Analysis of intelligence and academic scores as a Noncommissioned Officers.

Analysis of intelligence and academic scores as a Noncommissioned Officers.
Calhoun: The NPS Institutional Archive
Theses and Dissertations
Thesis Collection
1987
Analysis of intelligence and academic scores as a
predictor of promotion rate for U.S. Army
Noncommissioned Officers.
Warner, Jerry B.
http://hdl.handle.net/10945/22191
B^CHT^
NAVAL POSTGBAl^O
NAVAL POSTGRADUATE SCHOOL
Monterey, California
THESIS
ANALYSIS OF INTELLIGENCE AND ACADEMIC SCORES
AS A PREDICTOR OF PROMOTION RATE
FOR U. S. ARMY NONCOMMISSIONED OFFICERS
|
by
Jerry B. Warner
June 1987
Thesis Advisor:
P.
A.
W.
Lewis
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v.^a unciud, sec.nr, Cis^.f,c.t,on)
^f^^ygiS OF INTELLIGENCE AND ACADEMIC SCORES AS A
PREDICTOR OF PROMOTION RATE FOR U.S. ARMY NONCOMMISSIONED OFFICERS.
PERSONAL AuThOR(S)
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This thesis systematically and comprehensively analyzes available
personnel data to determine if a significant relationship exists between
measures of intelligence and academic performance, and career promotion
Forty thousand Noncommissioned Officer
rate for Noncomiaissioned Officers.
this, using three approaches.
determine
(NCO) records were analyzed to
procedure which progressed from
sequential
The first approach was a
regression models.
multivariate
through
analysis of individual variable
scored in the top
who
of
analysis
NCO
s
The second approach focused on
more advanced
used
approach
third
The
three percent of promotion rate.
and
components
principal
of
the
use
statistical techniques, including
explanatory
influential
most
to better identify the
factor analysis,
variables.
(Continued)
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P. A.
W.
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MAR
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Lewis
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ABSTRACT SE.CyRlTY CLASSIFICATION
Unclassified
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Block 19.
(Continued)
ABSTRACT
During the analysis, eight measures of intelligence and
academic ability were used as explanatory variables.
Four
control variables were included in the analysis to discriminate
between subcategories of NCO's.
They were: sex, career field,
race, and paygrade.
Throughout the analysis consideration of Army promotion and
accession policy was included. Knowledge of these policies
resulted in elimination of some special groups which had
received promotions under significantly different conditions
than the rest of the sample. An example of this was Reserve
and National Guard members called to active duty.
This study found that there was significnat statistical
evidence to show that a high level of Armed Forces Qualification
Test (AFQT) score and prior service academic accomplishment will
correspond to a higher promotion rate.
Also, in-service
measures of NCO education and performance testing were good
indicators of promotion rate.
However, there was significant variance associated with the
explanatory relationship. As a result, a useful predictive
model could not be designed using regression methods. Although
the model could predict promotion averages for major population
subcategories, it was unreliable when used solely with the AFQT
variable.
The findings of this study suggest two policy recommendations.
The first recommendation was a confirmation of the
constraints placed on AFQT category and high school diploma
status by the 1984 Defense Authorizations Act. The second
recomiTiendation was to require promotion boards to consider NCO
schooling level and performance test scores in their proceedings,
but to avoid directly tying either score to promotion, in terms
of a minimum quota or scaled promotion point scale.
Finally, a suggestion was given for further research to
investigate the underlying reasons for different attrition
patterns observed among racial and ethnic groups.
S
N 0102-
LF-
014- 6601
SeCUNITY CUAtllFICATlON OF THIS PAOEfWhtn Dmia Bnffd)
Approved for public release:
distribution unlimited
Analysis of Intelligence and Academic Scores
as a Predictor of Promotion Rate
for U.S. Army Noncommissioned Officers
by
Jerry B. Warner
Captain, United States Army
B.S., United States Military Academy, 1976
Submitted in partial fulfillment of the
requirements for the degree of
MASTER OF SCIENCE IN OPERATIONS RESEARCH
from the
NAVAL POSTGRADUATE SCHOOL
June 1987
.
ABSTRACT
This thesis systematically and comprehensively analyzes
available personnel data to determine if a significant
relationship exists between measures of intelligence and
promotion rate for
career
and
performance,
academic
Forty thousand Noncommissioned
Noncommissioned Officers.
records were analyzed to determine this, using
Officer (NCO)
three approaches
The first approach was a sequential procedure which
progressed from analysis of individual variables through
The second approach focused
multivariate regression models.
of NCO's
who scored in the top three percent of
on analysis
The third approach used more advanced
promotion rate.
including the use of principal
statistical techniques,
identify the most
components and factor analysis,
to better
influential explanatory variables.
During the analysis, eight measures of intelligence and
Four
academic ability were used as explanatory variables.
variables
were
included
in
the analysis to
control
discriminate between subcategories of NCO's.
They were:
sex, career field, race, and paygrade.
Throughout the analysis consideration of Army promotion
Knowledge of these
and accession policy was included.
policies resulted in elimination of some special groups which
had received
promotions
significantly different
under
conditions than the rest of the sample.
An example of this
was Reserve and National Guard members called to active duty.
This study found that there was significant statistical
evidence to show that a high
Armed Forces
level of
Qualification Test
(AFQT)
score and prior service academic
accomplishment will correspond to a higher promotion rate.
Also, in-service measures of NCO education and performance
testing were good indicators of promotion rate.
However, there was significant variance associated with
the explanatory relationship.
useful
As
a
result,
a
predictive model could not be designed using regression
methods
Although the model could predict promotion averages
for major population subcategories, it was unreliable when
used solely with the AFQT variable.
The findings
two policy
of
this
study
suggest
recommendations.
The first recommendation was a confirmation
of the constraints placed on AFQT category and high school
diploma status by the 1984 Defense Authorizations Act.
The
second recommendation was to require promotion boards to
consider NCO schooling level and performance test scores in
their procedings, but to avoid directly tying either score to
promotion, in terms of a minimum quota or scaled promotion
point scale.
Finally, a suggestion was given for further research to
investigate the underlying reasons for different attrition
patterns observed among racial and ethnic groups.
.
..
.
TABLE OF CONTENTS
Page
I.
INTRODUCTION
A.
BACKGROUND
11
B.
PURPOSE
12
C.
ORGANIZATION
12
D.
PRELIMINARY INFORMATION
13
E
II.
III.
IV.
11
1
Intelligence Test Scores
14
2
Academic Scores
17
3
Promotion Scores
17
4.
Analytical Tools Used
19
SUMMARY
20
REVIEW OF PREVIOUS STUDIES
22
OVERVIEW OF THE DATA
29
A.
INTRODUCTION
29
B.
DESCRIPTION OF VARIABLES
30
C
PREPARATION OF THE DATA
31
D.
COMPARISON TO TOTAL ARMY STATISTICS
33
SUCCESSIVE DATA ANALYSIS
37
A.
INTRODUCTION
37
B.
UNIVARIATE ANALYSIS
38
C.
BIVARIATE ANALYSIS
58
D.
1.
Correlation Matrix
59
2.
Paired Scatterplots and Simple Regression
65
3.
3-D Empirical Density Plots
70
MULTIVARIATE GRAPHICAL ANALYSIS
72
5
..
.
E.
.
LINEAR MODELS
1
Analysis of Variance
74
2
ANCOVA
83
3.
The Final Model:
V.
VII.
Multiple Regression... 87
87
b.
Results
89
c
Interpetation
92
d.
Checking Assumptions
95
e.
Confirmation of Regression Findings... 96
f
Testing the Model
g.
Summary of Regression Analysis
.
SUMMARY OF FINDINGS
98
100
101
ANALYSIS OF TOP PERFORMERS
102
A.
INTRODUCTION
102
B.
COMPARISON OF MEANS AND VARIANCE
103
C.
SIGNIFICANCE TESTING
104
D.
ANALYSIS OF DISTRIBUTIONS
106
E.
VI.
A
Background
a
E.
74
SUMMARY OF FINDINGS
119
PRINCIPAL COMPONENTS AND FACTOR ANALYSIS
Ill
A.
INTRODUCTION
Ill
B
THEORY
Ill
C.
RESULTS
113
D.
SUMMARY OF FINDINGS
119
CONCLUSION
120
A.
OVERALL FINDINGS
120
B.
POLICY RECOMMENDATIONS
123
6
.
C.
SUGGESTIONS FOR FURTHER RESEARCH
APPENDIX A
CAREER MANAGEMENT FIELDS AND FREQUENCIES
APPENDIX B
AFQT TRANSFORMATION EQUIVALENT SCORES
124
.
126
127
LIST OF REFERENCES
128
INITIAL DISTRIBUTION LIST
130
7
.
LIST OF TABLES
I
II.
III.
Summary of Variables in Sample
30
Total Army vs. Sample Summary Statistics
34
Comparison of PRA vs Standard Normal Percentiles
..
44
Sample Race Percentages
46
Sample Paygrade Percentages
46
Sample Mental Category Percentages
50
Sample Highest Year of Education Percentages
52
Sample Education Level Percentages
52
IX.
Sample NCO Schooling Percentages
54
X.
Pearson Correlation Coefficients
62
IV
.
V.
VI
.
VII.
VIII
.
XI
.
Most Significant Correlated Variables
64
XII
.
Simple Least Squares Summary Data
69
One-way ANOVA Summary
76
Seven-Way ANOVA with Interaction Summary
81
ANCOVA with Interaction Summary
85
Regression Results
91
Net Possible Change by Explanatory
93
Sensitivity of PRA to Explanatory Variables
94
Comparison of Regression Data Sets
96
Comparison of Extreme and Average Predictions
98
XIII.
XIV.
XV.
XVI
.
XVII.
XVIII.
IXX.
XX.
XXI.
XXI
I
.
XXIII.
XXIV.
XXV.
Comparison of Predicted vs Actual PRA Averages
... 109
Top vs Sample Summary Data
103
Top vs Sample Hypothesis Test Results
105
Principal Component Tabular Results
114
Reduced Principal Component Tabular Results
117
8
LIST OF FIGURES
3.1
Army versus Sample Paygrade Bar Chart
35
3.2
Army versus Sample Race Bar Chart
35
4.1
Raw Promotion Rate Histogram and Statistics
40
4.2
Variable RATE Histogram and Statistics
42
4.3
Variable PRA Histogram and Statistics
43
4.4
Variable CMF Histogram and Percentages
45
4.5
Variable GTSCR Histogram and Statistics
47
4.6
Variable AFQTP Histogram and Statistics
59
4.7
Variable OAFQTP Histogram and Statistics
50
4.8
Variable EIMCAT Bar Chart of Percentages
51
4.9
Variables EDLVL and HIYRED Cluster Bar Chart.... 53
4.10
Variable NCOE Bar Chart
55
4.11
Variable PQSCR Histogram and Statistics
56
4.12
Lowess Scatter Plot of OAFQTP versus PRA
67
4.13
Lowess Scatter Plot of HIYRED versus RATE
67
4.14
3-D Empirical Density Plot of OAFQTP by PAYGD...72
4.15
3-D Empirical Density Plot of OAFQTP by RACETH..72
4.16
Coded Scatter
Plot of PRA versus CMF with SEX.. 73
X-Y Line Plot of ANOVA MEANS
78
4.18
Regression Residual Histogram
95
4.19
Regression Residual Scatter Plot
95
5.1
Cluster Bar Chart TOP vs Sample CMF Changes .... 107
5.2
Comparative Histograms of TOP vs Sample NCOE ..107
5.3
Comparative Histograms of TOP vs Sample PAYGD..108
4
.
17
6
.
1
Factor Plot
115
6
.
2
Factor Plot Reduced Variables
118
10
.
I
A.
INTRODUCTION
.
BACKGROUND
In almost any organization,
one hopes that individuals at
high levels of authority are gifted with higher
intelligence.
equal
Correspondingly, one
effort, a
work:
more
than average
would think that, given
intelligent
person
will advance
more rapidly than his contemporaries in an organization.
difficult,
not
is
It
however,
contradict our perceptions of
career advancement.
individual who
the
to find examples which
role
intelligence in
of
In almost any field one can remember an
was not
the most
intellectually gifted, but
through hard work and persistence, or other less quantifiable
advanced equally or
traits,
measured
better
There
ability.
mental
influences to overwhelm the value of
in the
eyes of
superior.
a
ample room for other
a
person's intelligence
An unattractive personality,
the tasks
an
at hand,
can discredit the merit of raw
other flaws
myriad of
a
of higher
is
intelligence to
inability to apply that
and
persons
than
intelligence
intelligence impacts
The degree at which
lies in
and
on advancement
of complex interaction between individuals
the area
organizations.
carries
It
with
it
much
of
the
uncertainty of quantification of human performance.
Despite
general
ample
reward
for
room
exceptions,
for
being
more
11
the
intelligent
concept of
still
a
seems
It may be,
reasonable.
looking at
manifestation requires
as possible.
large
a
numerically
large
number of people
It is the task of this thesis
fairly restricted,
The population is one
population.
which has had fundamental raw statistics
uniformly obtained/
promote personnel are unambiguous and
policies to
and where
see its
set of opportunities
to investigate this relationship within a
but
clearly
to
similar a
who have been affected by as
for advancement
that
however,
well documented.
B.
PURPOSE
The
purpose
question:
measures
of
Does
of
individual's
a
this
thesis
promotion
academic
and
rate
to
answer
a
central
relationship exist between
significant
intelligence
is
as
a
ability,
and
an
Noncommissioned Officer?
Put more simply, does being smarter,
as measured
by initial
test scores, or being better schooled, indicate that a person
will perform better and, hence, advance more quickly than his
peers?
The
answer
to
for Army policies of
this question has important implications
recruitment, retention,
and promotion.
It is also a matter of general interest to social scientists.
C.
ORGANIZATION
This thesis is organized fundamentally as a data analysis
investigation.
Chapters
and
I
II
provide
preliminary
information on the nature of the study variables, and briefly
12
review some related articles which have addressed this topic.
The remaining chapters discuss the analysis
forty-thousand
Noncommissioned
three related approaches.
procedure
standard
Officer
The
first
experimental
of
of approximately
(NCO)
approach
data
a
fairly
analysis.
This
procedure begins with analysis
of fundamental
individual
advances
increases
variables,
then
dimensionality
in
approach views
records using
is
attributes of
successive
through
complexity.
and
The second
subset of the population which distinguishes
a
itself by being in the top three percent of the NCO promotion
rates.
Comparison of
these top performers to the remainder
of the population identifies attributes which are found to be
significantly
associated
different,
cause
and
possibly
are
advancement.
rapid
for
hence,
In
an
third
the
approach, the statistical methods of principal components and
factor analysis are used to provide an alternative
critical variable
selection, as
method of
well as to lend credibility
to the results of the other two approaches.
D.
PRELIMINARY INFORMATION
This section contains
nature
of
data,
the
promotion system, and
in this
of
thesis.
looseness
intelligence
in
and
general
a
a
initial
an
discussion
of the Army NCO
overview
synopsis of the analytical tools used
As previously mentioned,
the
about the
effectiveness
academic
phenomena in Army promotion
data,
policy.
13
there is
of
a
degree
measurement
for
and also some confounding
Early
recognition of
.
should
problems
these
set
the
degree of caution which is
needed in reviewing the subsequent chapters of analysis.
analytical tools is intended to inform the reader
section on
of
conditions
the
The
under
which
analysis
data
the
was
conducted, and the hardware and software used.
1
Intelligence Test Scores
.
General
a.
for intelligence test scores falls into
The data
the category sometimes referred to as Defined Measurement.
Measurement
Defined
one
is
where
the
considered cannot be measured directly CRef
.
result,
actual
the
property.
a
In
this
intellectual
for
surrounded by controversy.
entire books
topic of
Army is the
6]
As a
:p.
case,
property
the
is
particular battery of tests.
The efficacy of intelligence
measure
being
the presumed related measurements are test
intelligence, and
scores from
1
property
is substituted for measurement of
related measure
a
.
A
ability
This
as
is
a
representative
itself
controversy
and studies.
Forces
Armed
tests
Vocational
an
issue
been the
has
The testing done by the
Aptitude
Battery, or
ASVAB.
Although not designed specifically as an intelligence
test,
the
Additional
ASVAB
research
does
has
predict
shown
verbal portions of the ASVAB have
ACT,
PSAT,
and
SAT
that
general
the
a high
trainability
mathematical and
correlation to the
college entrance examinations
The ASVAB has been studied,
.
C
Ref
.
2]
improved, and used for over forty
14
"
:
years.
recent
A
Measurement
and
article
by
Jensen
Evaluation
in
Counseling and Development
[Ref
3:p.
35],
in
,
states
"To the degree that success in various occupations and
training programs requires different levels of general
ability
(often called intelligence or
IQ),
an ASVAB
composite (it hardly matters which one) will be as
validly predictive as any test now on the market.
It
seems that the new ASVAB-14 is near the limit of
refinement, psychometrically
.
.
.
Generally
then,
established aptitude
is
determine
candidates,
academic
have shown themselves to
well
a
Although the
test.
specifically attempt to
potential
ASVAB
the
documented and
military does not
intelligence
the
portions
be reasonably
of its
of the ASVAB test
defined measurements
of intelligence.
Specific Tests.
b.
The ASVAB
consists of
a
battery of ten subtests.
Composites of the subtests of the ASVAB are used to determine
the
overall
acceptability
enlistment, and for which
intelligence
are
field
This score
the word
he
individual
she
or
requesting
would
best be
is the
Armed Forces
measures
aggregate
as
is the GT,
of
or general intelligence
aggregation of
knowledge^ paragraph
reasoning.
considers
taken
The first
intelligence.
score.
an
From the entire battery of tests, two derived scores
suited.
of
of
three submodules,
comprehension/ and arithmetic
The second derived measure of intelligence is the
Qualification Test
four
submodules,
15
Score, or AFQT
word
.
knowledge,
This score
paragraph
arithmetic
comprehension,
operations [Ref
.
reported
as
reasoning
10:sec 1-0,
.
An
1]
p.
numerical
and
AFQT
score is
percentile score representing the examinee's
a
relative standing in reference to
a
specific population.
There has recently been some additional
the reference population
In October of 1984,
the AFQT score.
manipulation of
for assignment of an individual's AFQT percentile was shifted
from
a
base reference population of 1944 to that of 1980.
base reference population is
represent
how
youth population would be
was
originally
until
percentiles.
