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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:""
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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
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Petrograph
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Isolated features
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Modified Rockshelters
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Pithouses
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Small Pueblos
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Medium Pueblos
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Large Pueblos
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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*
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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
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