descriptive Variable Lithic function is the best predictor of the population according to the chi-square analysis. In Table 31* the number of times that a variable differs significantly from the population 1U6 Table 30. The most satisfactory repetition. Economy Analysis Repetition Average Economy No. of Samples Chi-souare Analysis Percentage of Significant No. of Variables Samples 2 $1,881,339 97 11.6 87 3 l#8Ui.U79 96 1U.1 90 1 2,021.0b3 10£ 1U.2 100 2h7 Table 31• The frequency of significantly different occurrences of the six archaeological variables. Variable No. of Occurrences Percentage Lithic Function 8 3.5 Painted Ceramics 13 5.7 Site Type lii 6.1 Age 15 6.6 Unpainted Ceramics 21 9.2 157 68.9 228 100.0 Locale 11*8 values in the 279 non-CLUS samples is given. Painted ceramics, age, and site type are closely clustered in decreasing order as the next best predictors; unpainted ceramics is a slightly less efficient. Locale is undoubtedly the worst predictor. The lithic function variable assumes different non-quantitative values depending on the activity for which implements were used. Painted and unpainted ceramics and site type are formal because the morphology of selected attributes of these material culture traits determine the non-quantitative value of each variable. The slight disparity in the frequencies of painted and unpainted ceramics as significant variables is somewhat surprising. The age variable is obviously temporal in nature and depends completely on ceramic styl istic traits. The inadequacy of locale may be due to its non-cultural nature. A second explanation is that a flaw in the experimental design is manifest in this one variable. Another obvious explanation is that the locales are poorly formulated. This possibility can be tested by a secondary chi-square analysis that cross-tabulates the nature of the variable with the sampling scheme. One vrould expect the locale variable to appear in a significantly different state much more fre quently in non-stratified schemes that are not related to locale than in the positively related stratified scheme. In chi-square test, the STRAT schemes include the four variants and VECT STRAT, while nonSTRAT includes all other schemes employing QSEC as the sampling unit. The analysis of Table 32 shows that the difference in the frequency 11x9 Table 32. A secondary chi-square test of the validity of locales. Scheme No. of Significant Variables* Locale Non-Locale Total STRAT 59 (1*2.8) 6 (22.3) 65 Non-STRAT 39 (55.2) U5 (28.7) 81* Total 98 X2 = 32.209 df • 1 * Expected frequencies in parentheses. 51 1U9 of the locale variable between stratified and non-stratified schemes is significant. Therefore, it is concluded that the locales are im properly formulated. This explanation alone, or in combination with one or both of the others, accounts for the ineffectiveness of the locale variable. Conclusions The presence of one or fewer significant variables per sample at the 0.05 level of the chi-square test is the criteria used to judge the validity of results obtained by sampling. Most samples meet this criterion) STRAT DIS SIM, TRU SYS QSEC, and TRU SYS SEC the only exceptions. Eliminating the locale variable from the chi- square analysis produces only 17 samples out of 326 with more than one significant variable. This evidence is clearly related to the problem of this experiment. Each of the four aspects of sampling and therefore the complete sampling process produce valid conclusions in comparison to the population. These results and conclusions are quite clear and self-evident. However, the task of selecting which alternative of each of the four aspects of sampling produces the most valid conclusions is difficult. The index of economy has been shown (in the "Summary"sub section of the preceding Sampling Summary section) to be a more real istic and sensitive index than the percentage of significant variables based on the chi-square analysis. Therefore, this index ranks CHJS SIM, STRAT DIS SIM, STRAT DIS SYS, and STRAT PRO SYS in decreasing order of economy. The STRAT DIS SIM scheme must be eliminated 1£L because the percentage of significant variables exceeds the threshhold of 16.7 percent. The two variants of STRAT SYS are very closelyranked on the basis of economy, but are widely separated on the basis of chi square. Eecause STRAT DIS SYS has more than five time as many significant variables as STRAT PRO SYS, the former variant should be dropped to a lower rank. Therefore, the over-all ranking of the most effective schemes in decreasing order is CLUS SIM, STRAT PRO SYS, and STRAT DIS SYS. There is a second group of schemes that are less likely to obtain valid conclusions by the use of sampling. This group consists of SIM QSEC, STRAT PRO SIM, and SYS QSEC in decreasing order. TRU SYS QSEC cannot be recommended because of its extremely high percentages of significant variables. The two VECT schemes cannot be recommended for use because of the poor index of economy and because of the few samples that were tested. That GRAB, as well as R/W and CLUS SYS, are the most economical should remain a suspicion until more samples employing those three schemes are tested. It is also noteworthy that the schemes with a few number of samples occur at either extreme of the economy continuum. Perhaps, this situation is related to the use of variance in an unusual manner. There are also many subtle trends and naunces concerning the variants and schemes of the cluster tech nique that have been presented in this chapter. The results concerning sampling unit and repetition are quite clear. The complete section and the second repetition produce the most valid results on the basis of chi square and economy. That the 152 second repetition is the best population predictor implies than an archaeologist should make a "dry run" before performing the set of draws that will determine the sampling units to be surveyed. The choice of which sampling fraction produces the most valid conclusions is important, yet equivocal. It is important because the most predictive fraction is useful in answering the question: sampling useful to the archaeologist?" and 0.9 fractions. "Is The choice is between the 0.1» The latter can be eliminated because of statisti cal theory and archaeological pragmatics. High fractions generate samples that include a large part of the population. Therefore, it is expected that high fractions would produce results that closely approach the population results. Concerning the pragmatic reason, an archaeologist would not save much time nor money in surveying 90 per cent of a region, when only a 10 percent increase would produce a complete 100 percent survey. The O.li fraction is favored because of the converse of the statistical reason for eliminating the 0.9 frac tion and because of the quantum decrease in the number of significant variables at the O.Ii level. These archaeological and statistical . justifications favoring the O.k level support the usefulness of the sampling approach in archaeology. Summary A sampling method similar to Lloyd's discontinuous intensive survey as simulated in this experiment does produce conclusions that are as valid as investigating the entire survey area. The criterion of one or fewer significant variables per sample at the 0.05 level of 1*3 probability is the basis for this conclusion. There are many alterna tives of each aspect of the sampling process that produce valid conclusions. The best alternatives among the group of acceptable ones are CLUS SIM as the sampling scheme, the section as sampling unit, a fraction of O.lj, and second repetition. Additionally, the variable, lithic function, most accurately predicts the population values of the real 100 percent Paria Plateau survey. Adopting these guidelines in sample surveying would probably produce results that most closely approximate the true populations of sites and artifacts within an archaeological region. CHAPTER £ THE CONCLUSIONS OF THE EXPERIMENT In this experiment, the frequencies of occurrence of prehis toric cultural traits have been used to evaluate various