Manpower
prior
Data
Department of the Army
the
1980
was
(DMDC),
listing
test scores,
have not been manipulated.
the case with
AFQT
retake
tests
their
score,
to
soldiers
increase
and
AFQT
effected
by the
all subsequent
based on
AFQT
percentile
the sum
of the raw
for
expressed as
which are
base
1980
been computed
transformations can be found in APPENDIX
GT scores,
of values
test percentiles for
of
records have
A
the
1980
to
Center
reference.
designed to
This set
utilized
transformation
A
values
and had not been updated
1944,
in
thesis
soldiers who enlisted
Defense
distributed.
designed
This
1980.
of
scores of the entire American
AFQT
raw
the
set
a
A
A.
However, unlike the
have
been
allowed to
their original GT scores.
Retesting was introduced in 1982 when
a
minimum
GT score of
120 was enforced on eligibility for promotion to NCO rank.
16
.
.
2
Academic Scores
General
a.
The
defined
data
used
measurement,
intelligence.
academic
for
similar
ability is also
measures
the
to
years
value
This
the number of
independent of the quality of
is
education, and the grades that any given individual
through
indicative of
may have
assumes that continued attendance and
This study
progression
for
Specifically, the property of academic ability
is being represented by a simple assignment of
received.
a
educational
the
academic ability.
system
For example,
is inherently
a
high school
graduate has more academic ability than an individual with an
eighth grade
education.
The informational value of academic
It
is treated in
used
in the study:
scores is thus, not as useful as desired.
analysis as only an ordinal scaled variable.
Specific
b.
Three
present education
Army, and
scores
academic
education
level,
schooling
individuals who
is
made
entry into
Because advanced
available
only
to
those
service records, the military
have superior
education score carries with
upon
level
since entry.
military education
professional
are
additional information
it some
relative to the performance of the NCO.
3
Promotion Scores
Promotion within the Army is
somewhat complicated procedure.
17
It
a
closely supervised and
is
the
product
of a
.
number
considerable
policies
of
applied across the population.
within
rank
function
of
computation
which
Instead,
structure,
within
years
education.
of
of
career
individual's
an
not uniformly
are
they
are applied
field, or even as a
although
Thus,
promotion
the
rate is an easy
task, that value may have been influenced by several policies
that were peculiar to the individual,
General
a.
Promotion of NCO's is governed by Army Regulatic
AR 600-200.
This
eligibility,
and
establishes
regulation
outlines
process
the
requirements for
of selection.
system views the individual's performance as
includes
a
composite
score
based
on
a whole.
The
This
performance scores,
commander's ratings, service awards, and review by a board of
senior
composite
This
NCO's.
threshold value for the
promoting individuals
point value is used as
Department of
The
management field,
and as
to use when
next higher paygrade, as slots
to the
become available.
the Army
a
slots
are
accounted
for
by career
minimum threshold for
a
combat soldier to be promoted may be different than that of
a
support soldier.
A
such, the
general observation is that career fields
with more technical orientation
have higher
thresholds,
longer
and
subsequently,
promotion point
times to advancement
than those in the larger and less technically oriented career
fields
AR 600-200
also sets minimum times of service and grade
18
which an individual must have
promotion.
Unless
shortest period
four years
served
superceded
for promotion
to
by
a
considered for
be
special
is two
to E-5
policy, the
years,
and is
This rate includes waivers for both time
to E-6.
in service and time in grade.
Promotion to E-6 in four years
requires that the individual be advanced to E-5 in two years.
Specific
b.
Because of the lack
within
the
army
considerable care
population,
to
uniformity
of
this thesis we have taken
in
identify
address discontinuities
and
which would confound promotion based on merit.
the elimination of some
data,
and
the computation
manipulation or restriction of data was
which
in
point in the rank
advancement
discusses
in
structure, and
detail
of three
to produce
a
sample
individual started from the same
each
had equal
opportunity for
Chapter III, Overview of the Data,
merit.
by
This includes
The governing principle for
different promotion rate scores.
population
of promotion
identified
the
problems
and
what
corrective action was taken.
4
.
Analytical Tools Used
This
section
briefly
identifies
the
hardware and
software used in analysis.
a.
Hardware
Computational
included an
IBM 3033
MVS batch system.
resources
System 370
used
for
mainframe computer running
Additionally, analysis was done
19
analysis
for small
data sets using a standard IBM microcomputer.
b.
Software
packages were used for the majority
Two software
of the data analysis.
resulting in
for analysis
components
Version
SAS
tabular output, such as principal
analysis
factor
and
was used predominantly
5
.[
Ref
Graf stat
4,5]
.
an
mainframe data analysis and plotting program,
unreleased IBM
was utilized for analysis requiring graphical
confirmation of SAS tabular results [Ref
.
E.
-
.
output and for
6,7]
SUMMARY
The objective of this introduction has been to adequately
frame the scope
the
of
topic,
and
present sufficient
to
background to the reader so that he or she is alerted to some
of the difficulties
Also,
this
inherent
will establish
a
in
topic
a
of
this nature.
reference for some of the tools
used to conduct the analysis.
The length of this section is indicative of the degree of
preparation
relationship which has
to
analyze
a
significant complications
in both
dependent and independent
variables.
stripping of
reality of
required
Although
aberrant
such a
the
data
list
makes
assumptions
of
one
cautious
and
the
about the
study, each event should be considered on
its ability to uncover the answer to the
central question of
this thesis.
The central question again is, whether or not a
significant
relationship
intelligence
and
academic
exists
ability,
20
measures
between
and
an
of
individual's
promotion rate as
to
learn
whether
ability are
and if
a
so,
Noncommissioned Officer.
measures
of
It is
important
and
academic
intelligence
important indicators
of promotion
how strong that relationship is.
in the army,
If sufficiently
reliable and believable relationships can be determined, then
policies
could
to better identify and develop
designed
be
capable individuals for positions of leadership.
The
analysis
confounding
policies,
accession programs.
size, which
this
of
such
thesis
reduced
the
effects of
as discriminatory promotion and
It also used a sufficiently large sample
allowed the averages to outweigh the exceptions.
It drew on data from standard personnel records,
most effective use of that information.
21
and made the
.
topic
The
REVIEW OF PREVIOUS STUDIES
A
II.
intelligence
relating
of
to some aspect of
performance is an extensive and rich area of study.
topic
particular
interest
of
military manpower specialists.
quantity
done
work
of
scientists
and
demonstration
of the
simple
cross-
area,
a
and performance
test
237 citations from the Lockheed's DIALOG
list of
information
online
this
a
intelligence
referencing of the words
produced a
As
in
social
to
It is a
Restriction
files.
those
of
available
references
to
utilizing
military
intelligence test
scores and
statistical analysis
of those
tests relative to
some performance
methodologies.
commercial
a
analysis, a
analytical
institution making use of
there
source of
The
from an in-house military
by
results in a large number of
Within this restriction
citations.
study
measure still
a
is
study can originate
contracted study done
institute,
military
variety of
a
data
or
as
an
its
academic
media for
analysis
The nature
data is also varied.
of the
readministered the ASVAB tests to
other
studies
addition
to
used
the
relationship had
Examples of
IQ
ASVAB.
a
Several studies
selected test population,
other intelligence measures in
and
The
performance
side
of
the
an extensive number of dependent variables.
performance measures
22
were:
results of written
.
military
examS/
skills
test results, minority advancement,
and comparison to collegiate ACT, PSAT, and SAT tests.
This
chapter
will
review
four
the
of
most closely
related studies, concentrating for each one on:
1.
The objective of the study.
2.
The methodology used in analysis.
3.
The conclusion reached.
first
The
AFQT
and
analysis
Military
essentially an
from Are Smart Tankers Better?
is
Productivity
[
Ref
.
8]
This
study is
in-house military analysis, the authors being
Army officers assigned to the Office of Economic and Manpower
Analysis,
at
West
Point,
New
York.
As described in the
title, the paper presents the results of an
which
the
crews
of
tanks
were scored on their ability to
destroy targets on live fire ranges.
gunner
and
commander
tank
was
a
The
AFQT score
of the
one of several explanatory
variables, having the tank scores as
The analysis methodology used
investigation in
the dependent variable.
log-log production model with
ordinary least squares regression.
The result of their analysis is best summarized
in this
paragraph from the study:
statistically
positive,
a
exists
there
"That
significant relationship between AFQT and performance, is
result.
The coefficients on the model means
a powerful
that if we move, for example, from the AFQT score for an
average Category IV TC to the AFQT score for an average
(a 200% increase), we will increase the
Category IIIA TC
(the tank scoring exercise) by
performance on Table 8
approximately 20.3%."
,
23
.
In this study then,
regression,
AFQT was found, by means of least squares
have
to
relationship to
definitive
a
well-
a
defined skill measure, the conduct of tank firing.
The second study is an analysis done at the University of
Iowa
Research
Cada
the
by
Success in Training for
report uses the ASVAB
success
recruits
of
primarily regression;
concentrates
performed
6
and 7 .[Ref 9]
each
variable for
of the regression
differences
score
This
The methodology used is
implicit
for
Marine Corps
the scope
however,
sex
Females;
an explanatory
training.
in
On Predicting
Forms
score as
The
the
of
regressions
and
identifying
on
female performance.
discussion
Males
and ASVAB
Clerical Specialties
titled:
Group
between
result
the study's
in
differences
category
male and
that
is
was
the
useful
of
predictive value.
An
interesting note about this study was
that the inclusion
of
high
difference
between
school
male
the
completion
reduces the
female
regression
of articles
used in the
and
coefficients
The third
Report to
study is
a
section
the House and Senate Committess on Armed Services,
Defense Manpower Quality, Volume II, Army Submission
[Ref
.
10]
.
The section of interest to this thesis was a study
done by the U. S. Army Training and Doctrine Command (TRADOC)
Systems Analysis Activity (TRASANA).
The study uses AFQT, as
well as education level, sex, paygrade, time in service,
in
Military
Occupational
Specialty
24
(
MOS
)
,
and
a
time
dummy
variable
reflecting
General
Equivalency
completion as explanatory variables.
GED
Diploma
is a
rating given
to individuals who did not graduate from high school,
have taken examinations to be rated
school graduate.
conditions
as equivalent
but who
to a high
battery of tests given under controlled
A
resulted
in
dependent variable.
net
a
score
which
made the
was
The battery of tests was designed so as
to represent how proficient
career field.
(GED)
soldier
a
was
in
his specific
The test included a written, as well as hands-
on proficiency test.
The analysis method used was linear regression, with the
inclusion
AFQT.
of
Durbin
a
Instrument as
a
correction tool for
The results are again best summarized from the report:
"The most important result is that AFQT Category I-IIIA
soldiers performed approximately 10% better overall than
IIIB soldiers.
Furthermore,
AFQT was a much more
important influence on performance in virtually all
instances than either education or experience, whether
measured in terms of time in service, MOS, or unit.
Thus, these results strongly support the validity of AFQT
as
predictor
of
performance in these military
a
occupational specialties."
.
.
This report then, is
tank
gunnery
report,
regression to have
a
very similar
in
which
significant
AFQT
and
in conclusion
was
shown
measurable
to the
through
effect on
soldier performance in skill related tasks.
The last study reviewed is also from the collection found
in the Defense Manpower Study
study was
.
[Ref.
11]
The topic
for this
the estimation of promotion rate.
It is presently
central theme
of this thesis.
the most similar study to the
25
Using AFQT
independent variables, a duration
of the
as one
model is applied to estimate the expected speed of promotion.
This model
within two
was applied
and the career field of the NCOs
study
approaches
of promotion
This promotion estimation
.
aggregation
the
Specifically, by
manner as well.
categories, the paygrade
in a different
data
of
evaluating the possibility
for each individual over a series of years, the
dimension of time was entered into
analysis.
A
significant
advantage of including the time dimension was that changes in
the categorical levels of
the population
could be accounted
for, such as race or sex.
The methodology used in the promotion estimation study is
considerably
Rather than
complex
more
than
in
the
previous studies.
using standard regression models, the study uses
the Generalized Linear Model form.
the predictive
model is
a
Weibull shape parameter.
education, AFQT,
Specifically, the form of
log likelihood function using the
The explanatory
variables include
marital status, race, number of dependants,
time in service, sex, and high school completion
using
the
Weibull
the
model,
status,
Additionally, there are
assumptions
for
marital
and
the
no
status
requirements
residuals,
and
By
of explanatory
application
variables which are not continuous, such as sex,
completion
status.
is
for
high school
more
proper.
the normality
therefore,
less
subjectivity to the appropriateness of the model with respect
to the independent variables.
This method, however, does not
26
consider any
in-service information
and was calculated only
for very specific CMF and Paygrade combinations.
The results
are summarized as follows:
"A review of these promotion results reveals two
trends.
First, even after controlling
for high school
diploma status,
AFQT Category I-IIIA soldiers are
promoted approximately
10%
more
rapidly than 1 1 IB
soldiers.
Second,
high school
completion
is
less
important than AFQT score in determining promotion rates.
The remarkable aspect of this last result is that
educational attainment is an explicit part of the Army's
promotion point system, while AFQT scores are not.
These
trends are true for both promotion to E-5 and promotion
to E-e."
As considerable attention has already been
topic
positive results
and since
one
might
wonder
why
have generally
the
Deputy
Chief
further research in the
the Army.
Secondly,
of
been the result,
study should be undertaken.
another
this thesis is in response to
First,
of
measures of intelligence to performance,
relating
of
given to the
a
request by
the Office
Staff for Personnel (ODCSPER) for
relationship of
this thesis
approach and analytical procedures.
AFQT to
will be
success in
different in its
Following
is a
list of
the unique characteristics of this thesis:
1.
The perspective of this thesis is that the results will
an explanatory
or
as
management tool,
be used as a
In that light,
method for active duty Army personnel.
utilizes information collected from the
the study
such as his Skill
individual's in-service record,
NCO Schooling levels.
and his
Qualification Scores,
Similar to accession related studies, this analysis
academic,
and categorical
intelligence,
includes
variables.
explanatory
potential
as
information
However, the intent is not to justify accession of high
investigate the trends of
but
to
quality soldiers,
promotion for active duty personnel as a function of
available personnel data.
27
*
.
This study conducts significant investigation
into the data to identify and correct anomalies which
would confound the relationship in question.
Statistical analysis is done from the bottom up,
rather than by direct movement into regression models.
This approach finds that strict parametric models are
subject to error due to the inability of some data
variables to meet distributional assumptions necessary
The study then moves to
for parametric analysis.
nonparametr ic means to approach the issue.
For regression models, given the cautions on their use,
population is tested using the
an additional sample
Thus, the results from the initial model can be
model.
considered to have more believability and fidelity than
model based on analysis of a single population
a
sample
The use of
a
large data set.*-
Several explanatory variables have been made
available from the DMDC data base which have not been
They include the initial
used in previous studies.
education at time of entry, NCO education level,
and a
race variable with six categories.
The cho ice of promoti on as the dependent variable
rather than a set of performance tests.
Although prone
to more uncertainty t han results of performance tests,
promoti on is in ma ny ways an ultimate performance
measure
The servic e,
like any other organization,
recogni zes
superior
performance by promoting and
advanci ng individuals to higher positions of authority,
despite its problems, has a
As such
promotion r ate,
strengt h of recogniti on well beyond that of technical
perform ance
,
.
This study uses graphical methods for depiction of many
of the methods of analysis.
Study number four from Defense Manower Study uses both
large data sets and promotion as an independent variable.
28
Ill
OVERVIEW OF THE DATA
.
INTRODUCTION
A.
A
critical aspect of
screening of
creating
data.
the
demonstrate
Two general
data
set.
level
a
this thesis
guidelines were applied in
First,
the
homogeneity
of
selection and
was the
data
set
that
in
had
the
to
NCO's
considered would all have served under similar enlistment and
advancement policies.
Secondly, the selection of individual
records needed to be random and without unintentional bias to
meet
the
requirements
Section III
describes
C.
insure that
for
representative
a
detail
in
the
sample
measures
set.
taken to
the above two attributes were established in the
study data set.
Receding of data values
into numerical
required for several personnel record fields.
the level of
Military
service schooling
Schooling,
is
As an example,
the
NCO's in-
level, was recorded as mixed alpha-numeric
Transformation
characters.
which
equivalents was
involved
rank
ordering
the
available levels of schooling in ascending hierarchical order
and substituting
Chapter
variable.
IV
numeric value for the alpha-numeric value.
discusses
in
detail
the
background
of
each
Finally, as a check on the effects of manipulating
and restricting
a
a
comparison of
the sample data set, section III D. provided
statistics
for
the
entire
U.S.
Army NCO
database, versus the sample data set used in this thesis.
29
.
DESCRIPTION OF THE VARIABLES
B.
The data
categories:
variables used
in this
control variables,
The
promotion variables.
intelligence, were used as
intelligence variables, and
first two categories, control and
explanatory variables,
brief description of each variable is
Variable Category
Dependent
PRATE Promotion
RATE
Promotion
PRA
Promotion
while the
were used as the dependent variables
promotion variables
TABLE
study fall into three
tabulated in
A
.
Table
I
Summary of Variables in Sample
I
Meaning
Value
Raw Promotion Rate:
number of promotions
041-.21
per month to most
recent promotion
Promotion rate difference
from average for that
2.2-9. 4
paygrade (normalized)
Promotion rate difference
from average for that
3.4-8.
paygrade and CMF
normalized)
Scale
Ratioj
Ratio
Ratio
(
Explanatory
SEX
Control
CMF
Control
RACETH Control
PAYGD
Control
GTSCR
Intell
AFQTP
Intell
OAFQTP
Intell
EIMCAT
Intell
HIYRED
Intell
EDLVL
NCOE
Intell
Intell
PQSCR
Intell
Male/Female
0/1
Nominal
Career Management Field 11-99 Nominal
1-5
Race/Ethnic group
Nominal
5-7
Paygrade
Ordinal
General Intelligence
0-160 Ordinal
Score
Armed Forces
Qualification Test Score 1-100 Ordinal
Percentile
Same as AFQTP, referenced
1-100 Ordinal
on 1980 population
1-8
Mental Category; based
Ordinal
on OAFQTP
Highest Year of Education
1-12 Ordinal
upon entry into Army
1-12 Ordinal
Present Education Level
Military Education Level
0-13 Ordinal
Attained
0-100 Ratio
Army Proficiency Test
30
more
A
detailed
description
variables will be given in
first
the
each
of
part
of
the study
Chapter IV,
of
Successive Analysis.
C.
PREPARATION OF THE DATA
Preparation
data
the
of
began
acquiring
with
fifty
thousand records from the U.S. Army Military Personnel Center
in Alexandria,
Virginia.
Initial restrictions
on the data
were established to allow inclusion of only NCO's with a date
of entry
after January
members
to be
National
of
Guard
observation
the
Restricting
NCO's
the
a
not
were
who
Reserve or
provided for
recruited
a
the ending of the Viet Nam
establishment
focused the study on the standing
confounding as
and
restrictions
NCO's
period following
and following
Force.
Army,
These
those
only
reasonable time
War,
Regular
the
forces.
of
Further, NCO's selected had
1976.
1,
to
the All-Volunteer
of
Regular
forces alone,
Army soldiers
and avoided
result of different promotion and accession
policies in the Reserve and Guard Forces.
The records requested were randomly drawn by taking every
fifth
individual
from
estimated
an
meeting the above restrictions.
population of 250,000
The fifty thousand MILPERCEN
records were then matched and merged with
database
Monterey,
from
the
Management
Defense
California.
information, including:
a
similar personnel
Data
Center (DMDC)
DMDC database holds additional
The
the
ability
to
distinguish high
school equivalent certificates holders from actual graduates,
31
.
.
education
the highest year of
time of
at
EIMCAT scores renormed for
AFQTP and
enlistment, and
soldier
the
of
a
1980
population
After the raerging, data records which
of the critical variables fields were dropped.
in any
approximately
were
had missing values
Following
data.
thousand
ten
records
There
missing critical
analysis of promotion rates, two
initial
additional restrictions were
applied
the remaining
against
records
First,
grouping
a
several
of
hundred promotion rates
showed that individuals had been promoted to the
at
which
rates
were
Cross referencing of
group as
for
who,
duty.
them
NCO's who
a
variety
service
numbers
identified
this sub-
had served in Reserve or Guard units and
of reasons,
accelerated
Subsequently,
as one promotion per month.
high
called for active
had been
they were allowed by regulation to carry with
As such,
an
as
rank of E-5
promotion
to
former
their
rank.
serial number match and elimination was done
a
for all NCO's with recent listing as Reserve or Guard status.
A
level
promotion
second source of unusual
became
oriented
apparent
career
particular.
in
management
Research
indicated that during
some
rates
at
the E-5
technically
of
the
more
fields,
the
medical
field in
into Army special recruitment policy
the
early
1980's
special provisions
were made to allow persons with background ability in certain
technical fields
to enter
the Army
32
and be
promoted to NCO
status within
six months,
or in certain cases to receive NCO
status immediately following basic training.^
these anomalies,
all promotion
To correct for
rates which fell outside the
maximum time periods considering application of
both waivers
were discarded.
D.
COMPARISON TO TOTAL ARMY STATISTICS
In this
section, selected
attributes of the sample data
set and the complete U.S. Army database are briefly compared,
with
intent
the
checking the representativeness of the
of
sample set.
Population attributes such as distribution of sex. Career
Management
complete
Fields,
U.S.
paygrade
and
database
Army
were
records
obtained
from
consisting
of
the
over
250,000 NCO's.
As
described
in
paragraph
50,000 selected records had
personnel
who
entered
3.B,
been
Army
the
the sample data set of
filtered
to
contain only
after 1976.
Screening of
those 50,000 records for completeness of
of promotion
policy, reduced the number in the sample set to
approximately 38,000.
sample
final
set
to
It
was
1
prudent
then,
to
check the
see if it retained its representative
It should
character as a random sample.
that this
data and uniformity
be noted,
however,
comparison will not occur for all study variables.
MSG Knopp, NCOIC Defense Management Data
Monterey CA 93946.
El Estero Drive,
33
Center, West.
Reasons for this include non-availability of records from the
MILPERCEN database, and cases where the statistic was
computation by
produced through
the author, promotion rates
being the principal example.
1
Comparison of Army versus Sample Summary Statistics
.
Formal hypothesis testing for
means or distributions
was unavailable due to computational and software
with ANOVA
restrictions.
However, since the intent of this
identify any
simply to
section was
population shifts, and the magnitude
of those shifts, observation of summary statistics is assumed
sufficient.
to be
deviations of four
entire
set.
Specifically, the means and the standard
variables
population
NCO
obtained
were
from
both the
set and the thesis sample data
data
The percent difference between
the variable
means was
computed and expressed relative to the thesis sample data.
A
table of comparative statistics and the percent difference is
shown in Table II.
TABLE II
Tot al Army vs Sample Summary Statistics
Sample
Tota 1 Army
Sample Size
Variable
AFQTP
SEX
RACETH
PAYGD
The
three
variables
noticeable
changes
while
RACETH
the
(37,854)
Mean Std Dev
53.4 20.9
1.12
.328
1.65
.942
5.27
.464
(250 ,000)
Mean Std Dev
48.3
25.2
1.09
.283
.991
1.63
.597
5.75
between
variable
AFQTP,
the
SEX,
PAYGD
and
>
>
>
<
have
Sample and the Total Army,
doesn't
34
Percent
Difference
Sample 10%
Sample 2.7%
Sample 1.2%
Sample 5.2%
appear
to
have
been
affected much
by sampling.
closer look
A
at the discrete
distributions, and an overall conclusion about differences in
the two data sets follows.
2
.
Discrete Distributions
Figures
and
3.1
discrete distributions for
Both plots
illustrate differences in the
3.2
are Clustered
paygrade
and
Bar Charts,
each level of the discrete variable
race respectively.
and the percentage of
for both
the Total Army
and the Sample were plotted next to each other.
ARMY VS SAMPLE RACE PERCENTAGES
ARMY VS SAMPLE PAYGRADE PERCENTTAGES
80
CLUSTER BAR
r
SO
C2
CLUSTER BAR
60
TOTAL ARMY
TOTAL ARMY
'O
SAMPLE
<
C2
SAMPLE
ASIAN
OTVIER
40
20
-
20
m.
WHfTE
E-7
E-6
E-5
BJ^CK
HISPANIC
Figure 3.1
the tabular data and bar charts show
that there are some differences between
personnel,
AFQTP
the
slightly
related
INDIAN
Figure 3.2
Observation of
Specifically,
,
RACETH VALUES
PAYGRADE VALUES
contains
sample
more
scores.
the two populations.
women,
The
more
ranking
significantly higher
and
racial
lower
make-up of the sample
appears to be similar.
The restriction of random
entering the
service after
sampling to
1976 can
35
only those persons
directly or indirectly
explain these differences.
is
direct
a
result
First, the lower average paygrade
promotion
of
impossible to achieve a
above
rank
policy,
in which it is
E-7
less
in
than ten
Hence, the sample population should be demonstrate a
years.
Secondly, the slight increase in the
lower average paygrade.
proportion of
be explained by a general opening
women might
up of the services to women in the
eighties.
Thirdly, the
late seventies
higher AFQTP
and early
is a direct result of
policy restrictions begun in Fiscal Year 1981, and formalized
Authorization Act.
1984 Defense
by the
constraints on AFQT Category and high
[Ref.
lOrsec
1-0,
general improvement
services
Whether
p.l]
resulted
social
of
school diploma status.
these restrictions, or the
acceptance
the military
of
improvement is a question
AFQT
this
in
This placed quality
which would require significant study in itself.
In short then,
from the
different in
the sample is
It should be noted,
total NCO population.
that these results are intentional.
restricting
the
dangerous to the
soldiers who
sample
study
to
after
than
the
were accessed
Viet Nam War policies.
unless significant
will
The
shifts
however,
caused by
1976 are felt to be less
alternative
during the
of including
draft and the era of
Finally, it is only a matter of time,
changes in accession and promotion policy
occur, before the character
set
several ways
constitute
the
demonstrated by
norm
for
the sample data
all NCOs
.
concluded that the study sample is satisfactory.
36
Thus,
it is
SUCCESSIVE DATA ANALYSIS
IV.
A.
INTRODUCTION
In this chapter the
analysis
data
followed
reported.
be
systematic
a
method for
This method of analysis
format which is described by Chambers in Graphical
a
Methods for
an
will
results of
Data Analys is
understanding
C
Ref
the
of
descriptive
univariate
.
.
This procedure develops
12]
beginning
data,
with
simple
procedures, then progressing through
several increases in dimensionality of variables, and finally
into
more
the
procedures
inferential
complex
of
model
An abbreviated outline
building and multivariate regression.
of this procedure is shown below.
1.
2.
3.
4.
5.
In
Analysis of single variables.
Comparison of variable distributions.
Analysis of paired variables.
Multivariate graphical analysis
Linear Models including:
Simple Regression
a.
Multivariate Models
b.
addition
supplemented with
to
this
procedure
will be
non-graphical
measures,
such as
these
several
steps,
ANOVA, ANCOVA, and several tabular nonparametric methods.
be
noted
that
procedures
which
are
should
considered
investigation, or whose results
merit.
chapter,
reports
analysis
this
an
only
essential
provided
an
It
those
step
in
observation of
Many available procedures have not been used in this
as
a
consequence
of
37
the
data
failing
to meet
.
distributional assumptions, and for other reasons which would
During
make such analysis inappropriate.
chapter,
this
results
the
of
the development of
each level of analysis will
specify why the next set of analysis procedures
Alternatively,
if
popular
a
class
was pursued.
procedures
of
is
disregarded, the logic for disregarding is explained.
The objective of detailing this procedure is to present
depiction
thorough
the
of
a
nature of the variables, and to
explain the development of resulting inferences and models.
B.
UNIVARIATE ANALYSIS.
1
Dependent Variables
.
a.
PRATE
(1)
raw promotion
General
.
The variable
PRATE represents the
rate of a particular individual.
Numerically,
it is the total of promotions per month up to the most recent
promotion
(2)
Value.
The
variable PRATE was computed
using data obtained from the DMCD database.
The time to most
recent promotion in months was found by subtracting the basic
pay entry date from the date of latest
number
then
individual's
became
rank,
the
or
denominator
equivalently
,
award of
rank.
This
of a ratio having the
the
total
number of
promotions the individual has received, as the numerator:
Individual's Latest Rank
Prate
=
(Award Date of Latest Rank)
36
-
(Date of Entry in Army)
.
Ranks were
numerically represented with
an E-5 Sergeant,
ranks.
The
and with
variable were:
score of
and 7 for values of the
6
resulting
a
5
for
next two
of measurement for the PRATE
units
units of promotion per month of service.
Attributes of
(3)
PRATE qualifies
the Variable
The variable
.
as a continuous variable with a ratio scale.
The continuous nature of the variable relies on the fact that
number
the
service
months
of
combined
three
with
rank
structures yields sufficient combinations of values, actually
to use as measures.
190 in all,
There
are
problems
inherent
some
score, since
promotion
minimum time
thresholds for
policies
are
with
effect
in
promotion.
the raw PRATE
which set
Thus, the promotion
of an individual who is presently an E-5 will be incomparable
to the
promotion rate
of an E-7 whose three promotions have
time
been affected by the minimum
minimum
time
in
service
Generally, the
policy.
promotions grows as rank
between
increases, and more senior soldiers will
normally have lower
raw promotion rates
A
second
source
of
bias
potentially found in the
is
Career Management Field (CMF) of the soldier.
policy is
based on
be attained within
promotion.
a
a
system of minimum performance points to
CMF
Generally, the
order
in
of the
to
be
more technical
higher promotion point thresholds
The distribution
Army promotion
fields will have
than non-technical fields.
variable PRATE
39
considered for
and its summary
Figure
statistics are
shown
histogram
positively
is
in
flat
shape
median value,
just
until
a
be
a
few individuals
sloping
steep
generally
a
After the
occurs.
tail
A
shape is that there appears to
of this
promoted at
who are
block
then
of the
a
median value.
the
downward
gradual
rough interpretation
partitions,
past
shape
The
demonstrating
skewed,
first
ascending slope in the
4.1.
average
very fast rates,
promotion
rates, then a
diminishing tail of individual promotion rates
which fall to
followed
by
a
of
the right of the seventy-fifth percentile.
HI STOGRAM TABLE
PRATE HISTOGRAM AND STATISTICS
(N=37854)
X
SELECTION
X LABEL
NO. OF ELEMENTS
X MEAN
STD. DEVIATION
SKEW.'ESS
KURTOSIS
5-PERCENTILE
25-PERCENT I LE
MEDIAN
75-PERCENTILE
95-PERCENT I LE
0.0-+
0.08
0.12
0.18
X MIN.
X MAX.
dm
»
PRATE
ALL
PRATE
37854
0.109+6
0.036322
0.59367
2.5854
0.051225
0.08
0.10204
0.13514
0.17857
0.041667
0.20833
O.JO
PRATE
Figure 4.1
Distribution
transformation
attempted, primarily because
its
of
this
variable
usefulness
in
was not
testing or
modelling is limited by the problems associated with the bias
factors described above.
40
.
b.
RATE
General
(1)
expression
of
The
.
variable
the
variable
PRATE.
RATE
individual rank removed by normalizing each
a
re-
bias due to
has
It
is
individual score
relative to his or her paygrade
Values
(2)
To compute the variable RATE,
.
the
average PRATE value for each paygrade was calculated, as well
as
the
standard
deviation
for
that paygrade.
Individual
scores were then normalized by the transformation:
RATEt
PRATEi
=
-
AVERAGE for that Rank
STANDARD DEVIATION THAT RANK
Attributes of
(3)
RATE is
also
the Variable
continuous ratio
a
The variable
.
scale variable, as it is
a
transformation of PRATE.
The removal of influence due
computing the
rank
to
correlation coefficient
RATE and PAYGD.
in Table
As seen
X,
was
confirmed by
between the variables
a
value of
near zero
resulted where the previous correlation coefficient for PRATE
and PAYGD had been -.495.
from PRATE results in
The distribution
a
Thus, the
transformation to RATE
variable independent of PAYGD.
shape of
the RATE
histogram, shown in
Figure 4.2, appears slightly non-normal, but
summary
statistics
closely
to
the
for
standard
a
check
of the
quantiles show that they correspond
normal
quantiles.
Thus,
the
assumption of normality for procedures using this variable is
41
1
observation
still reasonable, based on
the distribution
of
shape and the close agreement of quantile values.
Figure 4.2 presents
histogram and summary statistics for
a
the RATE variable.
g
ni3
RATE HISTOGRAM AND STATISTICS
(N=37554-^
SELECTION
X LABEL
NO. OF ELEMENTSX MEAN
STD. DEVIATION
SKEVMESS
KURTOSIS
S-PERCENTILE
25-PERCENT I LE
MEDIAN
75-PERCENT I LE
95-PERCENT I LE
lO
_
8
r
o
;
o
o
—
_
1—
o
-
04
_
g
___
-
o „. J.
i_
_J
-i
-2
:
RATE
ALL
RATE
37854
:
-1 .555E-
X
—
-
!>-
X MIN.
X MAX.
~n,
:
:
:
:
0.99997
0.21408
2.3767
-1.5476
-0.77573
-0.03757
0.70754
:1
:
:
.5234
-2. 2681
3. 6685
RATE
Figure 4.2
c.
PRA
General
(1)
recomputation of
the raw
The
.
variable
promotion rate.
is another
PRA
PRA controls for
the career management field as well as paygrade.
of
normalized
promotion
PAYGD and CMF.
the.ge
which
was
is set
are independent of
Verification of the independence
variables
coefficients.
scores,
It
of PRA from
also confirmed by checking correlation
Both variables CMF
and
PAYGD
had
near zero
values of correlation with PRA.
(2)
Values
.
in the same manner as in
Computing the variable PRA was done
RATE, however
42
a mean
and standard
3
1
deviation for each CMF and PAYGD combination was computed and
used in the normalization equation.
Attr butes
(3)
with
3
ratio scale.
a
PRA is
.
continuous variable
The distribution of PRA appears normal,
with the quantile values very close
A
a
to the
standard normal.
comparison of percentile values for PRA versus the standard
normal are shown in TABLE III.
PRA HISTOGRAM AND STATISTICS
(N=37854)
HISTOGRAM TABLE
SELECTION
X LABEL
NO. OF ELEMENTS
X MEAN
STD. DEVIATION
SKEV^ESS
KURTOSIS
5-FERCENTILE
25-PERCENT I LE
MEDIAN
75-PERCENT I LE
95-PERCENT I LE
o
o
—
1
o
<
—
s
a:
-
«
d-2
c^
^
t
4
X MIN.
X MAX.
PRA
ALL
PRA
37S54
7.41E-9
0.99881
0.21406
2.6552
-1 .5518
-0.75252
-0.04146
0.69604
1
.7086
-3.4988
4.5374
PRA
Figure
A
comparison
of
4
.
percentiles
for
the
PRA distribution
versus the standard normal distibution is shown in Table III.
Specifically, the PRA percentile
corresponding standard
data point.
while
a
a
values are
listed with the
normal percentile values for the same
For example,
-1.5510 indexed in
-1.5510 is the PRA five percentile,
a
standard normal table results in
six percent value.
43
Comparison of PRA vs
N ormal Percentiles
TABLE III
Standard
St andard Normal
6%
PRA
5%
22.6%
48.4%
75.7%
96.3%
25%
50%
75%
95%
Normality
this
for
variable
general distribution shape and
will
be assumed based on
correspondence of
close
the
the data percentiles to the standard normal percentiles.
2
.
Control Variables
d.
SEX
The variable
SEX is discrete and nominal.
are represented by a numerical value of one,
represented with
a
two.
Males
and females are
12.29 percent
In the study sample,
of the sample was female, and 87.71 percent were male.
e.
CMF
Career
variable
with
Management
nominal
scale.
represented in the sample.
assigned a
Each
(CMF)
Thirty
is
discrete
a
three
CMF's
Career Management
are
Field is
numerical value, for example, the Infantry branch
is designated as CMF 11.
of the
Field
These assignments
are
a
Department
Army numbering system, and can be reviewed along with
the CMF percentage and frequency table in Appendix
There
is
some
system, for instance,
ordinal
information
in
the
A.
numbering
low CMF numbers are indicative of
44
a
combat branch,
such as Infantry or Armor.
Center CMF values
are indicative of combat support branches, such as Signal and
Chemical.
values
CMF
Upper
from the combat service
are
support branches, such as Medical and Language Specialist,
Figure
histogram,
CMF
the
4.4,
does
reflect
the
distribution of the three general groupings of CMF densities:
and
combat
service
support
values
have roughly equivalent
combat, combat support,
combat
and
combat
representation,
while
the
upper
numbered
support.