alternatives of the process of sampling a hypothetically unknown region. The sampling process is manifestly useful in archaeological survey. An Appraisal of the Experiment The experimental results are only as valid as the methods, data, and theory on which the results are based. The sampling theory has been presented in Chapter 3. Therefore, a synopsis of the research methods of the Paria Plateau Survey is presented in this section so that the reader can continue to evaluate the data and the results of the experiment. Research Methods Problem Orientation. As frequently happens in archaeology, the topic of. this experiment was formulated after the completion of the field work. Therefore, the experiment depends on data that was collected to solve non-sampling problems. If the problem of this study had been conceived prior to field work, it would have been possible to collect interval level data (such as the area of the site, of surface refuse, and of dwelling units) and to perform a controlled, proba bilistic surface collection. - This would have added two interval 13k l# variables — artifact and debris densities — and allowed for the em ployment of more powerful statistical tests. However, chi square and rho are adequate nominal level statistics compatible with the nominal data. The data are quite amenable to the solution of the sampling problem in spite of the lack of a preconceived problem for the follow ing three reasons: (1) completeness, (2) lack of bias, and (3) spatial controls. Completeness. It would be pretentious to claim that the sur vey resulted in the discovery of all sites or that the survey area was uniformly covered in spite of my after-the-fact controls to correct for the incomplete and unequal coverage of the entire survey area. I have the intuition that during the 1968 season, 80 to 90 percent of all extant sites in the assigned priority areas was recorded. There undoubtedly are variations in the intensity of coverage of the survey area between 1967 and 1968, as well as intra-annum variation among survey members and teams. In spite of these inconsistencies and deficiencies, the project is a Type IV survey in which the complete ness of the site inventory compares favorably with most other surveys. Bias. The survey also partially overcame observer bias in favor of large, conspicuous, and spectacular sites. This was espe - cially true in the 1968 survey when most of the "unspectacular" sites (including sherd and lithic scatters, as well as isolated features) were recorded. Undoubtedly some of these sites were not discovered or possibly even consciously neglected in spite of instructions to record every locus of past human activity. Sherd scatters that 156 appeared to represent one broken vessel were not recorded. Another bias was the failure to search for agricultural devices such as check dams and linear borders (Woodbury 195U). In spite of the recognition of these biases the quantitative expression of sampling bias is not possible because of the lack of interval variables. Spatial Controls* The consistent finding and plotting of U.S. G.S. markers as one of the objectives of the survey may be unique to archaeological survey. At least, that part of the project helped to establish in the field the refined spatial controls necessary for precise site location and plotting. Additionally, the use of minutely- detailed and current aerial photographs helped to insure the accuracy of the spatial data necessary for this experiment. Archaeology and Sampling Theory The salient fact that emerges from this study is that archae ological survey is more concerned with space than with other major dimensions of culture. In this section, the hierarchy of spatial units as used in archaeology will be related to statistical concepts involving space. Archaeological Survey as the Cluster Sampling Technique Summary of Previous Discussion. The hierarchy of sampling concepts based on the scale of decreasing inclusiveness includes uni verse, population, sampling unit, and element. The population is defined as either a collection of all elements or of all sampling units. The element is the basic entity about which information is 157 sought. The sampling unit is the unit that is selected for investiga tion and in some cases corresponds to the element. The list of all possible sampling units or elements is called a frame. The universe is a very abstract statistical concept that is beyond the limits of the problem of this study. There are two major kinds of sampling techniques — element and cluster sampling. In the former, the sampling unit corresponds to the element, and the frame is a list of elements. On the other hand, the frame of cluster sampling is a list of clusters, each of which includes at least several elements. The hierarchy of spatial units used in archaeology includes, in decreasing order of inclusive size, the concepts of world,area, subarea, region, locality, and site. The American Southwest corre sponds to the culture area; the Colorado Plateau to a subarea, and the Paria Plateau to a region. Willey and Phillips' (19£8) concept of locality has been modified for analytical reasons of this study to environmental locales which have been described in Chapter 2. Each locale has been subdivided for sampling purposes into equally sized quarter-sections. Archaeological Space. Within the locale, the site is the next smaller unit of archaeological analysis. From a regional perspective, the site may be considered as a point in space. In other words, when examining the distribution of sites within a region a site appears as a single indivisible point on a map. When tallied as frequencies, artifacts found at a site are considered to be variables that describe 1*8 the site. This conceptualization of archaeological space conforms to the regional perspective that is usually employed during the survey phase of archaeological research. On the other hand, the site may be considered a three-dimensional, divisible, spatial unit with the locality. In this case, artifacts are found at points within the site and can be plotted by reference to the three dimensions. The smallest, indivisible unit of space is the point at which artifacts are located. This conceptualization of archaeological space conforms to the site perspective that is usually employed during the excavational phase of research. Ideally, these two perspectives have been complimentary, and the combination of perspectives is desirable in archaeological analy sis. The site perspective is quite narrow for a proper analysis of excavated artifacts. Excavated artifacts from one site are commonly compared to those of other sites in the region. This method of analy sis is referred to as the comparative aporoach. It is an expression of the principle of archaeological context in that the site is analyzed in terms of its artifactual associations with other sites in the region, instead of being considered as an isolated point in space. The Relationship of Archaeological Units and Sampling Concepts. The prime importance of space in archaeology means that there are two kinds of populations: (1) spatial, and (2) cultural populations. The spatial population consists of an aggregate of quarter-sections, the number of which can be and usually is fixed and finite. The cultural population consists of an aggregate of sites, which are the elements 1*9 to be observed and analyzed. The cultural population is obviously- related to the spatial population since sites occur in space. To discover the cultural population, one must necessarily perform an archaeological survey of the spatial population in which the sampling units are always units of space. Each spatial entity (such as a quarter-section) must then be considered as a cluster of elements in sampling terminology or a cluster of sites in archaeological jargon. This situation exactly conforms to definitions of cluster sampling given by Kish (1965) and Cochran (1963). Several results of this experiment, when combined with statis tical theory, also support this assertion. The fact that CLUS SIM is the most highly ranked scheme is obviously supportative. Blalock's advice that cluster sampling is most effective when each cluster con tains as much internal heterogeneity as possible is the relevant statistical theory. ways. This theory has been empirically verified in two First, the section is more effective than the quarter-section. This larger unit frequently includes several locales and hence more environmental heterogeneity than the smaller quarter-section. One would also expect greater cultural diversity in a larger unit, although this has not been tested. Secondly, the two-stage variant of CLUS SIM is more effective than the three-stage counterpart. The former contains all seven clusters and all environmental diversity within • the survey area, while the latter variant randomly excludes at least one cluster. The discovery of the section and the two-stage variant of CLUS SIM as the best population predictors thus strengthen the simi larity between cluster sampling and archaeological survey. 