The
service support
CMF's are about two thirds the size of the other groups.
CMF HISTOGRAM
(N=37854)
COMBAT
COMBAT SPT
COMBAT SVC SPT
y
c
<
O
2
20
40
60
BO
100
CMF
Figure 4.4
f.
RACETH
The race-ethnic
variable.
The values
variable is
represented and
shown in table IV.
45
a
discrete, nominal
their percentages are
TABLE IV
Sample Race Percentages
Percent
Race
Value
Cumulative
Percent
52.43
52.43
White
38.59
Black
5.58
Hispanic
.26
American Indian/Alaskan Native
Asian/Pacific Islander
1.15
Other/Unk nown
1.99
1
2
3
4
5
6
g.
91 .02
96.6
96.86
98.01
100.00
PAYGD
Paygrade
selection of NCO rank
is
a
from
discrete, nominal variable.
personnel
enlisting
The
after 1976
representation by paygrades E-5 through E-7 only
resulted in
The distribution of PAYGD is shown in Table V.
Sample Paygrade Percentages
TABLE V
Value
5
6
7
Percentile
Rank
73.29
25.89
0.81
Sgt E-5
Staff Sergeant E-6
SEC
E-7
Cumulative
Percent
73.29
99.19
100.00
The 0.81 percent for E-7 results in only 307 SFC's in the
sample.
other
Despite the
ranks,
a
preponderance of
sample
size
representation by the
of 307 for the E-7 rank still
allows for adequate representation of that subcategory.
46
3
.
Intelligence and Academic Scores
h.
GTSCR
The General Intelligence
individual
the
ordinal scale.
The lower
is
a
continuous
Test
Score
variable with at least an
The range of values run from 50
value of
(GTSCR) of
through 160.
the corresponding minimum
50 represents
score of ASVAB modules that would allow for enlistment in the
The histogram of the
Army.
4.5,
GTSCR variable, shown in figure
is approximately normal.
larger density
in the
Checking the quantiles shows
distribution to the left of the mean,
with slightly lower valvaes for quantiles right of the mean.
HISTOGRAM TABLE
GTSCR
ALL
SELECTION
GTSCR
X LABEL
37S54
ELEMENTS
NO. OF
108.23
X MEAN
14.275
STD. DEVIATION
0.129
SKEWNESS
3.3632
KURTOSIS
84
5-PERCENT I LE
.99
25-PERCENT I LE
:109
MEDIAN
:117
7 5-PERCENT I LE
:130
95-PERCENTILE
GTSCR HISTOGRAM AND STATISTICS
(N=37a54)
X
:
:
:
8.
a.
4/>
O
z o
o
o
nru.,
JZl
60
60
10O
a
120
140
GTSCR
Figure 4.5
47
160
X MIN.
X MAX.
:54
:156
.
AFQTP
i.
The Armed Forces Qualification Test Percentile is
a
continuous
represents the
variable
with
relative
standing
score referenced
ordinal
scale.
of
Its
value
individual's test
an
against a 1944 population.
This means that
an individual's raw AFQT score is compared against a standard
was developed
values that
table of
of raw
AFQT test
the entire 1944 American youth
scores for
resulting
population.
Hence,
simply
corresponding
the
represent the distribution
designed to
values from 1944 was
a
This table of
in 1944.
individual
percentile
AFQT
score is
of the individual raw
AFQAT score relative to the entire 1944 population
AFQT test
distribution
The histogram
in Figure 4.6.
about
the
and summary statistics for AFQTP are shown
The density
mean.
of AFQTP
is partially symmetric
lower five percent quartile is at a
The
value of 21, demonstrating the restriction
and VI
study is primarily for comparative reasons.
any developed
reference
population
subsequent
chapters,
model since
has
AFQT
CAT V
Use of the AFQT score for this
personnel since 1980.
used in
applied to
ceased.
was
cannot be
scoring against the 1944
As
will
be
seen
in
discarded anyway when OAFQT
proves to a better explanatory variable.
48
AFQT
AFOTP HISTOGRAM A.ND STATISTICS
(N=37854)
HISTOGRAM TABLE
AFOTP
ALL
SELECTION
AFOTP
X LABEL
37854
NO. OF ELEMENTS
53.^19
X MEAN
20.965
STD. DEVIATION
0.29913
SKEWNESS
2.2128
KURTOSIS
21
5-PERCENTILE
37
25-PERCENT I LE
50
MEDIAN
75-PERCENT I LE
:68
X
:
o
a.
Iso
O
20
40
60
80
•100
95-f'ERCENTILE
X MIN.
X MAX.
:91
:10
:99
AFOTP
Figure 4.6
OAFQTP
j.
The OAFQTP variable is
ordinal scale.
is
It
continuous variable with
a
fundamentally
the same
as the AFQTP
variable, excepting the reference for measurement, which is
1980 population.
a
The distribution for OAFQTP is considerably
lower values
more dense in the
Explanation of
than AFQTP.
this shift can be seen by reviewing the transformation tables
in
Appendix
scores.
A
points.
1944-based
scores
to 1980
The transformations for values below 80 result in a
1944 based score to
amount of
converting
for
be reduced
reduction varies,
Only when the
but it
scores
increasing transformations.
49
every case.
in almost
go
can be
above
85
The
as much as four
are
there any
HISTOGRAM TABLE
OAFQTP
SELECTION
ALL
X LABEL
OAFQT
NO. OF ELEMENTS
37854
X MEAN
45.319
STD. DEVIATION
24.779
SKEWNE5S
0.53139
KURT05IS
2.1725
S-FERCENTILE
14
25-PERCENT I LE
25
MEDIAN
41
75-PERCENT I LE
64
9 5-PERCENT I LE
92
OAFQT HISTOGRAM AND STATISTICS
(N=37854)
X
5 o
^ 8
O
O
50
60
40
20
X MIN,
1
X MAX.
99
100
OAFQT
Figure 4.7
k.
EIMCAT
EIMCAT
based on
EIMCAT
the
is
is
discrete
a
ordinal
and
assignment of categories is
and is
population
reference
1980
a
mental category of an individual
the
a
scale
AFQT
test score.
variable.
Department of Defense standard/
common reference for all services.
The breakdown of
values is as follows:
TABLE VI
Value
1
2
3
4
5
6
7
8
Sample Men tal Category Percentages
Category
AFQT
Cat
Cat
Cat
Cat
Cat
Cat
Cat
Cat
01-09
10-15
16-20
21-30
31-49
50-64
65-92
93-99
V
IV C
IV B
IV A
III B
III A
II
I
The
Percent
.33
6.736
9.788
19.187
26.116
13.053
19.99
4.8
50
Cumulative
Percent
.33
7.067
16.854
36.041
62.157
75.21
95.2
100.000
8
histogram of the EIMCAT values follows in Figure 4.8.-
A
SAMPLE EIMCAT DISTRIBL/TION
BAR CHART OF PERCENT
~
25
-
20
_
V/
7/
PERCENTAGE
-
T/
V)
5
-
v?
-
V
n
3
4
5
6
EIMCAJ (MENTAL CATEGORY)
Figure
Observation
clearly the
of
the
4
.
above
figures
demonstrates
fact that categorization into EIMCAT category is
not evenly distributed across the scale of OAFQT scores.
center EIMCAT,
example, the
points, while EIMCAT
point
eight
EIMCAT
scores.
discrete
more
scale
For
value five, spans almost twenty
contains
only
the
upper seven
does make available an established,
measurement
representing
intelligence test
scores for use in appropriate statistical procedures.
1.
HIYRED
HIYRED is
the highest
the individual upon entry into the
and
ordinal
scale
variable.
year of education held by
army.
It
is
a
The values and distribution
percentages are shown on the next page in Table VII.
51
discrete
)
TABLE VII
Sample Hi ghest Year of Education
Percent
Cateqorv
Value
Cumu.Lative
Percent
1
2
3
4
5
5.5
6
7
8
9
10
11
12
1-7 Years
0.018
0.153
Years
1.397
1 Year High School
4.7
2 Years High School
3-4 years HS (no di ploma
6.935
High School GED
4.813
High School Diploma
71.274
1 Year College
3.305
2 Years College
3.453
3-4 Years College (no degree) 1.337
College Graduate
2.560
Masters or Equivalen t
0.05
Doctrate or Equivale nt
0.005
8
.018
172
1 .569
6 .269
13 .203
18 .017
89 .29
92 .595
96 .048
97 .385
99 .945
99 .995
100 .000
.
EDLVL
m.
EDLVL is the present
individual.
level of
education for the
These scores are related to HIYRED, in that any
education taken by the individual subsequent to enlistment is
recorded in
a
this variable.
A
GED equivalency is included as
value of six for high school completion.
TABLE VIII
Value
Sample Education Level Percentages
Cateqorv
Percent
1
1-7 Years
2
3
Years
1 Year High School
2 Years High School
3-4 years HS (no diploma)
High School Diploma
1 Year College
2 Years College
3-4 Years College (no degree)
College Graduate
Masters or Equivalent
Doctors or Equivalent
0.042
0.011
0.198
0.793
1.503
80.443
6.089
5.828
2.037
2.948
4
5
6
7
8
9
10
11
12
8
52
0.1
0.008
Cumulative
Percent
0.042
0.053
0.251
1.043
2.547
82.99
89.079
94.907
96.944
99.829
99.992
100.000
9
Observation of
Figure 4.9, or percentages in Table VIII,
shows an observable upward
enlistment.
This is
shift
education
of
level after
possible, and encouraged with official
continuing education and high school completion programs.
HIYRED AND EDLVL PERCENTAGES
CLUSTER BAR
80
P
U60
<
u 40
CZl
L
20
tTL
JZ!
5
\A
4
a
level
discrete
of
individual.
Officer
Education variable,
It reports
and ordinal scale variable.
military
Military
organized in three
advanced.
12
11
.
The Noncommissioned
the
10
NCOE
n.
is
HIYRED
EDLVL
_e:01__CZ2.
7
8
YEARS EDUCATION
6
Figure
NCOE,
El
accomplished
schooling
categories
schooling
ascending
levels:
At the two lower levels,
are seperate courses for combat
and
by
the
are generally
primary,
basic and
primkry and basic, there
non-combat
CMF's.
In
some cases, there has been an award of an On-The-Job Training
qualification.
NCO who
The OJT award is
used to
give credit
to an
can achieve technical competence in advance of being
53
.
eligible for promotion to the next higher paygrade.
As previously
mentioned, attendance
at military schools
an individual being previously
is sometimes
associated with
identified as
a
the advanced
level schools where selection for attendance is
superior performer.
through Department of the
primary level,
local commanders
selection
procedures
attendance
a
Table IX
Army
and
often
locally mandatory
and
Figure
4.10
This is
Selection
true mostly in
Boards
.
At the
have authority to establish
will
make
primary school
requirement for junior NCOs
demonstrate
categories and
the
distribution of NCOE.
TABLE IX
Value
1
2
3
4
5
6
7
8
Sample NCOE Percentag BS
Category
P Brcent
Nonpar tici pant
21 19
Primary NCO Course (CBT CMF)
4 46
Primary Leadership Graduate
39 36
On-The-Job Credit for E-5 skills
5 38
Primary Technical Course Graduate 2 82
On-The-Job Credit for E-6 skills
Basic Technical Course Graduate
5 11
Basic NCO Course (CBT CMF)
15. 99
On-The-Job Credit for E-7 skills
01
Advanced NCO Course Selectee
2. 28
Advanced NCO Course Graduate
3. 06
01
Advanced NCO nongraduate, OJT
06
On-The-Job Credit for E-8 skills
,
9
10
11
12
Figure 4.10 presents
,
-
a
Cumulative
Percent
21.19
25.65
65.25
70.63
73.45
73.45
78.56
94.55
94.56
96.84
99.89
99.9
100.00
histogram of NCOE discrete levels
54
40
SAMPLE NCOE SCHOOLING PERCENTAGES
BAR CHART
r
30
UJ
<
o
20
7/
a.
10 -
m
^M^
A
2
1
3
5
4-
7
5
UTTWn
8
10
9
11
12
U
14
13
NCOE EDUCATION
Figure
4
.
10
PQSCR
o.
Occupation
report
PQSCR
is
Skill
Qualification
individual.
It is
a
of
Test
Score
(SQT)
The SQT is a service related test which is used
competence of
the technical
used by
promotion
promotion.
correct
Separate
The
answers
boards
as
on
a
are
of
the
soldier.
SQT score has been
qualitative
a
to determine
measure for
value represents the percent of
numerical
tests
SQT
a
Military
and ratio-valued variable.
continuous
a
Primary
the
written
hands-on
and
evaluation.
written for each CMF, although the
structure of the tests are similar.
The distribution of PQSCR, shown in Figure 4.11,
dense in
is more
the upper values, with an abnormally long left tail
extending to
a
lower
bound of
An explanation
21.
for the
shape of the PQSCR distribution is an involved topic, and has
itself been the subject of study.
that
PQSCR
has
previously
been
55
A
general observation is
used
in
a
manner where
1
individual soldier scores were often aggregated as
comparison of the parent unit of the soldiers
.[
Thus, significant units and individual training
Ref
means of
a
11 :p.
.
emphasis has
testing in previous years, and pressure
been focused
on SQT
to perform we]
1
was
a
positively skewed distribution, rather than
As
result,
a
43
influenced by
the parent organizations.
a
is understandable.
normal distribution,
PQSCR HISTOGRAM AND
HISTOGRAM TABLE
PQSCR
SELECTION
:ALL
X LABEL
:PGSCR
NO. OF ELEMENTS
37854
X MEAN
78. 384
STD. DEVIATION
1
609
SKEWNESS
-0.70832
KURTOSIS
3. 5739
5-PERCENTILE
:57
25-PERCENTILE
:71
MEDIAN
:80
75-PERCENT I LE
:87
95-PERCENTILE
:95
STATISTICS
X
(N=37854)
J
8
S
:
:
:
(A
:
1
.
:
-
:
—
"
o
^ g
CM
-
—
o
20
J.
-.
80
eo
4-0
X MIN.
X MAX.
:21
:100
100
PQSCR
Figure 4.11
3
.
Summary
The fifteen variables used in this
a
wide
variety
of
characteristics.
56
study demonstrate
All of the dependent
.
variable choices were
continuous
with
showing
departures
from normality.
slight
only
RATE
two,
and PRA,
The other
continuous variables did not have identifiable distributions,
and could
not be transformed to normality using power or log
transformations. Nor is it entirely clear that one would need
to use a transformed variable in subsequent analysis.
The
independent
variables
compris
continuous and discrete values,
scales.
Within
the
with both
independent
principal sets of related
mixture
of
ordinal and ratio
variables
variables.
are all derived from the ASVAB.
another
a
there are two
The intelligence test
OAFQTP, EIMCAT, and to a lesser extent GTSCR,
scores, AFQTP,
one
of
varying
in
These
degrees,
expression, transformation, or
variables differ from
and
derived
similarly
a
either
are
a
re-
set of
scores
academic performance measures, EDLVL and HIYRED,
The two
are
related,
in
that
EDLVL
is
simply
addition
of
sets
of
differences
in
the
additional schooling since entry into the Army.
Despite
variables,
it
within
similarities
the
is
felt
these
sufficient
that
two
informational value are present in each expression.
since the variables used
are
all
standard
Further,
data collection
items for the DMDC database, each variable expression will be
studied.
The
variable from
relative
this study
merit
may be
of
any
single
useful to managers seeking
appropriate data sources for other studies.
57
or combined
An
important
variables
Analysis
Of
Variance
distribution as
hypothesis
testing.
seek
use
to
similar efficiency,
scale
or
be checked.
replacement or as
of the
In this
standard
However, if results of the analysis are
requirements fails, or if
assumptions,
those
examination of assumption
If
there is
nonparametric
a
test of
nonparametric tests will be conducted as
a
confirmatory precedure.
BIVARIATE ANALYSIS
This
section
concentrate
will
relationships between
as
function
a
categorical, variables.
Three
used in this
section.
The
association
using
correlations.
the strength
of scatterplots of pairs
and
of
Jittering
is
Pearson
provide intital
between any
effects, or
analysis will be
method
analysis of
product-moment
information as to
two variables, and
relationship, being
or negatively correlated.
LOWESS
first
of association
the
of
methods of
matrix
a
This will
the direction of that
identifying
on
pairs of variables, and in identifying
shifts in distribution
of
of the necessary
the scale of the variable.
distributional
to
assumptions will
C.
parametric
initially
will
parametric methods.
a
many
that
these study
(ANOVA), and possibly regression will
well as
analysis
sensitive
of
These include assumptions about the form
not be met.
study,
standard
for
analysis
the
of
observation
the
is
assumptions
result
either positively
The second method will be analysis
of variables,
to
58
using the techniques
better view any trends in the
variables.
This method will give initial information on what
type
fitted
of
relationship
exists
variables.
Of
significant
relationship
is
fundamentally
possibly
between
polynomial
method used will be
distribution
hence
and
line,
independent
interest
linear,
analysis of
plots.
dependent
and
be whether the
will
whether
or
curvilinear.
or
mathematical
what
it
is
The third and final
three-dimensional empirical
will demonstrate some shifts in
This
distribution within several of the effects variables.
1
Correlation Matrix
.
As earlier mentioned,
product-moment
Pearson
pairs of variables which
purpose
the
correlation
have
and a value of zero
linear association
that
indicates
with each other.
an exact direct linear relationship,
inverse
association.
a
preliminary
variables
the
The
while
a
-1
indicates an
measurement of
This
indicative of
tool to
have no
value of +1 indicates
A
relationship.
linear
association is not completely
is only
to identify
is
the correlation coefficient, rho, is from -1 to +1,
range of
exact
matrix
strong
a
reviewing the
of
dependency, and
identify candidate variables
for testing and subsequent inferential statistics.
Remembering the central question of this thesis, the most
important
pairs
variables
of
intelligence and academic scores
rate
variables.
interval
scale
Of
effects
almost
will
paired
equal
variables
59
then
be
with
interest
any
of
the
the promotion
will
demonstrating
a
be any
strong
linear relationship with the promotion variables.
strength
The
relationship
linear
the
of
between two
variables/ or its level of significance/ is based on how much
variance there
the estimated
is in
is dependent
the variance
of rho
considered.
For example/
then
effectively demonstrate
needed to
for
if the sample size were small,
or minus
of plus
significance.
Conversly,
large sample set with very small standard deviation for
a
rho,
a
smaller
much
value
rho
An estimate
significant.
could
sample
Considering
size.
37,854,
the resulting estimate
rho is
.005139.
Thus,
a
be
considered
for the standard deviation of rho
can be found by computing the inverse of
the
and
positive or negative value of rho would be
large
a
Further/
sample size being
on the
standard deviation
the value of rho had a
.3/
value of rho.
the square
root of
the
thesis sample size of
of the
standard deviation of
value of rho different from zero by
plus or minus .01, could be considered significant.
In
Table
correlation
X
matrix
complete
the
Pearson product-moment computation is
assumes pairs
the preferred method since
correlations with
are
variables.
primarily
This is
interested in
RATE or PRA variable as one of
either the
the pair of variables.
the Spearman
we
The
parametric method and
a
and continuous
of normal
product-moment
study variables is given.
the
for
Pearson
Additionally,
nonparametric method,
it is
possible, using
to compute a correlation
value rho for pairs of ordinal, or higher scale variables.
60
.
[Ref.
251-253]
13:pp.
free method
The Spearman method is
The last
lists
correlations
Comparison of
there
was
distribution
providing correlations based on the ranks of the
variables.
the
a
an
column on
the second
part of
Table
X
computed using the Spearman method.
Spearman
versus
acceptable
Pearson
values
correspondence
methods/ and Pearson values are used
showed that
between
the
two
exclusively to simplify
analysis
Even with
application of
methods there remained several
not
meet
the
Spearman and Pearson
both the
characteristics
distributional
assumed
variables which did
pairs of
These variables are
correct interpretation of the rho value.
the
CMF.
discrete,
Their
variables
nominal
results
interpretation of
are
the rho
most important rho values
SEX,
included
in Table
PRA column and are underlined.
61
RACETH, and possibly
Table
in
value would
X
for
X,
but any
be ineffective.
are
The
located under the
TABLE X
PRATE
Pearson Correl ation
RATE
.822
PRATE 1.000
.822 1.000
RATE
.790
.951
PRA
.118
GTSCR
.035
.100
.155
AFQTP
OAFQTP .177
.209
EIMCAT .174
.200
.168
HIYRED .156
EDLVL
.085
.139
NCOE -.200
.047
-.019
.013
SEX
-.074 -.143
CMP
RACETH-.064 -.084
PAYGD -.495
.000
.039
PQSCR
.101
PRA
1
GTSCR
AFQTP
.035
.118
.107
.100
.155
.133
.177
.209
.177
.174
.200
.170
.039
.101
.094
.741
.734
.937
.689
.903
.955
.274
.308
.315
.305
.066
100
.093
-.013
-.042
-.128
.097
L.OOO
.790
.951
.000
.107
133
.177
.170
.177
.162
.006
.036
.000
.057
.000
.094
1
.
-
.000
.741
.734
.689
.210
.266
.039
.055
113
.
.495
.000
.000
.143
.087
.031
.023
.001
.098
.433
.057
.053
.016
.000
.097
1
.157
.168
.178
.210
.215
.245
.209
.000
.708
-.063
.131
.146
.024
.000
.066
1
.085
.139
.162
.265
.258
.266
.242
.708
.000
.004
.114
177
.039
.098
.100
1.000
.903
.215
.257
.955
.245
.266
1.000
-.009
-.060
-.062
.159
106
.050
.074
-.325
.031
.315
.062
.067
.
-.242
-.305
.143
.274
.087
.398
.
-.200
.047
-
.005
.039
.009
-.060
-.062
-
.063
.004
1.000
-.081
184
.
.015
.432
.093
62
OAFQTP EIMCAT PQSCR
1.000
.937
PEARSON COEFFICIENTS CONTINUED
PAYGD
HIYRED EDLVL NCOE
SEX
PRATE RATE PRA
GTSCR
AFQTP
OAFQTP
EIMCAT
HIYRED
EDLVL
NCOE
SEX
CMF
RACETHPAYGD 1
PQSCR
C oef f icients
CMF
-.018
-.075
-.142
.036
.054
.159
.049
.063
.131
.114
.000
.113
.107
.074
.068
.146
.177
-.081
1.000
.258
.042
-.056
-.013
-.184
.013
.209
.241
-.314
.023
.305
SPEARMAN
RACETH PRATE
-.064
1.000
.084
.808
.777
.020
.075
.165
.158
.147
.038
-.208
.020
-
-.056
-.242
-.306
-.325
-.313
.025
.024
.039
.015
.042
.025
1.000
-.054
-.042
-.016
-.128
.258
1.000
.
-.069
-.092
-.535
.
The
significant
most
observations
from the tables are
summarized as follows:
For the variable RATE there is zero correlation
PAYGD variable.
did remove
the transformation
Thus,
influence
the
paygrade
of
with the
of PRATE to RATE
promotion rate.
on
Similarly, for the variable PRA, both PAYGD and CMF have zero
correlation
As expected,
the three
highly correlated in
With
two
promotion rate
variables are all
positive direction.
a
exceptions,
the
correlation
values
for the
effects and independent variables have similar magnitudes and
signs across
expressions of
all three
first exception is the NCOE
negatively
correlated
promotion rate.
variable.
with
a
Under
PRATE
The
it is
value of 0.2, and positively
correlated with lower values for RATE
and PRA.
This result
makes sense when one considers that NCOE is highly correlated
with PAYGD,
lower for
Specifically, raw
(0.565).
higher grade NCO's due to time in service and time
(-.495).
in grade requirements,
correlated
with
relationship.
as
it
is
promotion rates are
in
PAYGD,
When the
RATE
and
will
Hence, NCOE, which is highly
also
reflect
that
inverse
influence of paygrade is eliminated,
PRA,
this negative correlation is
incidentally removed.
The second exception is for the variable SEX
positive signed
RATE.
where it is
for PRATE and PRA, but negatively signed for
The magnitude for all three values are close
63
to zero.
.
.
explanation
An
will
RATE
difference in sign between PRA and
the
for
presented
be
analysis
the
in
of
empirical
distributions and coded scatterplots
Groups
closely
of
correlation
same
related variables have generally the
across
Specifically, AFQTP,
three
the
promotion
OAFQTP, EIMCAT, and to
GTSCR, all demonstrate
a
strong positive
variables.
lesser extent,
a
correlation against
each other, and show the same trend when compared against the
promotion rate variables.
EDLVL demonstrate
weaker
variables HIYRED and
similar characteristics, however, EDLVL is
HIYRED
than
The academic
with
respect
to
the
promotion
rate
variables
Considering
RATE
PRA
and
as
variables to model with, and allowing
from
each
the
of
the
better
for only
promotion
one variable
related groups, the six most significant
correlated variables were selected.
These
in descending absolute value of rho,
are shown in Table XI.
variables,
listed
Most S igni ficant C orrelated Variables
Consi.d erin g both RATE and PRA
Variable
Rho Va lue
approx 0.17
HIYRED
OAFQTP
approx 0.14
GTSCR
approx 0.10
PQSCR
approx 0.09
RACETH
approx -0.06
NCOE
approx 0.006
TABLE XI
These
used
as
variables,
the
starting
either
paired
basis
64
for
with RATE or PRA, were
multivariate
regression
analysis.
effects
The
variable
SEX
included
was
subcategory analysis in an effort to detect any
for
influence it
might have on the primary relationships.
2
Paired Scatter Plots and Simple Regression
.
Plots of
paired independent
were implemented
to
purpose
visually
was
patterns.
to
two
search
purposes.
for any dominant plotting
to detect
nonlinear
only linearity, it is quite possible
relationships
could
explanatory and dependant variables.
relationship was strictly Y=X*
be
The first
Since the rho values found in the previous section
are designed
that
accomplish
and dependent variables
zero.
Thus,
relied
one
if
For example,
computed
a
,
between
exist
the
if the X-Y
rho value should
only
on
correlation
coefficients to detect relationships, he would be misled into
thinking
that
variables.
variable.
relationship
Simply
explanatory
require
no
variables
specification
plotting
between
scatterplots
X-Y
the
two
of
the
the promotion variables did not
with
of
existed
the
Visual observation
detect dominant patterns of
response
of
could then
any
form.
the
dependant
be relied upon to
These scatterplots
used two special procedures, LOWESS and Jittering, which will
be described in analysis of Figures 4.12 and 4.13.
Secondly, simple
for
all
variables
significantly
least squares
which
had
The
correlated.
regression procedure
yielded
been
a
65
regression was performed
previously found to be
simple
least
squares
value called the Coefficient
.
of Determination, or R2
related to
is mathematically
R2
the rho, and in the one variable case, the square
of rho is equal
qualitatively
R2
to
can
R2
strength
the
The advantage
accounted for by the
assumption
also
of
used to
be
linearity
of
of producing
represents the
R2 directly
results for
Thus,
.
interpret
simple linear model.
was that
(R-square).
for a
R2 values
proportion of variance
linear
a
model.
The
each of the regressions and an explanation of R2
will be discussed in analysis of Table XII.
Paired Scatterplots
a.
interpretation
Since
coefficients assumes
scatterplots was
linear or
correlation
the
of
linearity, visual
analysis of pairwise
search
observable patterns,
used
otherwise.
to
for
This visual
interpretation of single derived
approach did not require
parameters to
identify any
patterns
producing
In
used.
the
scatterplots the LOWESS procedure was
Locally Weighted Regression
LOWESS, which stands for.
Scatter Plot Smoothing,
CRef.
12:pp 94-95] is a nonparametric
smoothing procedure which is designed to
relationships between
quadratic
discrete
Y and
relationship
variables
In particular,
X.
assumed.
is
against
the
variables, the discrete variables
repeated plotting
small random
For
continuous
no linear or
scatterplots of
promotion rate
were Jittered
to overcome
Jittering involves generating
of points.
increments,
estimate functional
which
66
are
then
added
to
the X
values.
when the X-Y plot is performed fewer
As a result,
values are repeatedly plotted in
the
same
location,
X
and
a
better visual interpretation can be made of the quantity of
X
values at
a
discrete level.
The overall results of the LOWESS
predominant pattern
was indeed
plots showed
linear.
that the
Further, the linear
pattern was demonstrated most clearly between pairs of highly
correlated variables.
linearity
and
Figures 4.12 and 4.13 demonstrate that
LOWESS
the
respectively.
As a result,
Jittering
and
techniques
linear modelling techniques were
considered to be the best choice for subsequent analysis.
LOWESS SCATTERPLOT OF HIYRED VS PRA
LOWESS PLCT OF PRA V3 OAFQTP
(N=200C)
•
_
CM
•
•
>
u
•
•
*
•
•
•
•
•
\
•
Q.
o
o
•
_
•
•
•
• •
•;
<
*
;•
.
•
•
•
1-
1
••
•
i
•
^
•
r
C i s
..
•
1
CM
;
•-
•
•
•
•
" ^
•
.
J
:.'
•
•
•
•
•
\
•
1
i
20
1
1
1
40
I
1
!l
eo
e
BO
OAFQTP
JIHEf^ED HIYRED
Figure 4.13
Figure 4.12
b.
Simple Regression
For pairs of significantly
a
simple
8
least
squares
regression
67
correlated variables,
plot
using PRA as the
10
independent variable
accomplished.
was
yields quantitative results in
for pairs
squares regression
simple least
The
terms of slope values, intercept values,
tests of
the slope
and intercept values, and the R2 value.
The R2 value represents what proportion of total variance
was explained by the
from zero
values range
indicate
simple
that
a
linear
model.
does
model
values.
such,
As
account
not
for any
Correspondingly, a value
of zero would be the estimate of the slope of the line.
significance of
R2,
determine the significance of
T test
for the
slope of
R2 value,
a
the model
a
rejected.
model
of a
If the T
greater T value
hypothesis
Thus,
we can be confident of the linearity
and
the
derived
of
slope of zero is strongly
a
estimate.
slope
function of
sample size.
if the T test for the slope
value
would
necessarily
qualification for
a low R2
considerable 'noise'
T
Thus,
value,
Sample
statistic
value
of the
size is
is computed
even with a small R2
were significant,
held as significant.
be
To
results of the
null
considered in this test because the
as a
the
are checked.
statistic is large and the probability
small,
The
is related to sample size.
like rho,
its
R2 value of zero would
An
to one.
the dependent
variance of
linear
would be
the R2
The only
that there exists
or unaccounted variance in the response
of the dependent variable.
A
summary of results are shown in
Table XII.
68
.
.
TABLE XI]
Simple Least Squares Summary Data
using PRA as Dependent Varia ble
Variabl e Intercept
GTSCR
AFQTP
OAFQTP
EIMCAT
HIYRED
EDLVL
NCOE
SEX
CMF
RACETH
PAYGD
PQSCR
-0.856
-0.338
-0.336
0.004
-0.005
0.011
-0.020
0.011
-0.023
-0.009
-0.045
-0.059
Slope
Std Err
(0.0061
(0.014
(1.6E-02)
(0.027
(0.047
(0.054
(0.021
(0.028
(1.6E-02)
(0.018
(0.093
(5.4E-02)
)
)
)
)
)
)
)
)
)
0.008
0.006
0.007
-0.003
-0.001
-0.003
0.003
-0.018
0.000
-0.001
0.007
0.007
Std Err
R2
(5.6E-04)
(0.0002
(3.2E-04)
(0.005
(0.008
(0.008
(0.003
(0.024
(2.6E-04)
(0.010
(0.018
(6.9E-04)
)
)
)
)
)
)
)
)
I
.013*
.018*
.033*
.000
.000
.000
.000
.000
.000
.000
.000
.008*
13.8
26.1
22.5
-.5
-.2
.02
1.1
-
-
-
.7
.9
.
1
.3
10.6
Important observations from the simple paired regression
analysis are summarized in the following paragraphs.
Very few sets of pairs result in
Those that
for these
GTSCR, OAFQTP, and PQSCR.
do are:
these variables have
pairs did
significant R2 value.
a
positive slope.
a
All three of
Analysis of residuals
normality of residuals
show reasonable
and did not demonstrate any lack of homoscedasticity
The remaining variables
negative
slope.
For
each
Confidence Interval for the
value of
have
of
a
low
these
slope shows
value
positive or
variables,
the upper
the 95%
or lower
the slope to be either positive or negative.
no observable ascending
or
descending
relationship
Thus,
can be
claimed
Using the
the simple
variable RATE
as the
regressions results
69
independent variable in
in the
variables EIMCAT and
AFQTP having measurable R2 values and positive slopes.
coincide
analysis
results
the
expected,
As
with
the
simple
observations
taken
of
regression
from
the
correlation table.
When considered
one at
time,
a
handful of variables demonstrating
promotion
the
with
there appear to be only
reportable relationship
a
variables.
a
The low R2 value for each
regression indicates either a large proportion of pure error,
unexplained variance due to other explanatory
or significant
variables not being included.
3
3-D Empirical Density Plots
.
empirical density
Three dimensional
plots were used
check for distribution changes in the continuous
to visually
variables within the subcategories of SEX,
PAYGD and RACETH.
Two such plots will be discussed because they depict visually
data characteristics
These
identified in
characteristics
restrictions
by
earlier tabular results.
application
the
were:
congressional
mandate
in
1980,
of
and
AFQT
the
differences in OAFQT scores across racial groups.
depicted in
Figure 4.14, where
empirical densities for OAFQT are plotted
for each paygrade.
The AFQT
Observing
the
restriction is
three
densities
shows
that
only
the
paygrade distribution contains scores less than twenty.
makes sense,
prior to 1980.
plot
is
that
considering that
Another
high
all the
interesting
OAFQT
scores
70
E-7
This
E-7 enlistments were
observation
become
from this
more dominant as
paygrade increases.
E-7 density
This is most
to either the E-5 or E-6.
of OAFQT across the
tends to
apparent in
three paygrades
manifest itself
that a low AFQT
score
in the
is,
This shift in density
suggests that attrition
lower AFQT caetgories, but
itself,
in
comparing the
prohibitive in
not
achieving senior enlisted rank.
The second 3-D empirical density plot. Figure 4.15, shows
differences
the
subcategories.
renormed
in
A
distribution of
AFQT
scores
across
racial
large discrepancy between the white and the
black
hispanic
or
races
easily seen,
is
although Indians have a similar AFQT to that of whites.
observation
coincides
promotion rates
However, to
races
Daula,
tRef.
inferences
about
require
further
ll:pp.
7-10]
racial
different
occurrence
the
of
different
between different racial categories as well.
make
would
with
This
groups
policy among
promotion
research.
As pointed out by
attrition
the
shifts
pattern among
averages
the
for
both
promotion rate and AFQT among the races over time.
Since the
of prediction,
it is more
account for
it in the
purpose
of
this
thesis
important to identify the
model.
An explanation
one
is
effect and
as to
the cause
of this phenomenon
does not appear to be easily obtained from the thesis data.
What is important about this
demonstrates the
OAFQT is
a
plot
correlation between
significant
determiner
of
RACETH will be an important covariate.
71
is
that
RACETH and
promotion
it visually
OAFQT.
If
rate, then
3-D EMPIRICAL DENSITY PLOT
OAFQT BY PAYGD
^-^
Figure
4
.
o^f
^"^^
14
3-D EMPIRICAL DENSITY PLOT
OAFQT BY RACETH
0^
ao^
0^^-^^
Figure 4.15
D.
MULTIVARIATE GRAPHICAL ANALYSIS
analysis consisted
Multivariate graphical
Draftsman
Plots
relationships
when
consideration.
procedures,
the
Coded
and
CRef
more
.
Coded
than
Scatter
Plots
two
dimensions
to
135-139]
12:pp.
Scatterplot,
72
of the use of
will
One
be
look
for
were
under
of
these
utilized
to
—
demonstrate
significant
a
characteristic being
to CMF and PRA,
Coded
that
of SEX, correspondent
in Figure 4.16.
effects variables as
involved
third
a
independent variable
the PRA
characteristic,
the distribution
Scatterplots
In Figure 4.16,
data
delineating
dimension,
against
a
while
of
the
plotting an
dependent promotion variable.
CMF values were Jittered and
variable, and
one
plotted against
the plot points were coded as periods
for males and the letter F for females.
CODED SCATTERPLOT
PRA VS CMF WITH SEX
T
2
1.1
.:
-U
a.
*?
'''ft
Fi-
r
J
eo
L
J
20
40
L
I
80
CMF
Figure 4.16
Figure 4.16 demonstrates
personnel
the
in
technically
oriented
corresponds to
found in
upper
Table
.
highex-
density
of female
CMF range, which contains the more
management
career
the CMF-SEX
X.
the
fields.