160 Ramifications Concerning Statistical Inference. The ramifi cations of this fact are quite important in statistical inference and hypothesis testing. If formulas derived for simple random sampling are applied to clustered data, the significance level may be radically altered. Blalock notes that "Instead of having significance at the 0.05 level, the true level (as obtained by correct cluster sample for mulas) may be as high as 0.50 . . ." (Blalock I960: I4O9). Thus, a level of probability that is chosen because it is conservative and "tight" is probably in reality quite liberal and "loose." The effect of this actual laxity is that hypotheses that should be rejected are in fact being accepted. Thus, some statements that are currently accepted as true are false statements of prehistoric cultural reality. The reason for this is ". . . that cluster samples are less efficient ^not to be confused with economical.7 than simple random samples of the same size" (Blalock I960: JU09)• efficiency of a cluster sample with N random sample with N a 500. e He postulates that the 800 may be similar to a simple "If simple random sample formulas are used with an N of 800, therefore, we are more likely to obtain significance than if the correct procedures were used" (Blalock I960: 1x09)• Many formulas, such as Student's t-test, chi square, use M as the denomi nator of a fractional index. In these formulas, the use of the in correct N (equal to 800 in this hypothetical case) as a divisor will produce a smaller result than if the denominator, corrected to N = 500, were divided into the same numerator. That is, the incorrect N pro duces values of the statistical test smaller than does the adjusted N, 161 allowing for greater probability that the statistic will be less than the listed value by which significance is determined. Consequently, it is more likely that significance will be attained with the un adjusted, incorrect N than cluster sampling results are tested with simple random sampling formulas. Miscellaneous Sampling Conclusions Limitations of Conclusions. The target and sampled populations of the Paria Plateau survey do not correspond in all cases. For the Bureau of Land Management, the target spatial population is the Arizona Strip District. The target spatial population for the experiment con sists of the 110.5 square miles in priority areas 1-11, while the sampled population consists of those 85.25 square miles that were actually surveyed in 1967 and 1968. The I488 sites that lie within the 85.25 square miles constitute the target and sampled cultural popu lations• The substantive conclusions of Chapter 2 apply only to the sampled population of priority areas 1-11. Available evidence for the additional unsurveyed 25 square miles of areas indicate that there are environmental differences, for example, the Kaibab detrital sublocale or Hole-in-the-Rock, beyond the sampled populations. Because of these environmental differences, it is not proper to extend the substantive conclusions of prehistoric culture to any target population such as the Paria Plateau or the Arizona Strip District. Sampling Fraction. Both Haggett (1965: 192) and Moroney (1965s 135) state as a general rule and without qualification that sample size should be as large as practical. results of the experiment. This rule conflicts with the It may be possible to increase the pre cision of the general rule in several ways. First, Haggett (1965: 192) claims that the relationship of sample size to accuracy is known to vary by sampling scheme, but he does not state the relationship. Haggett's claim is generally supported by this study, but a more pre cise statement is not possible. Blalock (I960: Ull) presents a general formula that is useful for every kind of scheme utilizing interval variables and also claims that sample size depends on the relationship of sampling to non-sampling errors. Neither of these assertions were tested. Stratified and Cluster Sampling. STRAT is a form of element sampling, while in cluster sampling, the clusters and their spatial subdivisions are sampled (Blalock I960: h06). In the experiment, this requirement of cluster sampling was satisfied by grouping the spatial elements (quarter-sections) into the larger sampling unit, the partial township. For the stratified schemes, the elements of the spatial universe were not grouped but were listed individually on the stratum frame. A second difference concerns the criterion for dividing the population. The spatial population was divided on the basis of en vironment for the stratified scheme, while the arbitrary townshiprange grid system served to divide the population for cluster sampling. This difference seems to conform to sociological stratification in which "... such simple variables as sex, age, occupation, or area 163 of residence" (Blalock I960: U00) are used, while cultural or spatial subdivisions such as city blocks, census tracts, are used in cluster sampling. A third difference is that the elements tend to be dispersed throughout the population according to the stratified scheme while the elements are obviously clustered in cluster sampling. This clustering represents a significant saving in the cost of survey for the sociolo gist. The target spatial population of the archaeologist would have to be very extensive as in a Type I survey to effect a significant saving. A final difference concerns the nature of strata and clusters. Strata should be so formulated as to maximize homogeneity within the stratum. Each stratum, however, should be as different as possible from other strata in order to represent the full variability within the population. The quarter-section seems to be small enough to satisfy this criterion and, yet it can be aggregated by similar locale to produce strata that are environmentally dissimilar. Cluster sampling, on the other hand, should maximize internal heterogeneity and minimize inter-cluster variability. The section seems to satisfy these requirements better than the quarter-section. Sociological Analogy. Must of the statistical and sampling literature is written by sociologists, for example, Kish and Blalock. The extrapolation between generalized forms of sociological and archaeological survey was a constant task in using the above sources. An explicit statement of this extrapolation may ease the burden for other archaeologists. 16U The individual culture-bearer is the sociological element, while the archaeological site is the element in a surveyed region. The sampling units that can be employed to meet various objectives in sociological survey are an apartment, a house, a block, a town, or a census tract, and a city, in order of increasing size. The corre sponding archaeological units are the quarter-section, the section, the township, and the region. In both kinds of survey it is probable that only the city and the region can serve as the target population. Smaller units seem to serve only as sampled populations. Entities larger than the city and region can serve as target population in some cases. This generalized comparison should be modified for particular research objectives. Pragmatic Archaeological Considerations In this section, some concrete suggestions for conducting archaeological survey are presented. The relative advantages of most alternatives of the sampling process will be discussed from archaeolo gical and sampling perspectives. Sampling Scheme Simple Random Sampling. This scheme corresponds to the archae ological approach to sampling except that the feature of equal proba bility of selection is generally ignored. The archaeological concep tion of this scheme then reduces to a "hit or miss" method. An unqualified advantage is that the simple random scheme allows for the exact number of sampling units to be chosen so that the selected sampling fraction can be employed. The exact number can be drawn 16? because of the comparative lack of rules of the random scheme. This characteristic applies equally to experimental projects and to sampling programs planned for real surveys. Simple random sampling is most effective in small regions and localities where there is no diversity. This condition would probably be encountered when surveying a locality adjacent to a site that is being excavated -- that is, a Type II survey. This advantage is par tially mitigated by the fact that such small areas can be completely surveyed and need not be sampled at all. A corollary to this proposal is that simple random sampling can also work in regions and localities where the recording of environmental diversity is not essential for the research objective. In these cases, survey areas that exhibit environmental diversity are effectively treated as homogeneous, un differentiated units. Thus, simple random sampling is useful in any of Ruppe's (1966) four types of survey. Simple random sampling can also be used to maximal effective ness when the frame of sampling units is ordered in any periodic or cyclical manner. The random nature of the scheme will probably over come both kinds of periodicities and cycles — those that are obvious, as well as those that are hidden from the observer. A disadvantage to this scheme is that the sampling units are dispersed irregularly throughout the survey area. creases the costs of performing the survey. This feature in A procedure for minimizing these additional costs resulting from the dispersion of sampling units is offered at the conclusion of this section. 166 Systematic Sampling. This scheme corresponds to the statisti cal approach to sampling, because no archaeological or environmental data are needed to implement this scheme. Like simple random sampling, the systematic scheme works well in survey areas where there is no environmental diversity or where such diversity is not essential to the research objective. This scheme has the disadvantage that when the selected inter val coincides with hidden periodicities in the frame (that is, the units are arranged in a cyclical fashion that is not visible to the investigator) the resulting sample will be extremely biased. The net effect is that the sample would contain the same bias as if a sample were to be drawn from only one stratum of a stratified scheme. Hidden periodicities in a frame are probably not a disadvantage if they are not related to the variables being studied. This coincidence of hidden periodicities can be prevented by randomizing or juggling the order of sampling units on the frame prior to a systematic selection. This maneuver would probably produce the same results as simple random sampling. Another disadvantage is that it may be difficult to achieve an exact sampling fraction. This difficulty is caused by the combina tion of a randomized starting point, a constant interval between selected units, and the number of sampling units on the frame. Under certain conditions, an extra unit(s) will be included in the sample, causing a slight departure from the intended fraction. This disad vantage is true only of the THU SYS scheme, not of SYS. 167 An equivocal feature of the systematic scheme is that the selected units may be dispersed in a regular manner throughout the survey area. The systematic rules of the scheme make this a likely possibility. This is an equivocal characteristic for two reasons: (1) the dispersion increases survey costs on one hand, but (2) the regularity of dispersion implies that systematic survey can be more easily executed in the field than the simple random scheme. Stratified Sampling. This scheme represents the archaeostatistical approach to sampling because of the integration of archae ological and statistical data to influence the form of the scheme. It is commonly thought to the highest level of sampling by archaeologists. This scheme requires more prior knowledge of the survey area than any other scheme. The criteria for stratifying the survey area must be formulated prior to the process of discovering sites. Blalock's advice is the following: "It is usually neither essential nor feasible to hunt around to obtain a single 'best' criterion for strati fying" (i960: U00). The criterion should probably be environmental in nature, rather than cultural because of the ease of observing the environment and because the cultural population is probably unknown in most cases. Therefore, the scheme is best suited to accomplishing objectives concerning the prehistoric environment. The extant environmental locales may be compared to the pre historic environment reconstructed from excavated data. It is pos sible to conceive the extant environment as the expected and the prehistoric environment as the observed frequencies in a manner 168 analogous to chi square. At any rate, an awareness of both present and prehistoric environments is necessary for performing contemporary environmental archaeology. It is also necessary to enlist the assist ance of a geo-botanist in formulating the environmental locales, instead of relying on an environmentally-untrained archaeologist. This scheme is useful in regions where the diversity is dis tributed in spatially discrete parts of the survey area. No single part of the region should be a microcosm of the whole survey area. One would expect that the full variability within the population would be expressed in the sample because of the process of stratification. The experimental results show that the simple cluster scheme is more representative than the stratified schemes despite the theoretical expectation concerning the stratified schemes. Archaeological survey is particularly amenable to stratifi cation because the dimensions of the research unit and of the strata are generally known. This knowledge is an absolute necessity for calculating the stratum sampling fraction for the stratified propor tional sampling scheme. If neither the total survey area nor the size of each stratum is known, the stratified disproportional scheme is most applicable. Locating the strata and their boundaries on the ground in the survey area is a time-consuming prerequisite to success ful stratified sampling. This part of the sampling process should not be regarded as an encumbrance to finding sites. Cluster Sampling. This scheme represents the archaeostatistical approach to sampling in the sense that its adoption is 169 influenced by the feature of coat reduction. This scheme does more to minimize the cost of survey than any other scheme. The financial saving results from the fact that the sampled units are clustered together, and travel time between sampling units is minimized. The amount of cost savings probably increases in direct proportion to the size of the survey area. Thus, a Type I survey (Ruppe 1966) that covers a large area is best approached with the aid of the cluster scheme. This scheme will be most useful if the survey area can be subdivided into a series of smaller parts of each of which contains all the diversity of the large area. An example is the west coast of the Andean mountains where approximately 30 valleys have been formed by rivers that flow to the sea. Each valley is a replica of all others and contains as much diversity as the total subarea. This environmental situation represents