This
correlation coefficient of 0.258
Likev/ise,
the distribution
of both the
female and male PRA scores are symmetric about the zero line.
73
.
corresponds
This
the
to
value
zero
for
correlation coefficient also found in Table
PRA-SEX
the
X.
LINEAR MODELS
E.
1
.
Analysis of Variance
One
ANOVA
Way
intermediate
step
detect
defining
in
ANOVA's usefulness
been
has
differences
used
was
means
in
variables.
For example,
and EIMCAT
as the
an
as
among
as
an
inference model
final
a
thesis
this
in
investigative
tool to
classes of explanatory
using PRA as the
dependent variable
independent variable,
One-Way ANOVA will
compare and test the equality of the average PRA score across
eight
the
levels
through eight.
eight
all
alternate
EIMCAT,
of
In the testing,
category
mental
hypothesis
hypothesis is that
the null
means are equal, while the
PRA
that
is
mental categories one
i.e.,
they
are
test
The
not.
statistic used to reject or accept the null hypothesis is the
F
statistic.
rejection of
exists
As
such,
the null
significant
a
large
F
hypothesis would
differences
and subsequent
value,
indicate that there
between
the
means
of the
promotion scores for some of the eight mental categories.
In
general, a large F value can be considered to be any computed
F statistic greater than 3,8,
for
a
one degree of
differences could be
freedom
a
the asymptotic 95 percent point
model.
The
nature
of these
large discrepancy between a simple
74
pair of categories,
categories,
small
combination
any
or
discrepancies
between
difference conditions.
of
Thus, ANOVA has limited value in discerning the
magnitude of
the differences
does identify
location and
between category means, but it
differences
if
all eight
exist
and
strong those
how
differences are.
Table XIII
for separate
tabulates
One-Way
twelve by three matrix of results
a
ANOVA
The
's.
rows
the twelve
are
explanatory variables and the columns are the three promotion
variables.
Using
three
all
independent variable
promotion
allowed for
a
measures
as the
check of ANOVA values and
trends across those measures.
In addition to the results of the F
is reported.
This
of levels,
a
single
all variables
Further, because
of
variable categories,
of
a set
With
had some level of R2 reported.
and hence,
computation, the values
is because the
continuous variable.
increased
the
This
independent variable as
considers the
rather than
One-Way ANOVA,
value of R2
a
R2 value is different than that reported
in the simple linear regression model.
ANOVA procedure
test,
R2
informational
value of
more degrees of freedom for
increased
above
the simple
regression reported values.
It
should
be
noted
that technically, when the defined
into ANOVA,
continuous variables were put
grouped, and
discrete.
their values were
then the variables were treated as if they were
Because
the
SAS
75
software
and
computational
could handle
resources used
all the
integer values for the
score ranges of AFQTP and the other continuous
possible
was
gain
to
insight
into
the
variables,
it
existence
of
differences between individual score cells.
nonparametric
Additionally,
evaluate
relationships.
the
procedures
CRef.
the F
statistic for
to
The
the variables and
testing the hypothesis of
Having agreement
equal level means.
used
250-2553
13:pp.
nonparametric ANOVAs utilized the ranks of
also yielded
were
between the parametric
and nonparametric values removed the need of having to pursue
confirmation of
also
allow
assumptions for
analysis
of
parametric ANOVA.
results
It will
to focus on the resultant
values of F and R2 tabulated in Table XIII.
TABLE XIII
Variable
PRATE
F
SEX^
CMF»
One-Way Anova Summary
5.9
RACETH
35.
90.
PAYGD'
6292.
GTSCR
AFQTP
OAFQTP
EIMCAT
HIYRED
EDLVL
NCOE
PQSCR
18.
32.
36.
37.
96.
37.
156.
1.9
RATE
R2
.00016
.02788
.01177
.24953
.04250
.07046
.08441
.01076
.02950
.01076
.05097
.00375
F
13.3
93.3
165.0
0.0
13.4
20.6
25.3
71.5
106.0
71.5
76.4
6.6
R2
.00351
.07415
.02133
.00000
.03184
.04623
.06101
.02035
.03272
.02035
.02499
.01341
PRA
F
48.4
0.0
80.0
0.0
10.9
17.3
19.
96.9
117.
96.9
46.8
5.8
R2
.00128
.00000
.01049
.00000
.02636
.03908
.04657
.02739
.03590
.02739
.01583
.01181
^The Pr>F (1 evel of rejection of the null hypothesis
of no d ifference in means) was .0145 for PRATE, .0003 for
RATE an d .0001 for PRA.
2The Pr>F for PRA is 1.0.
Pr>F for RATE is 1.0, and for PRA is 1.0
3 The
Values of Pr>F for the remainder of the table were .0001.
76
Review
Table XIII demonstrates some anticipated
the
of
results, which are summarized in the following paragraphs.
Since the variables PAYGD and CMF were controlled
derivation
the
of
there
PRA,
relationship between those variables
variable.
for in
correspondingly
is
and
the
no
PRA promotion
Likewise, the variable PAYGD was controlled for in
the derivation of RATE, and there was no
demonstrated
for
that
statistic and R2 for
The
pair.
those
linear relationship
values for the
zero
variable
F
combinations documents
this fact.
Using RATE or PRA as the dependent variable, and allowing
for only one, most significant variable
each of
same
set
to be
selected from
the intelligence and academic groups,
results in the
of
explanatory
correlation analysis.
variables
These variables were:
GTSCR, PQSCR, RACETH, NCOE,
variables were the ones which had the larger
R2 value.
in
HIYRED, OAFQTP,
most significant
The
and SEX.
found
were
as
F
statistic, and
there are
This set is not ordered, however, since
differences in order between the PRA and RATE models.
Another interesting
development from
ANOVA results when
the explanatory variable mean and variance for each level are
plotted against
the promotion variable.
analytical plot, but it does provide
on the
This not
a
standard
some visual information
size, direction, and dispersion about the center line
of an independent
discrete
variable.
This
plot
similar to a strip box plot for continuous variables.
77
is most
example
An
plotted against
the sum
Figure 4.17.
shown in
each individual's PRA score was
where
plot
EIMCAT and
of his
HIYRED score is
Figure 4.17 the two center lines
In
scores
plotted represent the sum of
for
EIMCAT
and HIYRED
seperated between the GED qualified personnel and High School
The outside two lines trace the
Diploma Qualified personnel.
lower
and
upper
bounds
deviation
standard
one
from the
computed means.
X-Y PLOT OF MEANS AND VARIANCES
PRA VS HIYRED + EIMCAT
UPPER BOUND
LOWER BOUND
J
I
s
12
20
16
EIMCAT + HIYRED
Figure
By plotting
a
4
.
17
separate line for each high
school diploma
category it can be seen that while both groups have
a
increase in promotion rate, as the
of EIMCAT
and
HIYRED
consistently
school
increased,
a
the
GED
combined level
qualified
fixed level lower than
graduate.
Thus,
a
fully
similar
personnel
were
qualified high
the additional merit of an actual
78
high school diploma did manifest itself in promotion
A final
ANOVA involves specifying
look at
the set of the seven most
checking
then
and
rate.
model using
a
significant independent variables,
interactions among them.
for
Table XIV
gives the results of the Seven-Way ANOVA using this model:
RATE
7 Main Effects
=
Table
depicts
XIV
individually in
Two Way Interactions
+
seven
the
significant
most
Effects rows,
the Main
variables
and the interaction
terms in the Interactions rows.
The advantage of this
Seven-Way ANOVA
is that inclusion
of all of the explanatory variables simultaneously allows for
comparison of the significance
variables relative
each
of
Additionally, specifying
others.
to the
the explanatory
of
combinations of two-way interactions checks to see if any two
of the explanatory variables are significantly related to one
another.
term.
An example of an interaction would be a SEX and CMP
female personnel tend to
As has been previously shown,
be associated with higher CMP values.
If the ANOVA model for
which was
the product of the two
promotion included
a
term
two
values, SEX*CMP, then the
considered in
found to
entries
the ANOVA
model.
be significant,
for
CMP
and
attributes
SEX
If the
then the
would
would
be jointly
interaction term was
two individual variables
be
removed
and only the
interaction term retained.
An additional
consideration in
79
the Seven
Way ANOVA was
that the
were some combinations of the
have any
factor
degrees
of
freedom
which
levels
entries in the ANOVA cells.
be seen in the SEX*OAFQT term.
76
Unbalanced means that there
unbalanced.
model was
An example of this can
Specifically,
there are only
for the interaction term, while the
individual degrees of freedom for SEX and OAFQT are
respectively.
Thus,
the
combinations without entries.
SEX*OAFQT
As a
computed will be only approximate.
step in analysis was
did not
term
result, the
1
had
F
and 79
three
statistic
Since the purpose of this
exploratory, the
F
statistic estimates
were considered adequate.
Table XIV
RATE
as
the
presents the results of a Seven Way ANOVA using
dependant
variable.
Similar
obtained using PRA as the dependant variable.
80
results
were
,
TABLE XIV
7-Way Analysis of Variance with Interaction
DEPENDENT VARIABLE: RATE
SOURCE
DF
SSQ
MEAN SQUARE
MODEL
14966 18869.39 1.260818
ERROR 22887 18981.65 0.829364
CORRECTED
TOTAL 37853 37851.04
SOURCE
DF
Main Effects
RACETH
5
SEX
1
OAFQT
79
HIYRED
12
GTSCR
93
NCOE
13
PQSCR
78
Interactions
RACETH*SEX
5
SEX*OAFQT
76
SEX*HIYRED
9
SEX*GTSCR
72
SEX*NCOE
11
SEX*PQSCR
70
RACETH*OAFQT 335
RACETH*HIYRED 46
RACETH*GTSCR 326
RACETH*NCOE
46
RACETH*PQSCR 288
OAFQT*HIYRED 593
OAFQT*GTSCR 2864
OAFQT*NCOE
614
OAFQT*PQSCR 3631
HIYRED*GTSCR 564
HIYRED*NCOE
88
HIYRED*PQSCR 518
GTSCR*NCOE
604
GTSCR*PQSCR 3383
NCOE*PQSCR
542
Three important
XIV.
F
ANOVA SS
VALUE
PR
1.52
F VALUE
194.69
16.02
25.50
124.42
15.63
87.73
7.85
0.00
440.59
66.03
72.80
57.76
53.06
0.00
107.84
0.00
8.41
104.24
112.62
2418.55
954.24
3182.33
130.88
276.98
0.00
6.99
8.85
484. 13
observations can
R2
F
0.49852
ROOT MSE
0.91069421
807.35
13.28
1670.54
1238.25
1205.22
945.89
507.52
718.86
2997.93
504.44
>
0.0001
1
.87
1.06
0.28
3.80
1.13
1.44
1
.0001
.0001
.0001
.0001
.0001
.0001
.0001
1
.0000
.0001
0001
.22
6.33
0.91
0.00
2.83
0.00
0.22
0.44
0.23
1.02
1
PR
.07
1.12
1
1.
1.
1.
1.
0.
0.
0.
1
0.
0.
0.
0.
0.
0999
0001
6795
0000
0001
0000
0000
0000
0000
2570
0001
0137
0000
0001
0251
0001
0051
0268
be obtained from Table
The first observation is that there are few significant
interaction terms.
Only those terms marked with an asterisk
81
.
.
demonstrated statistical significance
with
the
PR
Of these, only three had F values greater than
level .0001.
These interaction terms were OAFQTP, HIYRED,
3.8.
the Seven-Way ANOVA
correlation
model
HIYRED
with
previously
was
Table
matrix.
and NCOE,
The presence of interation seen in
all interacting with SEX.
correlated
where
X,
SEX
OAFQTP,
and
observed
The implication of having
significant
in the
positively
was
and
(0.05,
respectively), and negatively correlated with NCOE,
0.131
(-0.081).
interaction
terms is
would need to be included in any predictive model.
that they
Thus,
F at
>
identification
interactions
of
using
ANOVA
was
critical
effects variables continue to be
the main
Secondly, all
significant, even when used simultaneously by the model.
Lastly, selecting the single most significant explanatory
variable from
and education
the academic
same unordered best set
groups yields the
the One-Way
as did
ANOVA:
OAFQTP,
HIYRED, GTSCR, NCOE, RACETH, and SEX.
In
summary,
fundamental
the
result
ANOVA was the
of
confirmation that there are differences in the level means of
promotion
scores
variables,
and
explanatory
due
an
several
to
agreement
variables
as
independent
to
which
considered
when
explanatory
were
the best
separately
or
simultaneously
Also,
EIMCAT and
plotting the means
HIYRED versus
and
variances
PRA demonstrated
82
of
the
sum of
that there was a
increasing
good
linear
trend
of the level means with PRA.
However, there was considerable
The choice
level.
variables was
discrete
variance
of EIMCAT
important
each class
and HIYRED as the explanatory
because
representatives
within
from
those
variables
academic
the
are both
aptitude
and
education groups.
2.
ANCOVA
The
use
One-Way
of
previous section
Analysis
was primarily
Beyond
independent variables
levels of
acknowledging
the independent
there
that
available to
in the
the existence of
to confirm
significant differences among the
variables.
Variance
of
some
are
explain promotion rates,
Seven-Way ANOVA
did not provide any numerical measure of the
structural form
of the
variable
to
analysis of
the
the
contribution of
model.
[Ref.
14:p.
In addition,
10]
variables,
continuous
given independent
a
nature
the
in
of the
variable was changed to represent a discrete valued variable.
continuous
Incorporating
achieved through
the intermediate
utilizes metric continuous
qualitative
variables
values.
The
into
ANOVA
method of ANCOVA.
variables
as
well
was
ANCOVA
as nonmetric
result of ANCOVA was an improved
multivariate model with the inclusion of continuous variables
in
their
linear
proper
form.
coefficients
for
ANCOVA
the
provided estimates of the
continuous
variables,
and
reported on the px-oportion of variance accounted for by each
83
variable
categorical
of variables
basis for further removal
the set previously identified.
considered
model
The
These results provided the
well.
as
[Ref.
or interactions from
15:
on the results of the
based
was
343-349]
pp.
previous chapters and consisted of the following form:
Promotion
=
f
(
OAFQTP, PQSCR GTSCR HI YRED, NCOE, RACETH, SEX
,
plus interaction terms
SEX*HIYRED, SEX*GTSCR, SEX*OAFQTP)
The variables OAFQT,
continuous,
HIYRED
,
PQSCR,
NCOE
and
GTSCR
and
metric and
are
discrete and metric, and
are
RACETH and SEX are discrete and nonmetric.
A
representation of the model using notation consisted of
the following form:
Yi
=
Bo
BiXi
+
is
the
coefficients
PQSCR.
for
through
.
D4
.
+
Ii
...
Is
is the promotion variable PRA,
Yi
Bi
of the
represent the discrete
Ii
.
and
Bx
through
Bs
are
continuous variables OAFQT, GTSCR and
the
all levels
D2 +
+
D^
+
intercept,
linear
The coefficients
same for
NCOE.
BsXs
+
above notation,
In the
Bo
+82X2
through
are assumed to
other variables.
variables
I3
Bs
RACETH,
Di
SEX,
be the
through
D«
HIYRED, and
are the interaction terms OAFQT*SEX,
HIYRED*SEX, and NCOE*SEX.
This model is also
estimates.
unbalanced
The results
of the
shown in Table XV.
84
and
the
F
statistics are
ANCOVA using this model are
TABLE XV
ANCOVA with Interactions
DEPENDENT VARIABLE: PRA
SOURCE
DF SSQ
MEAN SQUARE F VALUE
MODEL
55
2423.68
44.07
47.13
ERROR 37798 35339.29
0.934
CORR 37853 37762.98
TOTAL
SOURCE
Main Effects
OAFQT
RACETH
SEX
HIYRED
GTSCR
NCOE
PQSCR
Interactions
OAFQT*SEX
SEX*HIYRED
SEX*NCOE
TYPE III SS
DF
1
5
1
12
1
13
1
12.89440024
152.10095609
5.31950192
517.91751116
3.65772995
132.83314221
80.15632971
13.79
32.54
5.69
46.16
3.91
10.93
85.73
0.0002
0.0001
0.0171
0.0001
0.0479
0.0001
0.0001
4.03387863
10.16825209
18.42527136
4.31
1.21
1.79
0.0378
0.2844
0.0496
1
11
T FOR HO:
main
the
R2
F
PR
F
PR
PARAMETER ESTIMATE
PARAMETER=0
INTERCEPT 0.25501
0.31
OAFQT
0.00094
1.26
-1.98
-0.00104897
GTSCR
PQSCR
0.00422902
9.26
First,
>
VALUE
9
There are three
PR
0.0001
0.0642
ROOT MSE
0.966
important
effects
>
IT
0.7592
0.2077
0.0479
0.0001
observations
variables,
>
F
STD ERROR OF
ESTIMATE
0.83191986
0.00074544
0.00053034
0.00045674
Table XV.
from
with the exception of
GTSCR, are still significant in their ability to
account for
variance in the model.
Secondly, no interaction terms are significant.
F for
these terms are much greater than .0001 and
small F
value.
Thus,
the
effect of
The PR
>
each has
a
the interaction terms
will be assumed to be negligable.
Lastly, the bottom
estimates
of
portion
regression
of
the
coefficients
85
ANCOVA
for
the
table lists
continuous
estimates
These
variables.
were
tested,
using
the
T
statistic, to see if they were significantly different from
hypothesized
value
of
zero.
different
significantly
from
estimate
the
If
then
zero,
was
a
not
explanatory
the
variable did possess sufficient predictive ability.
The PQSCR coefficient has
zero.
0.0042, and is significantly different from
value of
with a
The OAFQT variable has
magnitude,
and
zero.
positive slope
but
small,
a
but
a
slope
with the
correct sign
is not significantly different from
it
The GTSCR variable demonstrates
a
negative
slope and
again is not significantly different from zero.
estimate value, combined with the knowledge
The negative
that GTSCR is strongly
condition
correlated
multicollinearity
of
with
between
Multicollinearity implies that one
surrogate
predictor [Ref.
15:p.
coincident
OAFQT
.
with
other
the
for
4151
OAFQT,
the two variables.
variable may
little
Thus,
the
indicated a
or
no
be simply a
effect as
inclusion of GTSCR
was
considered
detrimental
development of a regression
model, and
it was
to
a
to
the
dropped from
subsequent analysis.