a proper application of the clus ter scheme because each cluster should represent a microcosm of the survey area. Vector Sampling. This scheme can be beneficially employed in regions that have not been mapped and staked as has been done by the U.S.G.S. In such regions, vector sampling can be used in conjunction with the rectangular sampling unit which does not require a gridded area, as do the quarter-section and section. Additionally, I would expect that this scheme would be advantageous in survey areas that have very regular and straight-sided borders. The regularity of the survey area prevents vectors from becoming inescapably "trapped" in a nook or cranny of an irregularly shaped survey area. 170 Grab Sampling. This scheme would also work where the surveyarea has not been gridded, although some spatial controls to insure that the proper sampling fraction is attained are necessary. Addi tional requirements are a knowledge of the contemporary environment and of the prehistoric settlement pattern as guides in predicting the location of sites. Sampling Fraction The O.U fraction has been determined to be the best predictor among all tested fractions. This is obviously useful to archaeologists because of the savings effected in avoiding the expenses of a complete 100 percent survey. Sampling Unit The determination that the section is the most useful sampling unit seems to conform to the data requirements of settlement archae ology (Struever 1971! 11). The section is the largest sampling unit tested, and a large unit is necessary in order to obtain a picture of the continuous distribution of all types of sites with respect to the natural landscape. In fact, it may be argued quite convincingly that areal sampling in general is antithetical to the objectives of settle ment archaeology. This possibility was not evaluated during the experiment. Repetition In order to satisfy the results of the experiment, archaeolo gists should execute one repetition, or "dry run," of the sampling 171 process prior to the repetition to be used in the actual survey. This exercise is not difficult since it essentially consists of making a second set of random draws using the same scheme, fraction, and unit as the first draw. Thus, a second repetition is a fairly simple act after the sampling program has been established. Variable The only functional variable, lithic function, is the best predictor, including purely formal variables. This conclusion suggests that a functional, generalizing approach may be a more representa tional mode of analysis than a formal, particularistic approach in which the frequencies of individual artifact types are tabulated. Continued testing of this possibility is necessary for a definitive statement. Guidelines for Implementing a Sampling Program The following outline summarizes the steps necessary for the implementation of a sampling program: 1. Define the survey area and its boundaries on maps and on the ground. 2. Subdivide it into sampling units of equal size. a. If not previously subdivided, select either a grab or a vector scheme in step 3. b. Stratify the survey area (if applicable), verifying the location of the strata on maps and on the ground. 3» Construct a frame. 172 U. Select sampling units for survey according to the four aspects of the sampling process. 5. Label the selected units on a map. 6. Survey intensively the selected units in a manner similar to either the Ackmen-Lowry or the Paria Plateau survey. Step £ is a crucial step because it is the point at which most of the additional time and money consumed for purposes of sampling can be minimized. Archaeologists who are reluctant to adopt sampling because of the increased time and money will find herein a method for minimizing sampling costs. The procedure that I will describe below is the most efficient way I know to expedite the admittedly difficult task of locating sampling units on the ground. It is necessary to list on paper (step 3) and to sketch on a map (step 5>) all the sampling units to be surveyed intensively. The archaeological approach to sampling omits one or more of these steps. The procedure to be described is what I am calling the grid line tactic, in accordance with my previous use of the term tactic. This tactic involves the systematic walking of one grid line that serves as a boundary for the sampling units. When one of the selected units that is indicated on the prepared map (step £) is found and iden tified (by examining the U.S.G.S. markers), that unit is intensively surveyed. The alternate walk-and-survey tactic is continued along the full length of both sides of the grid line until the borders of the sur vey area are reached. The survey team then skips the next grid line, 173 because the selected units adjacent to it on side have been surveyed on the preceding grid line, or for the opposite side, will be surveyed on the succeeding grid line. The third grid line would be found and ex amined in the same walk-and-survey tactic as the first grid line. Alternating grid lines in this manner will expose the surveyors to every sampling unit on the frame. The grid lines should be aligned parallel to the cardinal directions of the compass, if possible, to allow easy compass reading and to facilitate following an "imaginary" line on the ground. The grid lines should be walked parallel to the longest dimen sion of the survey area since this tactic would encounter a maximum number of sampling units along a minimum number of grid lines. The difficult task of this grid line tactic is, initially, to locate and, subsequently, to follow a grid line for the entire length of the sur vey area. The reason for sketching all the sampled units on a map prior to the actual survey is obvious — to prevent "backtracking" to survey a unit that was overlooked after having traced out a grid line. An experienced survey crew should be able to follow a grid line in a four-wheel vehicle particularly when they are in sight of an obvious landmark that indicates the direction of the grid line. Without this grid line tactic, the task is hopeless, and the archaeologist is helpless to implement the above sampling program. Suggestions for Future Research Experimental Research This experiment lacked sufficient GRAB, VECT, and CLUS SYS samples to make solid conclusions. It would be very desirable to program survey data onto a computerized coordinate system so that the VECT schemes could be drawn mechanically. This suggestion would also allow for the formulation of additional schemes that could be sepa rately tested with the rectangular unit. At present, the uniqueness of both the VECT scheme and the sampling unit prevent the analytical separation of these two factors. The manual selection and calculation of the variance makes the VECT scheme difficult to test thoroughly. A second improvement concerns the use of multiple regression rather than chi square to determine the relative predictive qualities of the six variables. The first step involves the calculation of a correlation coefficient between the expected and observed frequencies of all values for each variable. The second step is the regression analysis in which the contribution that each variable in decreasing order of the correlation coefficient cumulatively makes to the total variability of a sample. Variables that account for a large increment of diversity will be considered the more effective in predicting the population. The number of times that an effective variable apoears in each sample can be tallied to determine those as the best population predictors• There is a myriad of statistical "games" that can be experi mentally performed with archaeological data. Perhaps the most impor tant concerns the normality of survey data. A gross and preliminary analysis indicates that the frequencies for all values of the site type and locale variables assume the shape of a normal curve. More sophisticated techniq.ue-3 for the experimental resolution of this 175 problem are needed. Another "game" includes the comparative evaluation of sampling with and without replacement. Regarding the stratified scheme, it is possible to examine the relationship between the size and number of strata and the resulting differences (if any) in pre dictive qualities. It is also possible to combine stratified and cluster sampling so that clusters of nearly equal size are grouped in the same stratum. This scheme can probably be tested best with data from a Type I survey because of the immensity of the spatial popula tion. Survey data are a particularly profitable testing ground for the resolution of archaeo-statistical problems, because each sampling unit in two-dimensional space has an equal probability of being drawn. On the other hand, equal probability of all sampling units (or epsem according to Kish 1965s 20) is difficult to achieve in the threedimensional space of excavational research. The difficulty arises because overlying excavational units affect the probability of selec tion of underlying units. Alternatively, the archaeologist is faced with discarding non-selected units that overlie lower selected units. The question is whether the quantitative benefits of excavational sampling are worth the increased destruction of archaeological data. Field Research The regional perspective implemented in this dissertation can be used with any survey tactic in any part of the world. An archae ologist is essentially sampling from a spatial universe whether he is foot surveying, jeep surveying, or interviewing fanners and ranchers. 176 The procedure for sampling space must be given greater priority than the above traditionally conceived tactics for performing a survey. Thus, the methodological results of this experiment extend beyond the pedestrian tactic of the Paria Plateau survey. These same spatial considerations override environmental limitations, making the results of this experiment applicable beyond the Colorado Plateau subarea. The scheme used in Chapter 2 (see Methods) is suggested for conceptualizing a survey research program. The suggested sampling guidelines can be employed easiest where the survey area has been subdivided into spatial units of equal size. If the U.S.G.S. or an equivalent institution has not performed this service, it would probably be financially and technically diffi cult to accomplish. The perfect survey project should control the four sampling factors as suggested in Chapter U. The reliability of quantitative conclusions is weakened considerably when the preceding guidelines cannot be adopted. Back to the Starting Line This project began with a description of Lloyd's (1938) survey which employed the first repetition of the 0.f> fraction with the quarter-section. If the quarter-section were chosen on the same diagonal for all 33 sections, this scheme would conform to the TRU SYS scheme with i = 2 and a starting point of 1 or 2 (corresponding to either the northeast-southwest or the northwest-southeast diagonal). This combination of scheme, fraction, unit, and repetition is one of the worst population predictors according to the experimental results. 177 Changing the diagonal for each section would effectively transform the scheme to a simple random sampling. This change somewhat improves the predictive qualities of Lloyd's sample. However, a more accurate pre diction could be obtained by employing a CIAJS SIM scheme with the section as sampling unit at the 0.1+ fraction with the second repeti tion. APPENDIX A SAMPLING SUMMARY The computer-generated schemes that were described narratively in Chapter 3 are symbolically summarized in this Appendix. (The manually-selected samples ~ GRAB, VECT, CLUS, and Rfid -- cannot be summarized adequately by means of symbols, and the reader is referred to the appropriate sections of Chapter 3.) The formula(s) used to calculate the number of sampling units to be selected is designated by (a.), while (b.) indicates the formulas related to which particular sampling units in the frame are chosen. Symbols used in the formulas have the following meanings: S c Q * the number of quarter-sections in the total sample s.f. c i = the interval between selected sampling units in a frame j = the randomized starting point, i.e., the position of first sampling unit (that has to be randomly determined) on a frame. k = the arbitrary starting point, i.e., the position of first sampling unit (that is arbitrarily determined) on a frame. L = the number of locales in the spatial population, i.e., L = 8. q a q1 = the number of quarter-sections in a particular stratum which is given below: the number of sections in the total sample the sampling fraction for the total sample the number of quarter-sections drawn from within a particu lar stratum for a particular sampling fraction. 178 179 Strata 21 1 69 2 19 3 13 23 69 6 88 7 UO 8 20 I. SIM a. S = (70) x (s.f.) for S3M SEC Q • (3U1) x (s.f.) for SIM QSEC b. Randomly choose S or Q units as appropriate by means of RANF. II. SYS a. S = (70) x (s.f.) for SYS SEC Q - (3U1) x (s.f.) for SYS QSEC b. 1. subdivide the frame into seven or 3h groups of sections or quarter-sections respectively. 2. For every group of ten sampling units, choose (s.f. x 10) sampling units beginning with the unit where k = the number of the repetition. HI. TRU SYS a. S = (70) x (s.f.) for TRU SYS SEC Q - (3UD x (s.f.) for TRU SYS QSEC b. 1. TRU SYS SEC: Choose every i^h section starting with the jth unit (randomly determined) and stopping when S units have been drawn in accordance with the following schedule: 180 Maximum Value of j s»f« i 0.1 10 0.2 5 0.3 3 10 0.1* 2 16 o.5 1 36 0.6 1 29 0.7 1 22 0.8 1 15 0.9 1 8 10 2. TEU SYS QSEC: Choose every i^1 quarter-section starting with the unit (randomly determined) and stopping when Q units have been drawn in accordance with the following schedule: s.f. i . Maximum Value of J 0.1 10 10 0.2 5 5 0.3 3 38 0.1* 2 71 0.5 1 172 0.6 1 137 0.7 1 103 0.8 1 69 0.9 1 35 STRA.T DIS SIM a. Q a (3Ul) x (s.f.) No STRA.T scheme was tested with the section as sampling unit. b. 1. Stratify the frame into groups of quarter-sections in the same locale. 2. Randomly choose q quarter-sections from each locale by use of RA.NF in accordance with this schedule: 181 s.f. S Ji 0.1 ll 32 0.2 9 72 0.3 13 loh o.U 17 132 0.5 21 157 0.6 26 179 0.7 30 195 0.8 3k 211 0.9 38 227 For all s.f. greater than O.U, the full sections cannot be drawn because is less than q in some locales. The following formula generally determines £, despite arbitrary rounding to the nearest complete integer (in the above schedule): (s.f.) x (3Ul) q " L V. STRAT DIS SYS a. Q « (s.f.) x 3U1 b, 1. Stratify the frame as in IV b. 1. above. 2. Choose every i*'*1 quarter-section from each stratum where q' i « —> q (s.f.) x 3hl and L 1 < j -s: i. VI. STRAT PRO SIM a. Q = (3U1) x (s.f.) b. 1. Stratify the frame. 2. Randomly choose by means of RANF £ quarter-sections from each stratum where 182 q • (s.f.) x (q1) VII. STRAT PRO SYS a. Q » (3UD x (s.f.) b. 1. Stratify the frame. 2. Choose every i^ quarter-section from each stratum beginning with the jth unit making a total of £ units where •5 » q' q q = (s.f.) x (q), and APPENDIX B FINANCIAL AND STATISTICAL DATA The following is modified from Mueller, Staley, Harrison, Ralph, Sartwell, and Gauthier (1968). I« Actual survey costs - 1968 season A. Total Costs Salaries Student Crew (7 @ $200/raonth) $li,200 Field Archaeologist (l month) 300 Laboratory Technicians (2 @ 337.5>0/rnonth average) 675 Project Director (11 days @ $H£/day) U95 Administrator & ComotroLler (3 days each @ $f>0/day) 300 Subsistence Food (approximate average: $2.33>/man day) &0 Transportation Rental (2 four-wheel vehicles @ $22$/month) 900 Operation (2,620 mi. @ 10^/mile) 262 Other Insurance and Taxes (l% of salaries) 1*17 Supplies & Equipment (U3 Field days @ $10/day) h30 $8,529 Total Expenses 183 18U B. Unit Costs, Approximation $35/quarter-section (2U1 quarter-sections surveyed) R/W survey costs A. $ 35.00 per quartersection Total Costs Salaries Student Assistant (5 days @ $12/day) Supervisor (5 days @ $20/day) Administrator (2 hours/day @ $3/hour) $ 60.00 100.00 30.00 Subsistence 2 men Food (5 days @ $6/man-day) 60.00 Shelter (2 men, 3 nights @ $6/night) 36.00 Transportation (2E>0 mi. @ 10^/mile) 2£>.00 Other Supplies and Equipment (£ days @ $!?