In summary,
remaining
interaction
predictive model.
demonstrated
and
the
ANCOVA resulted
a
The
elimination of the
consideration
estimated values
GTSCR,
was
considered in
86
in
the
of OAFQT and GTSCR
multicollinearity in
variable,
remaining variables to be
from
terms
condition of
weaker
in the
the model,
eliminated.
The
subsequent analysis
.
.
OAFQT, PQSCR,
were:
HIYRED, NCOE,
RACETH, and SEX.
results were considered satisfactory,
variable set
professional
education,
testing,
contains single
well
as
the remaining
measures of academic aptitude,
education,
performance
military
categorical
two
as
in that
These
variables:
SEX and
RACETH.
3.
The Final Model;
Regression
was
important
The
Multiple Regression (ANCOVA)
Background
a.
variables
A
coefficient
the
final
result
values
analysis
of
which
variables.
independent influence
a
reduced
set
of
step in successive data analyses.
this
analysis
estimated
statements about the independent
explanatory
with
of OAFQT
of
of
numerical
each
importance
and HIYRED
set
a
qualitative
influence
specific
Of
was
of the
was
the
in predicting an
individual promotion rate.
In the
development of
the regression model this section
will:
1
Review the pertinent results which led to the
regression model definition.
2.
Compare the model using the three promotion rate
variables
3.
Select
4.
Interpret the resulting regression estimates and
conduct sensitivity analysis.
5.
Check model assumptions and confirm the model using
an alternate data set and nonparametric procedures.
6.
Test the model by comparing actual versus predicted
promotion rates for population subcategories.
a
single promotion variable for the model.
87
Previous results are reviewed in the following paragraphs.
ANOVA
demonstrated
ANCOVA
and
the explanatory
differences exist between internal levels of
variables as
Paired
plots
function of average promotion rates.
a
scatterplots
level
the
of
significant
that
utilizing smoothing techniques, and
means
found
consistently
ANOVA,
in
demonstrated an ascending linear pattern when plotted against
promotion variables.
ANOVA and ANCOVA models, using interactions,
the
elimination
variables
of
additive
sufficient linear
Further, this
model.
which
effect
analysis as to
individual
the
nature
identified
subsequent analysis, these
allow for
only the
and
groups
demonstrate
not
included
in the
that there was no
remaining variables.
combined with
variables,
be
to
analysis confirmed
significant interaction among the
Correlation analysis,
did
resulted in
the in-depth univariate
scoring
groups
were
strongest unique
procedures
of the
of variables.
then
In
restricted to
variable to be entered
into the model.
The final set of variables for
entry into
the model are
the following:
Promotion
This
model
=
f
is
(OAFQT, PQSCR, HI YRED, NCOE, RACETH, SEX)
a
mixed
scale
and
variable
type
including both discrete and continuous variables.
input variables have nominal scale, RACETH and SEX.
model,
Two of the
To allow
for their entry into the model, these values were transformed
88
dummy
into
receded as
a
five dummy
variables.
Specifically, the variable SEX was
0/1 variable,
while RACETH was
0/1 variables:
the RACETH score of
every
for
1
1,
For example,
.
for
the dummy variable Dl was coded with a
entry
1
Dl through D5
represented with
and
zero
a
for
all others.
This
procedure was applied for the next four levels, while score
was left as a 0/0 entry.
After
application
[Ref.
332-341]
15:pp.
the receding just described,
of
6
the
regression model can be defined with the notation:
Yi
In
=
Bo
+
Bi Xi
*
above
the
variables.
B2X2
B3X3
notation,
the
is
Bo
+
+
B«X4
linear
and
are
B4
coefficients
...
+
+
the
of
intercept, and
coefficients for the continuous
Bs
Dl
one
is
Yi
+
Bi
variables OAFQT,
Ds
+
D»
promotion
and
Ba
are
and PQSCR.
the discrete and ordinal
for
variables HIYRED and NCOE.
Di
through
Ds
represent the dummy
variables for
De
represents
the dummy variable
RACETH, and
for SEX.
The data set of
two
separate
provided for
data
a
was randomly
37,854 records
files
different
regression coefficients
regression
for
data
set
from the
to
analysis.
confirm
first set.
split into
This
analysis of
Paragraph e.l.
of this section compares resulting regression coefficients of
the model using the second data set.
b.
Results
Table
XVI
the
lists
89
regression results of the
When computing
basic model variables.
effects variables
RATE the
reintroduced
respectively.
into
the
allowed
This
coefficients and R2 value
became more restricted.
the ANOVA results of the
statistic.
explanatory
of
comparison
for
variables
variable
of
the dependent variable
changes as
In Table XVI the top paragraph shows
model
reports
and
the
F
and R2
Each column then gives the regression results of
each promotion rate model, including
of the
then CMF and PAYGD were
CMP and
set
PRATE and
models for
strength of
rejection for
for the estimate value.
Values
a
Pr>T value
a null
of Pr>T
as measure
hypothesis of zero
less than
.05 are
considered acceptable for consideration of that variable.
90
TABLE XVI
Added Variables
ANOVA F
Pr>F
PRATE
PAYGD
1317.4
RATE
CMF
360.3
PRA
None
218.5
.0001
.3116
.0001
.0948
.0001
.0546
0.022222
-1.03692
.055368)
CMF,
R2
Intercept
(std error)
Pr>T
OAFQT
(std error)
Pr>T
HIYRED
(std error)
Pr>T
PQSCR
(std error)
Pr>T
SEX
(std error)
Pr>T
NCOE
(std error)
Pr>T
Dl (RACETH)
(std error)
Pr>T
D2 (RACETH)
(std error)
Pr>T
D3 (RACETH)
(std error)
Pr>T
D4 (RACETH)
(std error)
Pr>T
D5 (RACETH)
(std error)
Pr>T
CMF
(std error)
Pr>T
D7 (PAYGD)
(Std error)
Pr>T
D8 (PAYGD)
(std error)
Pr>T
Regression Results
.002558)
.0001
.0001355
(00000871)
.0001
.0005341
.000152)
.0001
.000089
.000014)
.0001
- .0008582
.00050325)
.088*
.00008839
.00000625)
1573*
.0026347
.0011286)
.0196
.0037888
.0011266)
.0008
.0009404
.001279)
.4623*
.00028892
.0032534)
.3745*
(
(
(
(
(
(
.
(
-
(
-
(
(
-.000224
.0018127)
(
-.000147
.0000052)
(
(
.0001
.148352
.004851)
.0001
.001608
.000449)
.0001
.022904
.01562)
1427*
.012688
.0017808)
,0001
.053088
.035653)
.1365*
-.096320
.035570)
.0068
-.0239592
.040383)
.5530*
.089059
.102707)
.3859*
-.021530
.0572261)
.7067*
-.0053672
.0001654)
.0001
NA
(
.
(
(
(
.01497054
.0363905)
.6808*
-0 .0898693
.0363089)
-
(
(
.0013
.0417668
.04122033)
.3109*
.01007473
1048355)
.9234*
.0138649
.058409)
.8124*
NA
.
-
(
.0001
(
.0058817
.0002444)
(
.9016*
.05600)
.0001
.0042608
.0002492)
.0001
.139484
.0049298)
.0001
.00327211
.0004583)
.0001
.0564079
.0155310)
.0003
.0073740
.0017949)
.0001
,0001
(
(
-1 .28822
(
.060127
.0017904)
.0001
.017999
.001774)
NA
.0001
91
NA
NA
.
the regression
Observations from
table are summarized in
the following paragraphs.
The
variables
input
maintained
positive
a
HIYRED,
OAFQT,
PQSCR
and
statistically
and
all
significant
coefficient value across all three dependent variables.
The
inclusion
significantly
PAYGD
of
increased
Conversely, the
with
the
R2
value
the
influence of
variable
PRATE
the
of
OAFQT, HIYRED,
model.
PQSCR, and the
other explanatory variables was severely diminished.
model is very similar to the PRA model, and has
The RATE
generally larger estimate values and
the estimates
for RACETH
higher R2
a
.
However,
and SEX did not have significant T
values
although
The PRA model,
generally smaller
result for SEX.
less nominal
has fewer,
having
lower
a
estimate values,
value and
had an acceptable T test
Additionally, the
PRA model
explanatory variable, CMF,
and more
R2
reliable nominal
contained one
The PRA model then,
explanatory variables.
Since the objective of the study was to focus on academic and
educational measures
model
was
chosen
predictors
as
as
Subsequent analysis of
of
promotion,
the PRA
most effective predictive model.
the
regression
coefficient
results were
regression
coefficients
conducted with the PRA model,
c.
Interpretation
Interpretation
will include
two points.
of
the
First,
92
the explanatory variables
.
which
effect
can
variable
will
the
identified.
be
demonstrate the
greatest
amount
variable required
change
Secondly,
change
of
in
the
in
a
dependent
an example will
given explanatory
to achieve a five percent shift in the PRA
estimate
The amount of change in PRA caused by
of
an
explanatory
variable
regression coefficients.
that an
change of one unit
be read directly from the
However, the total amount of change
explanatory variable can cause in PRA depends on the
range of the
ordered
can
a
explanatory
listing
the
of
variable.
Table
explanatory
variables,
categorical variables, from most to least
measured by
Net Possible Change.
simply the number of
units in
XVII
gives an
excluding
total influence as
The net possible change is
of the explanatory
the range
variable multiplied by the coefficient estimate.
TABLE XVII
Variable
Ne t Possi ble Change by Explanatory Variable
Estimate
Range
HIYRED
OAFQT
PQSCR
NCOE
1-12
1-99
21-100
0-14
In a
qualitative sense,
explanatory variable
number of
can
Net Possible Change
.13948378
.00426083
.00327212
.00737408
1.6738
0.4218
0.2585
0.1106
the sensitivity of PRA to each
demonstrated
be
by
deriving the
explanatory variable units needed to move from the
median PRA value up five percent.
To compute the
average for
average
value
for
PRA,
variable was
each explanatory
93
the population
entered into the
The resulting PRA value was 0.0185, which,
regression model.
normal approximation,
using the
of the PRA distribution.
standard
Using the
distribution,
PRA
percentile was 0.1434.
variable
explanatory variable
a
Checking
the
consisted
of
increase
produce
a
of
Alternatively,
if
the
its
to
sensitivity
changing
number of
average.
explanatory
percent
5
the PRA
55.7
of each
single
a
units to result
while holding all other explanatory
variables at the population
the
approximate
to
corresponding
value
sufficient
in a PRA value of 0.1434,
percent would
5
the 55.7 percentile.
lie at
tables
normal
the
explanatory
An upward shift of
value to
the PRA
then require
lies at the 50.7 percentile
Table XVIII tabulates
variable
upward
shift
amount
required
percentile was not possible within
the
necessary to
units
percentile.
PRA
in
reach the 55.7
to
range
the input
of
variable, the maximum amount of available change was listed.
TABLE XVIII
Variable
S ensitivity of
PRA to Expl anatory Variables
A verage
Chanqe to
HIYRED
OAFQT
NCOE
PQSCR
Value
Pra
Chanqe
55.9
55.7
54.0
53.4
7.0
74.0
14.0*
99.0*
6.01
45.3
3.06
78.4
%
*max value
Interpretation
of
demonstates that HIYRED
variable.
This
coefficient
the
is
observation
structure of the variable
most
the
is
clearly
important explanatory
understandable
is discrete,
94
values
and that
since the
changes to
adjacent values
background.
value of
represents major distinctions in educational
The example of shifting from
seven, represents
value of six to
a
the difference
of having a high
school degree versus having gone to one year of college.
percentages of
HIYRED,
constitutes moving from
that
center group of high school
qualified
a
NCO's,
to
a
In
large
the upper
ninety percent of the HIYRED distribution.
OAFQT is the second most significant explanatory variable.
A
shift of roughly one quarter of its
can
change
PRA
plus
or
minus
explanatory variables NCOE and
range,
five
45 to 75,
i.e.
The other
percent.
considerably less
PQSCR have
influence on the dependent variable,
d.
Checking of Assumptions
To
model,
verify
requirements
the
performed
residual analylsis was
program.
Representative
plots
of
for the regression
using
the Grafstat
the OAFQT residual are
shown in Figures 4.18 and 4.19.
REGRESSION REDISUAL HISTOGRAM
REGRESSION RESIDUAL SCATTER PLOT
(N=5C0)
«
Figure
60
OAFQTP
res
Figure
4.18
95
4
.
19
100
histogram
The
residuals,
of
shown
Figure
in
the residual distribution is approximately
demonstrates that
Homoscedasticity is checked in Figure 4.19, in which
normal.
residuals
have
been
plotted
against
OAFQT variable.
the
There does not appear to be any patterns in the
plots of the
the uniform pattern was considered sufficient
residuals, and
to justify the assumption of homoscedasticity.
each
4.18,
observation
represents
Lastly, since
different
a
independence of each observation from one
person,
the
another is assumed
true.
Confirmation of Regression Findings
e.
Second Data
(1)
conducted on
the
comparison of
Set
Regression analysis was
.
partition
second
the
of
data
set.
A
those results with the first data set is shown
in Table XIX.
TABLE XIX
Comparison of Regression Data Sets
Independent Variable
PRA
2nd Set
1st Set
Coeff
Std Err
Estimator
OAFQT
.004260
(.00025)
(.00493)
HIYRED
.139483
(.00046)
PQSCR
.003272
The above results are
Std Err
Coeff
(.00032)
(.00636)
(.00060)
.004729
.131559
.003197
felt to
be sufficiently comparable
to accept the original model coefficient scores.
(2)
Nonparametric Regression
contained an ordinal variable,
using
nonparametric
terms
was
96
.
Since the model
a
regression result
included
as a confirmatory
HIYRED,
.
measure.
Nonparametric regression
least squares
approximation for
produced the
same linear
the model estimates, so the
regression coefficient for HIYRED was still 0.1395.
for nonparametric
estimate
the
regression the
value
coefficient.
used
regression
The
test for the acceptance of
Spearman
the
However,
correlation
rank
coefficient
HIYRED was
for
tested using this procedure.
First, for each value of PRA and HIYRED
U was
found by computing U
PRA
=
-
(0.1395
a
predicted value
*
HIYRED).
Then,
the Spearman rank correlation coefficient, rho, was computed,
based on
the ranks
of HIYRED
found to be 0.02482 with
the
null
hypothesis
coefficient
was
regression.
[Ref.
hypothesis,
that
a
was
equal
to
and the
Pr> R
I
the
of
0.0001.
value
0.1395,
regression
U.
regression
value
the
It was
In this test
the
of
265-271]
13:pp.
the
I
ranks of
found
in
test the null
To
coefficient
estimate
is
correct, rho was compared against a rejection region computed
using
the
tailed
two
approximation.
The
Spearman
rejection
Quantile,
regions
with
for
a
normal
this Spearman
Correlation parameter were values less than 0.0085 or greater
than
Since
0.9915.
the
either rejection region, the
rejected, and
a
HIYRED
value of rho did not fall inside
null
hypothesis
regression coefficient
acceptable
97
could
not be
of .1395 was
.
Testing the Model
f.
coefficients founc3
The mocfel
tested in
two ways.
by regression were
First, a predicted promotion rate value
was computed for the extremes and average of the model
extreme
values
used
input variables.
The
the
minimum or maximum values for the
average
promotion
rate
using sample averages for all input variables.
predictions
were
then
be
The
.
compared
against
was computed
The resulting
actual
the
distribution percentiles.
subsets
Secondly,
of
the sample population had average
promotion rates predicted using categorical values and sample
population averages.
actual sample
against the
for
PRA
The resulting predictions are compared
were
found
by
Again percentile values
values.
using
a
standard
normal
table
approximation
TABLE XX
Comparison of Extreme and Average Predictions
Model
Minimum Prediction
PRA Value
-1.0009
(.1000)
Data
Sample Percentile
Percentile
15.7%
PRA Value
-1.558
Sample Percentile
Percentile
89.1%
PRA Value
1.7866
Percentile
95%
(9.9%)
Sample Percentile
Average Prediction
PRA Value
0.01839
(0.223)
5%
(3.5%)
Maximum Prediction
PRA Value
1.23029
(.4098)
Percentile
PRA Value
-0.04146
Percentile
50.7%
(8.5%)
98
Percentile
50%
.
The model predictions were
very accurate
at the average
level, but this accuracy diminished at the extremes.
The
second
population
test
for
subcategories
predicted.
The
the
model was one where specific
their
had
subcategories
average
value
PRA
represented
were
four
combinations of SEX and the black and white RACETH variables
Additionally,
predictions
were
promotion rate of all NCO's with
all NCO's
with an
OAFQT of
85.
made
a
HIYRED
set to
value of
10,
and
As in the previous table,
unless the input variable is being used as
value was
check the average
to
subcategory, its
a
the overall population average.
Table XXI
shows the results of the predictions.
TABLE XXI
Comparison of Predicted vs Actual PRA Averages
Sample
Sample Size
Subcategory
Predicted %
(Lower-Upper)
Male/White
55.1
(45.7-64.2)
53.1
18,003
Male/Black
49.5
(40.3-58.9)
44.3
12, 121
47.7
2,485
59.5
1,842
75.7
969
Female/Black
47.
3
(37.7-56.
Female/White
%
1)
52.9
(44. 1-61 .5)
HIYRED=10
71 .7
(63.5-79.3)
2129
60.2
57.4
(44.7-69.4)
*The sample da ta point estimate was averag<3d over a
range of OAFQT 80 to 90.
0AFQT=85*
99
Testing of the regression
effective
reasonably
model
with
used
if
nominal variables, such as
indicates
input
that
it was
changes
of the
Changes in the
RACETH.
SEX and
value of HIYRED produces reliable estimates, and demonstrated
the considerable contribution of this variable as
a
predictor
The continuous variable OAFQT is difficult to test;
of PRA.
since it is
taken over
continuous
a
a
variance
the
OAFQT does
median.
the
estimate was
model
Predicted results are close to
range of values.
the sample value, but
spans the
variable
of
the
estimate still
move the predicted values of
PRA in the right direction, but its effectiveness is severely
hampered by
an
accurate
and diminishing ability to provide
its variance
prediction
value
extreme.
Other
prediction
OAFQT
their
results
and
predictive ability
g.
approaches
either
estimates were attempted using
demonstrated
the
lack
same
of
away from the center percentiles,
Summary of Regression Analysis
Regression
independent
PRA
as
analysis
contribution
predicting a promotion
intellgence aptitude,
of
provided
several
They
rate.
estimates
key
include
of the
variables
a
to
measure of
OAFQTP, a measure of academic ability,
HIYRED, two measures of military performance, PQSCR and NCOE,
and two nominal values SEX and RACETH.