/day) 25.00 Insurance and Taxes (7% of Salaries) 13.30 Total B. Unit Costs, Approximation (25 mi. right-of-way) $31*9.30 $ 7.00 per rectangle APPENDIX C THE EXPERIMENTAL DATA The raw data generated by the experiment outlined in Chanter 3 are presented in this appendix. These data were tabulated, summarized, and ordered to constitute the experimental results of Chapter h. The six archaeological variables have been abbreviated in the following way in the fourth column belox*: Loc, locale; Typ, site type; Age, relative ceramic age; Unp, undecorated ceramics; Dec, decorated ceramics; and Lith, lithic function. The experimental data of the computer generated samples are listed in Tables 33 through U2. The data from the samples that were manually drawn are listed in Table U3. 185 186 Table 33. SIM QSBC Sampling Fraction Chi-square Analysis Chance Significant Variables Variables Number Wo. Name REP 1 0.1 0.2 0.3 o.h 0.5 0.6 0.7 0.8 0.9 5 5 I* 6 6 6 6 6 6 1 1 2 0 0 0 0 0 0 REP 2 0.1 0.2 0.3 o.l* 0.5. 0.6 0.7 0.8 0.9 6 5 6 6 6 5 6 6 6 0 1 0 0 0 1 0 0 0 0.1 0.2 0.3 5 5 5 o.l* 6 6 6 6 6 6 1 1 1 0 0 0 0 0 0 Loc Loc Loc Cost Economy Analysis Variance Economy $ 1,951.50 3,201.00 1*,1*33.50 5,61*9.00 6,81*7.50 8,065.00 9,229.25 10,376.50 11,506.75 3.59b 2.17U 2.681 2.573 2.661 3.010 2.1*71* 2.311* 2.635 $ 5U2.988 1,1*72.1*01 1,653.671* 2,226.61*6 2,570.650 2,6?l*.l*01 3,730.1*97 1*,1*81*.226 I*,366.888 1,951.50 3,201.00 1*,1*33.50 5,61*9.00 6,81*7.50 8,065.00 9,229.25 10,376.50 11,506.75 3.163 2.120 2.870 2.332 2.711 2.1*67 2.890 2.1*13 2.55U 616.977 1,509.905 1,5U1*.773 2,1*22.381* 2,525.820 3,269.152 3,193.512 It,300.21*8 1*,505.383 1,951.50 3,201.00 ii,U33.50 5,619.00 6,81*7.50 8,065.00 9,229.25 10,376.50 11,506.75 5.750 2.1*20 3.13U 3.229 2.1*99 2.569 2.536 2.817 2.613 339.391 1,322.929 1,1*11*.61*6 1,71*9.1*58 2,71*0.096 3,139.353 3,639.291* 3,683.528 1*,1*03.651* REP 3 0.5 0.6 0.7 0.8 0.9 Loc Loc Loc 187 Table 3U. Sampling Fraction Chi-square Analysis Chance Significant Variables Variables Number No. Name SIM SBC . Cost Economy Analysis Variance Economy REP 1 0.1 0.2 0.3 o.U 0.5 0.6 0.7 0.8 0.9 5 5 5 6 5 6 6 6 6 1 1 1 0 1 0 0 0 $ 1,728.00 2,757.00 3,772.00 Loc 5,760.00 6,733.00 7,692.00 8,637.00 9,568.00 55.619 30.8U1 35.533 2U.099 31.820 2U.1UU 27.1i87 26.3U3 27.3U6 1 1 1 1 1 1 0 0 0 Loc Loc Loc Loc Loc Loc 1,728.00 2,757.00 3,772.00 U,773.00 5,760.00 6,733.00 7,692.00 8,637.00 9,568.00 U7.952 31.297 25.8U8 22.508 20.U92 20,283 25.980 2U.290 25.8UU 36.036 88.091 1U5.930 212.057 281.085 331.952 296.073 355.578 373.703 1 1 1 1 0 1 0 0 0 Loc Loc Loc Loc 1,728.00 2,757.00 3,772.00 U,773.00 5,760.00 6,733.00 7,692.00 8,637.00 9,568.00 U3.619 U0.066 21.81U 29.591 29.398 28.107 29.916 26.597 2U.5U7 39.615 68.811 172.916 162.357 195.931 239.5U8 259.119 32U.735 389.782 Loc Loc Loc U,773.00 0 $ 3i.o6y 89.393 106.15U 198.058 181.018 278.868 279.81a 327.866 3U9.886 REP 2 0.1 0.2 0.3 O.U 0.5 0.6 0.7 0.8 0.9 5 5 5 5 5 5 6 6 6 ? 3 0.1 0.2 0.3 o.U 0.5 0.6 0.7 0.8 0.9 nr 5 5 5 6 5 6 6 6 Loc 188 Table 35. SYS QSEC. Sampling Fraction Chi-square Analysis Chance Significant Variables Variables Number No. Name Cost Economy Analysis Variance Economy REP 1 0.1 b 2 0.2 0.3 o.b 0.5 0.6 0.7 0.8 0.9 6 6 6 6 6 6 6 6 REP 2 0.1 0.2 0.3 o.b 0.5 0.6 0.7 0.8 0.9 Loc Typ $ 1,988.75 2.387 $ 833.158 0 0 0 0 0 0 0 0 3,238.00 b,b70.25 5,685.50 6,883.75 8,065.00 9,229.25 10,376.50 11,506.75 2.122 2.661 2M6 2.351 2.328 2.31*0 2.281 2.1*98 1,525.918 1,679.913 2,32lt.l.07 2,928.009 3,l*6U.3h7 3,91*1*.123 1*,51*9.101 U,606.385 6 6 6 6 6 6 6 6 6 0 0 0 0 0 0 0 0 0 1,951.50 3,201.00 U,1*33.50 5,6b9.00 6,81*7.50 8,029.00 9,193.^0 10,31*1.00 11,1*71.50 1.907 2.837 2.1*85 2.359 2.330 2.31*3 2.275 2.520 2.71U 1,023.335 1,128.30b 1,78b.10b 2,39b.658 2,938.8bl 3,b26.803 b,0bl.098 b,103.571 b,226.787 5 5 6 6 6 6 6 6 6 1 1 0 0 0 0 0 0 0 1,951.50 3,201.00 U,1*33.50 5,6UU.00 6,8b7.50 8,029.00 9,193.50 10,31*1.00 11,1*71.50 3.765 2.758 2.518 2.1*1*5 2.1*36 2.31*1 2.608 2.811 2.761 518.326 1,160.623 1,760.722 2,310.b29 2,810.960 3,h29.730 3,525.115 3,678.762 b,15b.835 REP 3 0.1 0.2 0.3 O.b 0.5 0.6 0.7 0.8 0.9 Loc Loc 189 Table 36. SYS SEC. Sampling Fraction REP 1 0.1 0.2 0.3 o.U 0.5 0.6 0.7 0.8 0.9 Chi-square Analysis Chance Significant Variables Variables Number No. Name 5 5 5 5 5 5 5 6 6 1 1 1 1 1 1 1 0 0 Loc Loc Loc Loc Loc Loc Loc 1 1 1 1 1 1 1 0 0 Loc Loc Loc Loc Loc Loc Loc 1 1 1 1 1 1 0 0 0 Loc Loc Loc Loc Loc Loc Cost Economy Analysis Variance Economy $ 1,728.00 2,757.00 3,772.00 9,773.00 5,760.00 6,733.00 7,692.00 8,637.00 9,568.00 18.619 21.659 27.062 2U.386 25.8U5 25.073 25.U39 23.56U 92.808 127.320 139.38U 195.727 222.867 268.535 302.370 358.515 U06.0U3 1,728.00 . 2,757.00 3,772.00 U,773.00 5,760.00 6,733.00 7,692.00 8,637.00 9,568.00 25.619 32.071 26.933 28.269 26.869 26.925 25.219 2U.U83 25.968 67.U50 85.965 1U0.051 168.8U2 21U.373 250.06U 305.008 352.775 368.U53 1,728.00 2,757.00 3,772.00 U,773.00 5,760.00 6,733.00 7,692.00 8,637.00 9,568.00 U3.286 28.951 29.662 27.U5U 27.597 25.3U5 2U.U85 26.258 25.132 39.920 95.229 127.166 173.85U 207.718 265.653 31U.151 328.928 380.709 2U.091 $ REP 2 0.1 0.2 0.3 o.U 0.5 0.6 0.7 0.8 0.9 5 5 5 5 5 5 5 6 6 REP 3 0.1 0.2 0.3 o.U 0.5 0.6 0.7 0.8 0.9 5 5 5 5 5 5 6 6 6 190 Table 37. TRU SYS QSEC. Sampling Fraction Chi-square Analysis Significant Chance Variables Variables Number No. Name Cost Economy Analysis Variance Economy REP 1 0.1 0.2 0.3 o.U 0.5 5 6 0 0 1 1 0 6 6 5 0.6 u 2 0.7 0.8 0.9 5 1 1 1 REP 2 0.1 0.2 0.3 5 5 o.U 0 0 0.5 U 1 1 6 6 2 0.6 3 3 0.7 0.8 0.9 5 5 5 1 1 1 REP 3 0.1 0.2 0.3 5 5 1 1 6 6 5 5 o.U 0.5 0 0 i 0.6 0.7 0.8 5 5 5 0.9 6 5 1 1 1 0 Loc All All Loc Typ Age Unp Dec Loc Age Loc Loc Loc Loc Loc All All Loc Unp Loc Unp Dec Loc Loc Loc Loc Loc All All Loc Typ Age Unp Dec Loc Loc Loc $ 1,951.50 3,201.00 U,U33.50 5,6U9.00 6,8U7.50 3.765 2.819 1.610 1.1*2$ 1.6U7 $ 518.326 1,135.509 2,753.726 3,96U.210 U,157.559 8,065.00 3.055 2,639.93U 9,229.25 10,376.50 11,506.75 2.961 2.868 2.718 3,116.936 3,618.026 k,233.535 1,951.50 3,201.00 U,h33.50 5,6UU.OO 6,897.50 3.765 2.973 1.59U 1.U20 2.175 518.326 1,076.690 2,781.367 3,978.160 3,171.26U 8,065.00 2.212 3,6U6.021 9,229.25 10,376.50 11,506.75 3.057 2.866 2.712 3,019.05U 3,620.551 U,233.535 1,951.50 3,201.00 U,U33.50 5,6U9.00 6,8U7.50 3.765 2.973 1.610 1.U20 1.656 518.336 1,076.690 2,753.726 3,978.160 U,13U.963 8,065.00 9,229.25 10,376.50 11,506.75 3.1U2 2.87U 2.868 2.760 2,566.836 3,211.290 3,618.026 U,169.112 191 Table 38. TRU SYS SBC Sampling Fraction Chl-square Analysis Chance Significant Variables Variables Number No. Name REP 1 0.1 5 1 0.2 0.3 o.U 5 0 3 1 6 3 o.5 U 2 0.6 0.7 0.8 0.9 5 5 5 6 1 1 1 0 0.1 0.2 0.3 5 6 U 1 0 2 o.U 3 3 0.5 0.6 0.7 0.8 0.9 5 5 5 5 5 1 1 1 1 1 5 6 0 3 1 0 6 3 0.5 3 3 0.6 0.7 5 0.8 0.9 5 1 1 1 6 0 Cost Economy Analysis Variance Economy Loc Loc All Loc Age Unp Loc TT Mn unp Loc Loc Loc $ 1,728.00 U3.286 2,757.00 3,772.00 U,773.00 27.65U 13.5U8 1U.078 $ 39.920 99.696 278.U17 339.039 5,760.00 19.005 303.078 6,733.00 7,692.00 8,637.00 9,568.00 28.U51 28.368 27.626 27.1U6 236.652 271.150 312.6U0 352.U6U Loc 1,728.00 2,757.00 3,772.00 U3.286 19.302 17.262 39.920 1U2.83U 218.51U U,773.00 15.090 316.302 5,760.00 6,733.00 7,692.00 8,637.00 9,568.00 31.055 29.668 28.625 26.600 27.2U0 185.U77 226.9UU 268.716 32U.699 351.2U8 1,728.00 2,757.00 3,772.00 U,773.00 U3.286 19.302 13.5U8 15.090 39.920 1U2.83U 278.U12 316.302 5,760.00 15.193 379.121 6,733.00 7,692.00 8,637.00 9,568.00 28.060 27.0U1 27.626 25.820 239.950 28U.U56 312.6U0 370.565 REP 2 Loc Unp Loc Typ Unp Loc Loc Loc Loc Loc REP 3 0.1 0.2 0.3 o.U • 5 Loc All Loc Typ Unp Loc Age Unp Loc Loc Loc 192 Table 39. STRA.T DIS SIM. Sampling Fraction Chi-square Analysis Chance Significant Variables Variables Number Name No. REP 1 0.1 0.2 0.3 o.U 0.5 0.6 0.7 0.8 0.9 Economy Analysis Cost Variance Economy 5 1 1 1 1 1 1 1 1 1 Loc Loc Loc Loc Loc Loc Loc Loc Loc $ 1,877.00 3,3U9.00 U,507.00 5,503.00 6,376.25 7,173.75 7,705.00 8,281.00 8,801.25 2.UU8 1.970 2.hU5 2.2U3 2.277 2.303 2.312 2.97U 2.693 $ 775.71*8 1,700.000 1,813.353 2,1*53.1*10 2,800.285 3,111*.958 3,332.612 2,78U.U65 3,258.195 REP 2 0.1 3 3 1,877.00 2.61*5 709.61*0 0.2 k 2 Loc Age Unp Loc 3,3i»U.OO 2.621* 1,276.295 5 5 5 5 5 5 5 5 Typ 0.3 o.U 0.5 0.6 0.7 0.8 0.9 REP 3 0.1 0.2 0.3 0.U 0.5 0.6 0.7 0.8 0.9 5 5 5 5 5 5 5 1 1 1 1 1 1 1 Loc Loc Loc Loc Loc Loc Loc 1;,507.00 5,503.00 6,376.25 7,173.75 7,705.00 8,281.00 8,801.25 3.120 2.782 2.053 2.766 2.326 2.1*30 2.909 1,978.073 3,105.820 2,593.51*6 3,312.553 3,1*07.818 3,025.52k 5 5 5 1 1 1 1 1 1 1 1 1 Loc Loc Loc Loc Loc Loc Loc Loc Loc 1,877.00 3,3U9.00 U,507.00 5,503.00 6,376.25 7,173.75 7,705.00 8,281.00 8,801.25 2.190 2.731 2.717 2.921 2.288 2.959 2.313 2.237 2.576 851.077 1,226.290 l,658.8Ui 1,883.9U3 2,786.822 2,U2U.383 3,331.171 3,701.832 3,1*06.631* 5 ' 5 5 5 5 5 l,UUw55l 193 Table 1*0. STRAT DIS SYS. Sampling Fraction Chi-square Analysis Chance Significant Variables Variables Number No. Name Cost Economy Analysis Variance Economy REP 1 0.1 0.2 0.3 0.1* 0.5 0.6 0.7 0.8 0.9 5 5 5 5 5 5 5 5 5 1 1 1 1 1 1 1 1 1 Loc Loc Loc Loc Loc Loc Loc Loc Loc $ 1,877.00 3,3U9.00 1*,507.00 5,503.00 6,376.25 7,173.75 7,705.00 8,281.00 8,801.00 U.531 3.770 3.239 2.1*20 2.068 2.1*91 2.577 2.538 2.181* $ 1*11*.257 888.328 1,391.1*78 2,273.966 3,083.293 2,879.867 2,989.910 3,262.805 1*,029.876 REP 2 0.1 0.2 0.3 o.U 0.5 0.6 0.7 0.8 0.9 5 5 5 5 5 5 5 5 5 1 1 1 1 1 1 1 1 1 Loc Loc Loc Loc Loc Loc Loc Loc Loc 1,877.00 3,3UU.00 14,507.00 5,503.00 6,376.25 7,173.75 7,705.00 8,281.00 8,801.25 1.886 3.033 2.560 2.326 3.352 2.1*65 2.577 2.1*01* 2.181* 995.227 1,101*.187 1,760.5U6 2,365.861* 1,902.222 2,910.21*3 2,989.910 3,1*3U.675 1*,029.876 REP 3 0.1 0.2 0.3 5 5 5 1 1 1 1 1 1 1 1 1 Loc Loc Loc Loc Loc Loc Loc Loc Loc 1,877.00 3,3U9.00 1*,507.00 5,503.00 6,376.25 7,173.75 7,705.00 3,281.00 8,801.25 3.25U 3.379 2.913 2.235 2.120 2.7U5 2.618 2.1*87 2.181* 576.828 1,991.121 1,51*7.202 2,1*63.192 3,007.665 2,613.387 2,91*3.086 3,329.711* 1*,029.876 o.l* 0.5 0.6 0.7 0.8 0.9 . 5 5 5 5 5 5 19U Table hi. STRAT PRO SIM. Sampling Fraction Chi-square Analysis Chance Significant Variables Variables Number No, Name REP 1 0.1 0.2 0.3 o.U 0.5 0.6 0.7 0.8 0.9 REP 2 0.1 0.2 0.3 O.U 0.5 0.6 0.7 0.8 0.9 REP 3 0.1 0.2 0.3 o.U 0.5 0.6 0.7 0.8 0.9 • 6 5 6 6 6 6 6 6 6 0 1 0 0 0 0 0 0 0 6 6 6 6 6 6 6 6 6 0 0 0 0 6 6 5 6 6 6 6 6 6 0 0 Unp 0 0 0 0 0 1 0 0 0 0 0 0 Dec Cost Economy Analysis Variance Economy $ 1,951.50 3,201.00 U,U33.50 5,6U9.00 6,8U7.50 8,029.00 9,193.50 10,3U1.00 11,U71.50 2.802 1.963 2.U09 3.018 2.865 2.70U 2.327 2.780 2.701 $ 6<?6.U66 1,951.50 3,201.00 U,U33.50 5,6U9.00 6,8U7.50 8,029.00 9,193.50 10,3U1.00 11,U71.50 2.315 2.5UU 2.111 2.586 2.256 2.70U 2.513 2.889 2.66U 81*2.980 1,258.25U 2,100.189 2,18U.U5U 3,035.239 2,959.301* 3,668.376 3,579.1*39 U,306.118 1,951.50 3,201.00 U,U33.50 5,6U9.00 6,8U7.50 8,029.00 9,193.50 10,3U1.00 11,U71.50 3.516 2.018 2.961 3.110 2.583 2.768 2.286 2.706 2.798 555.03U 1,081.053 1,1*97.298 1,816.398 2,650.987 2,900.650 Ix,021.653 3,821.507 U,099.892 1,630.667 1,81i0.390 1,871.769 2,390.0^2 2,959.30U 3,950.795 3,719.78k U,2U7.130 195 Table U2. STRAT PRO SYS. Sampling Fraction Chi-square Analysis Chance Significant Variables Variables Number No. Name Cost Economy Analysis Variance Economy REP 1 6 6 6 6 6 0.1 0.2 0.3 O.U 0.5 0.6 6 6 6 0.7 0.8 0.9 REP 2 0.1 6 6 6 6 0.2 0.3 o.U 0.5 0.6 0.7 0.8 0.9 5 5 6 6 6 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 2.837 $1,281*.726 1,11*1.990 1,889.812 1,831*.686 3,298.1*10 3,5U7.9l*5 3,361.1*25 3,510.183 li,0l*3.531 1,951.50 3,201.00 U,U33.50 5,6U9.00 6,3U7.50 8,029.00 9,193.50 10,3U1.00 11,U71.50 2.578 2.257 2.310 2.669 2.19U 2.21*2 2.735 2.9U6 2.837 756.982 1,1*18.251* 1,919.261* 2,116.523 3,121.011 3,581.177 3,361.1*25 3,510.183 U,01*3.531 1,951.50 3,201.00 U,U33.50 5,61*9.00 6,8U7.50 8,029.00 9,193.50 10,3U1.00 11,U71.50 U.807 2.512 2.3W* 2.786 2.157 2.263 2.735 2.91*6 2.837 1*05.970 l,27l*.283 1,891.1*21* 2,027.638 3,171*.51*7 3,5U7.9!*5 3,361.1*25 3,510.183 U, 01*3.531 $ 1,951.50 Loc Loc Loc 3,201.00 It,133.50 5,61*9.00 6,81*7.50 8,029.00 9,193.50 10,31*1.00 11,1*71.50 1.519 2.803 2.31+6 3.079 2.076 2.263 2.735 2.91*6 REP 3 0.1 0.2 0.3 o.U 0.5 0.6 0.7 0.8 0.9 6 6 5 • 6 6 5 6 6 6 0 0 1 0 0 1 0 0 0 Age Loc Table 1*3. Manually selected samples. Scheme Sampling Fraction Chi-square Analysis Chance Significant Variables Variables Number No. Name Cost Economy Analysis Variance Economy Miscellaneous Sampling Fractions CLUS SIM 1,1 CLUS SIM 1,2 .03 .05 6 1* 0 2 CLUS SIM 2,1 CLUS SIM 1,3 .05 .08 6 3 0 3 CLUS SIM 3,1 CLUS SIM 2,2 CLUS SIM l*,l CLUS SIM 2,3 CLUS SIM 3,2 CLUS SIM 6,1 CLUS SIM 7,1 CLUS SIM h,2 CLUS SIM 8,1 CLUS SIM 9,1 CLUS SIM 3,3 CLUS SIM 1*,3 CLUS SIM 6,2 CLUS SIM 7,2 CLUS SIM 8,2 CLUS SIM 9,2 CLUS SIM 6,3 CLUS SIM 10,2 CLUS SIM 12,2 CLUS SYS 12,2 .08 .1 .1 .15 .15 .15 .18 .2 .2 .221 .221* .3 .3 .35 .1* .1*1* .1*5 .1*6 .5 .5 5 6 6 5 6 5 6 6 5 6 5 5 6 6 5 6 6 6 6 5 1 0 0 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 0 1 Loc Unp Loc Typ Unp Loc Loc Loc Loc Loc Loc Loc Loc $ 91*5.75 1,206.50 .333 1.1*56 $ 2,81*0.090 828.61*0 1,206.50 1,U67.50 2.308 1,51*8 522.71:6 91*7.997 1,1*67.50,. 1,728.00 1,728.00 2,21*9.50 2,21*9.50 2,21*9.50 2,510.75 2,757.00 2,757.00 2,979.00 3,016.00 3,793.00 3,793.00 1*,286.50 ii,801.00 5,211.00 5,28U.OO 5,1x30.00 5,795.00 5,795.00 3,790 2.300 U.683 2.186 3.63k 2.160 1.907 U.210 2.882 2.361* 2.703 3.502 2.229 2.638 2.1:19 2.51U 2.81*1* 2.732 3.119 2.970 387.203 751.30U 368.991* 1,029.01*8 619.011* 1,01*1.1-35 1,316.596 651*.869 956.295 1,280.152 1,115.797 1,093.095 1,711.659 1,631*.905 1,981*.701* 2,072.792 1,857.91*6 1,987.551* 1,857.967 1,951.178 Table U3. Manually selected samples—Continued Sampling Fraction Scheme CLUS CLUS CLUS CLUS CLUS CLUS SIM 7,3 SIM 8,3 SIM 9,3 SIM 10,3 SIM 12,3 SYS 12,3 .52 .59 .66 .70 .75 .75 Chi-square Analysis Chance Significant Variables Variables Number No. Name 5 6 6 6 6 6 Loproximation to Ideal Sampling Fraction 1/10 CLUS SYS 1/3 .085 5 6 CLUS SIM 5,1 .103 CLUS SIM 10,1 6 .191 CUJS SIM 5,2 .205 5 • CLUS SIM 5,3 6 .308 CLUS SIM 11,3 6 .598 6/10 CLUS SIM 3A 6 .598 CLUS SIM 12,1 6 .205 CLUS SYS 12,1 6 .205 1/10 CLUS SIM 1/h .1 5 1/10 CLUS SYS lA .1 U Economy Analysis Variance Economy 1 0 0 0 0 0 Loc $6,050.50 7,028.75 7,1*27.50 7,705.00 8,21*5.00 8,21*5.00 1 0 0 1 0 0 0 0 0 1 2 Loc 1,765.25 1,988.75 3,090.00 3,275.00 1*,51*3.75 8,029.00 8,029.00 3,275.00 3,275.00 1,951.50 1,951.50 3.857 2.718 2.595 2.852 • 3.183 2.606 3.021* 2.01*1 2.511 3.319 lw810 3,201.00 l*.l83 765.2U0 3,201.00 1,1*33.50 5,61*9.00 5,61,9.00 6,817.50 2.1*87 1.936 3.528 2.813 2.1*52 1,287.092 2,290.030 1,601.190 2,008.176 2,792.618 2/10 CLUS SIM 1/2 .2 U 2 CLUS SIM 2/10 CLUS SIM U/10 CLUS SIM CLUS SIM 5/10 CLUS SIM .2 .3 .U .U .5 6 5 6 6 5 0 1 0 0 1 11,1 1/2 1/2 11,2 3/h Cost Loc Loc Loc Unp Loc Typ Loc Loc 2.508 2.775 2.213 2.539 3.118 2.655 $ 2,1*12.1*80 2,532.882 3,356.303 3,03h.659 2,61*1*.323 3,105.1*61 h57.67U 731.696 1,190.751 I,lli8.3l6 1,1*27.505 3,080.966 2,655.092 1,611:.051 1,31k.261 587.978 U05.717 Table U3. Manually selected samples—Continued Scheme Sampling Fraction Chi-square Analysis Chance Significant Variables Variables Number No. Name Cost Variance $1,917.50 1,227.60 2,1*55.20 3,lii0.20 266.00 172.20 269.50 371.00 336.00 3.993 Economy Other Schemes GRAB 1/10 VECT SUP 2/10 VECT SUP 1/10 VECT STRAT VAL RA/ RIM R/W SINK R/W 2 SAND R/W 1 SAND R/W 2 0.10 0.092 0.181* 0.1 o.oih 0.009 O.Olli 0.019 0.018 5 6 6 5 6 5 5 6 1 0 0 1 1 0 1 1 0 Loc Loc Loc Loc Loc M3 •3bh .389 0.188 2.358 0.171 0.206 0.U03 $ 1^80.215 2,771.173 7,137.209 8,072.1(93 1,U1U.893 73.027 1,576.023 1,800.970 83U.7U6 VO Q3 LIST OF REFERENCES AIKENS, C. MELVIN 1966 Virgin-Kayenta Cultural Relationships. University of Utah Anthropological Papers, No. 79. Salt Lake City. BERRY, B. J. L. 1962 Sampling, Coding and Storing Flood Plain Data. United States Department of Agriculture, Farm Economic Division Agriculture Handbook, No. 237. Washington, D.C. BINFORD, LEWIS B. 196U A Consideration of Archaeological Research Design. 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