Testing
of
these
estimates
shows
that the predictive
ability of the model is limited to those variables which have
very
distinct
abilities
to
100
subcategorize
the
sample
.
population.
variables.
These variables are the SEX, RACETH,
The continuous variables for OAFQT, PQSCR, cannot
be relied upon to independently yield
can affect
and HIYRED
limited shifts
of the
estimates of
PRA,
but
PRA distribution within
a
subcategory
E.
SUMMARY OF FINDINGS
Chapter IV was the principal analytical
study.
It progressed
and resulted in an
independent set
through ascending
inferential model
exercise in this
stages of analysis
with
a
These explanatory
of explanatory variables.
variables did, in fact, rely on levels of
restricted and
intellegence tests
and academic background as values to predict promotion.
The model, however, demonstrated only limited utility as
preditive equation.
it
was
describing
It could only match the sample data when
an
population subcategory.
change
in
the
a
average promotion rate among
This
would
occur
variable
explanatory
had
only
a
a
large
where the
significant
partitioning effect on the population.
The next two chapters will investigate the relationship of
intelligence and academic ability as
a
rate but through different procedures.
101
predictor of promotion
ANALYSIS OF TOP PERFORMERS
V.
A.
INTRODUCTION
This chapter took an
distinguish
which
trends
approach
hoc
ad
performers^
top
promotion rate, from their peers.
three
top
the
percent
consist of
population,
the
of
scores.
referred to
set,
TOP data
on the basis of
Top performers
individuals, according to PRA
as the
identify any
to
This
or
data
1,047
set was
while
the remainder were
sections.
The first section
referred to as the SAMPLE data set.
Analysis consists of three
is a
shown
comparative tabulation of means and variances.
in
this
section
characteristics
predicted
EIMCAT and OAFQT scores.
with respect
Those
sections
of
were,
discrepancies
this
of sample
Chapter IV., such as higher
in
There
majority
the
however, discrepancies
distribution values of RACETH, NCOE and
to TOP
PAYGD.
confirmed
Results
chapter.
are
investigated
in
later
The second section reports the
results of formal hypothesis testing for differences in means
of the explanatory variables.
between each
investigates the discrepancies associated
and PAYGD.
Through
a
appears
to
with RACETH, NCOE,
presentation of graphics demonstrating
internal shifts of those
which
The last section
variable
interrelate
discrepancies is identified.
102
distributions,
the
three
an effect
distributional
B.
COMPARISON OF MEANS AND VARIANCE
The tabulated means and variances of
the study variables
for the top three percent and for the remainder of the entire
sample are presented in Table XXII.
table shows
the percentage
last column
The
and direction
in the
that the TOP data
set differed from the SAMPLE.
FABLE XXII
Variable /Type
Promotion
Mean
RATE
PRATE
PRA
Top vs Sample S ummary Data
Std Dev
2.06
178
2.33
.392
,037
.350
64.69
61.60
6.11
113.17
6.88
22.01
23.24
1.31
14.70
1.59
1.55
11.31
2.50
.
Comment
S ample
T op 3%
Mean
Std Dev
0.00
1.00
.036
1.00
.109
0.00
Intelliq<Bnce
AFQTP
OAFQTP
EIMCAT
GTSCR
HIYRED
EDLVL
PQSCR
NCOE
Effects
SEX
CMF
RACETH
PAYGD
7. 12
80.57
2.31
1.18
62.09
1.58
5.19
53.4
45.3
5.07
108.3
6.01
6.32
78.4
3.06
1.12
51.9
1.65
5.27
.390
27.146
Observations derived
.975
.405
from the
20.9
24.7
1.28
14.2
1.07
.97
1.6
2.81
.328
31.3
data in
.942
.464
Top
Top
Top
Top
Top
Top
Top
Top
17.5%
26.4%
17.0%
4.1%
12.6%
11.2%
2.6%
>
33%
<
Top
Top
Top
Top
>
>
>
>
>
>
5%
>
16%
4%
3%
>
<
<
Table XXII can be
summarized as follows:
The four aptitude test variables, GTSCR, AFQTP OAFQTP and
a
strong positive difference between
the TOP and SAMPLE scores.
The AFQT related scores are about
EIMCAT, all
demonstrate
twenty percent greater, with GTSCR greater by four percent.
103
.
The variables, EDLVL and HIYRED, were both positive, with
HIYRED slightly larger
twelve
at
PQSCR increased
percent,
slightly.
variables SEX
The effects
and CMP
both increased, with
CMF demonstrating a significant increase.
was
an
unexpected
result
The change
subsetting
of
The PRA variable was designed to
percent.
in CMF
to the top three
be independent of
and it should not have been affected as significantly as
CMF,
it was
The only variables which decreased in
SAMPLE and
TOP were
NCOE was the
had
a
NCOE, RACETH, and PAYGD.
largest.
unexpected result.
change
The
Regression
is the
NCOE
in
Of the three,
was
also an
analysis indicated that NCOE
positive influence on PRA.
top performers
proportion between
To have NCOE
reverse result.
decrease with
Paragraph D of this
section will attempt to explain the reason for this anomaly.
SIGNIFICANCE TESTING
C.
Significance
testing
for
means
of
the
explanatory
variables between the TOP and SAMPLE data set was included as
a
formal statistical confirmation of differences
two
data
sets.
Testing
utilized since the study
if continuous,
test for
test used
a
using
between the
nonparametric methods was
variables were
either discrete, or
did not meet the Kolmogorov-Smirnov one-sample
normal
distribution.
The type
of nonparametric
is dependent on the type scale of the variable and
whether it was continuous or discrete.
104
TABLE XXIII
Variabi e
Top vs Sample Hypothesis
Test Used
Intell iqence
GTSCR
Kruskal-Wallis Test
R esults
Resu Its
^
Chisq
"
671
AFQTP
Kruskal-Wallis Test
Chisq
=
1165
OAFQTP
Kruskal-Wallis Test
Chisq
=
1418
EIMCAT
2XC Contingency Table*
Chisq
'-
503
HIYRED
2XC Contingency Table
Chisq
-
931
EDLVL
2XC Contingency Table
Chisq
~
700
POSCR
NCOE
Kruskal-Wallis Test
2 X C Contingency Table
Chisq
-
26.1
Effects
SEX
CMF
2
2
*
RACETH
PAYGD
2
2
«
«
'
C
C
Contingency Table
Contingency Table
Chisq
Chisq
-
C
C
Contingency Table
Contingency Table
Chisq
Chisq
=
"
"
Strongly
reject HO:
Strongly
reject HO:
Strongly
reject HO:
Strongly
reject HO:
Strongly
reject HO:
Strongly
reject HO:
Reject HO:
Strongly
reject HO:
Reject HO:
Strongly
reject HO:
hypothesis is that
For this nonparametric test the null
The alternate hypothesis is
the populations are identical.
With
that one of the populations yields larger observations.
Mann-Whitney
test.
two populations this is equivalent to a
.95
the critical Chisquare value for
level a
of
At
a
rejection is Chisq > 3.84.
^
2For this nonparametric test the null hypothesis is that
the two populations have the same distribution as measured by
the probability of falling into one of the discrete variable
that the
is
The
alternate hypothesis
classifications.
The contingency table is set
distributions are different.
> 1.93 and
for the two rows to be the classification of PRA
PRA < 1.93, the C represents the number of discrete levels in
The Chisquare test statistic is
the variable being tested.
also used for this test with a rejection of HO: when Chisq is
larger than 3.84 at a .95 level a.
105
testing
Hypothesis
simple
means
strength
of
and
the
confirms
variances
of
difference
the
observations
the
study variables.
can
made on
interpretated
be
The
by the
magnitude of the Chi-square statistic.
ANALYSIS OF DISTRIBUTIONS
D.
This
section
investigates
further
distributions for those variables
shifts
the
which conflicted
in
with the
relationships derived in regression and correlation analysis.
Those
variables
were
NCOE
CMF,
PAYGD
and
Again, the
.
conflicts which arose were two-fold.
First/ neither
CMF or PAYGD should have been affected by
subsetting of the PRA variable. The PRA scores are normalized
differences from the average score for every paygrade and CMF
combination.
Assuming
a
policy then, no one CMF or
a
uniform
should
have
of promotion
paygrade should have dominated as
result of subsetting to the
NCOE
application
top three
percent.
Secondly,
slightly rather than decreased
increased
significantly by subsetting to the top three percent.
The three
inconsistencies appear
distributional change.
to be
linked in their
Observation of the three Figures 5.1,
5.2, and 5.3. demonstrate this.
106
1
TOP VERSUS SAMPLE CMF CHANGES
LU
4.
IN
PERCENT
i
<
o
.^JZi
izrv
^^^
^
jziZZ.
21
-4
-
I
-a L
16
11
23
64
54
29
74
92
81
95
CMF
Figure
Figure 5.1 demonstrates
CMF
percentages
away
service support MOS
and
Armor
MOS
'
s
'
s
.
lost
5
.
clearly defined
a
combat arms MOS
from
particular
In
total
a
redistribution of
'
s
to the combat
Infantry, Artillery,
of 15.5 percent,
Administrative Specialists (CMF 71) gained almost
9
while the
percent.
TOP VS SAk/PLE NCOE
CLUSTER BAR
40
30
UJ
^20
ca
Q.
H
10
1
m m
2
3
4
HS.
5
A
6. 7
TOP
SAMPLE
^
1011
rN
B
9
NCOE (1-11)
Figure 5.2
Figure 5.2 demonstrates transfer of
107
a
large percentage of
3
density away from the NCOE 7 to the NCOE
the sample
This was consistent
with
observations
the
Figure 5.1,
in
combat arms NCO's qualify for level
since only
level.
7,
the Combat
Arms Primary Leadership course.
TOP VS SAMPLE PAYGD
CLUSTER BAR
80
60
I-
z
u
o
m
a
g40
CL
TOP
SAMPLE
20
E-5
E-7
Figure
Figure
The last figure.
percentage from
5
.
a
displacement of
E-5 paygrade as a result of
to the
the E-6
shows
5.3,
extracting only the top three percent by measvire of promotion
rate
.
To
offer
explanation
an
these discrepancies
is
discrepancy
may
effects
normalizing
adequate.
by
well
The
mathematical error.
interrelationships
of
difficult.
Some
explained
be
the
PRA
observed
However,
do
the underlying reason for
act
scores
can
be
consistently.
108
of this
in that the removal of
discrepancy
it
measure
was
may
noted
not entirely
be
simple
that their
Specifically, the
reduction
paygrade
in
significantly reduce
likely
that
change
combat
and
the NCOE
NCOE
in
MOS's
both
combine to
level.
As such,
it is more
occured
coincident
changes in the two variables PAYGD and CMF.
demonstrated was
where
one
junior
with the
The effect being
service support
combat
NCO's were dominating promotion achievement.
E.
SUMMARY OF FINDINGS
Comparing the
changes in averages for the top performers
to the regression coefficients
very substantial agreement.
found
Chapter
in
IV,
Specifically, OAFQT was the most
significant intelligence test variable, while HIYRED
significant
most
change
in
OAFQT
variable.
academic
greater
is
HIYRED,
than
than
that
OAFQTP
of
PQSCR, SEX, and
regression
RACETH
Thus,
should
shifted
each
it
still
has
the predictive
more pronounced
be
less significant variables of
The
.
was the
Although the percent
considerably more variance than HIYRED.
ability of HIYRED in
shows
a
small, significant
amount in the appropriate direction.
The only
discrepancy between
change in the variable
been induced
This change
NCOE.
by changes
the two
procedures is the
is felt
to have
in the CMF and PAYGD distributions.
The effect is one where junior
combat service
support NCO's
replace NCO's from the combat MOS's.
An important
observation from
analysis of the top three
percent was that the increase in the value of any explanatory
variable was
not extreme.
In fact,
109
the largest increase was
only twenty-five percent.
NCO's
who
rather than
do
a
little
much better
inference,
As an
better
in a
appears that
in a combination of areas,
single area,
recipients of faster promotion rates.
110
it
are more likely
i
PRINCIPAL COMPONENTS AND FACTOR ANALYSIS
VI.
INTRODUCTION
A.
chapter more advanced statistical procedures are
In this
implemented to better
improve
and
or
Principal components
factor
and
independent variables,
the
simplify the cause-effect model.
least
at
related procedures
summarize
analysis
normally used in investigating
which are
the mutual relationships and communalities of
variables.
of
reduce
to
large number
a
identifying redundant variables, and by
By
variables
constructing composite
possible
two closely
are
it is
of independent explanatory
number
the
originals,
the
of
variables to only those which are significant and unique.
THEORY
B.
Principal components and factor analysis each
algebra
operate
to
on
a
P
use matrix
by P matrix of correlation or
covariance coefficients and produce
a
system
of eigenvectors
of the form:
Y<
3
)
=
ai
J
Xj
+323X2
+
resultant
represents the
linear combination
of the
..apjXp
+
composite
In the notation,
E.
variable
loading coefficients,
loading coefficients multiply each of the
Xo
,
n=l..p.
accounted
resulting
E
by
represents the
the
linear
eigenvectors
which
3
j
is the
.
These
original variables
amount of residual error not
model. CRef.
represent
111
at
Yj
328]
5:p.
a
set
of
The
orthogonal
components jointly perpendicular in the space of the original
variables.
[Ref.
15;p.
These components are jointly
4243
uncorrelated and individually account for levels of variance,
first principal component accounts for the largest
where the
proportion, and the last principal component accounts for the
smallest.
some
characteristic
aggregate
variables.
component may be representative of
resulting
A
example
For
strong factor loadings
a
input
resulting eigenvector which has
variables
original
for
original
the
of
of physical
strength and endurance could be called a factor of stamina as
an
aggregate
analysis
differ
that
in
require that number of
variables
initial
variance.
exists
a
set of
dimension of the
and
components
equal
the
to
account
to
for
the factor method assumes
composites in
original
a
factor
assume and
number of
the
total
that there
dimension smaller than the
number
of
variables
which will
622]
5:p.
.
needed
is
components
principal
components
In contrast,
suffice. [Ref
Principal
measure.
An additional aspect of factor analysis is that it allows
for rotation of the
more
unique
solution with
well-defined
and
there are five variables in
loading factors
in the range
factors by applying
result in
a
a
pattern
zero or close to one.
the intent
components.
nonsingular
to
.4,
linear
a
For example if
have intermediate
factor which
.2
of developing
rotation of common
transformations may
matrix in which the loadings are either
The end result is
112
ea
Ler to interpret
.
than
factor
the
numerous
with
mixed elements
Graphical
.
measures are useful with the rotation procedure and allow the
analyst
to
relative
the
see
uniqueness
the
of
input
variables
C.
RESULTS
The SAS procedure for performing factor analysis was used
with the
method of
component
method.
factor determination being the principal
basic
such,
As
component
principal
analysis was conducted, but limits were applied on the number
of
factors
composite
retained
that
so
would
factors
only
the
significant
The first set of input
kept.
be
most
variables included all of the twelve study variables.
XXIV
shows
each
component
aggregate
resulting
the
is
factors
which contributed
Following Table
an
factor solution.
interpretation
represent.
XXIII is
a
factor
each of the variables is coded by
plot,
any
Appended below
explaining
what the
The original input variables
the factor
most to
Table
a
have been underlined.
plot.
letter.
Figure 6.1,
where
By observing the
lack of uniqueness for a group of variables can be
noted where the coded letters are close to one another.
113
TABLE XXIV
Principal Components Tabular Results
Input Matrix of correlation coefficients
PRIOR COMMUNALITY ESTIMATES: ONE
2
1
EIGENVALUE
DIFFERENCE
PROPORTION
CUMULATIVE
4.0052
2.2717
0.3338
0.3338
EIGENVALUE
DIFFERENCE
PROPORTION
CUMULATIVE
7 FACTORS
0.5392
0.1892
0.0449
0.9372
WILL BE
8
FACTl
EDLVL
.4302
AFQTP
.9515
EIMCAT .9060
-.0085
NCOE
HIYRED .3834
SEX
1735
OAFQT
.9518
GTSCR
.8238
PQSCR
.4001
CMF
1677
PAYGD
.1216
RACETH--.3590
-
.
.
Intell
Tests
4
3
1.7334
0.2355
0.1445
0.4782
1.0634
0.2138
0.0886
0.6910
10
11
9
0.8496
0.0468
0.0708
0.7625
.5861
-.1133
-.1220
-.4507
.6410
.4212
-.1046
-.1128
-.2413
.5200
-.3467
.3130
Acad
FACT3
.5024
-.1195
FACT4
-.2544
.0637
-.0598
.2527
-.3281
.6516
1652
.6668
.4176
-.1113
-.1156
.0090
.1205
-.1449
.6770
.2547
-.
.0590
.0331
-.1150
.4985
.3367
.1229
Career
Status
0.7542
0.2149
0.0628
0.8922
0.0034
0.0003
1.0000
CRITERION
FACTS
-.0624
.0075
-.0096
-.0398
-.0637
.1857
-
-
.0092
-.0464
-.7312
-. 1171
-.1816
.4708
Sex
FINAL COMMUNALITY ESTIMATES: TOTAL
114
0.8028
0.0486
0.0669
0.8294
12
0.3500 0.2809 0.1196
0.0690 0.1613 0.1161
0.0292 0.0234 0.0100
0.9663 0.9897 0.9997
RETAINED BY THE NFACTOR
FACTOR PATTERN
FACT2
7
6
5
1.4979
0.4344
0.1248
0.6031
PQSCR
=
FACT6 FACT7
-.0693 - .029
.1548 - .024
.1478
.011
.0084 - 134
-.0830 - .124
-.0736 -.550
1535 - .023
.1350
.132
-.4527
.115
-.2587
.561
-.0495
.151
.6507
.216
.
.
RACE
10.706622
CMF
1
1
PLOT OF FACTOR PATTERN FOR FACTORl AND FACTORS
FACTORl
B
'
1
G
C
.9
.H
.7
.6
.5
.4
.3
.2
.1
JF
-.9- .8-.7- 6-. 5-. 4-. 3-. 2-.
A
E
I
F
A
K
.
.2
1
-.1
-.2
.3
-.4
-.5
-.6
-.7
-.8
-.9
.3
.4
.5
.6
D7 .8
C
.9
T
L
-
R
3
1
EDLVL=A AFQTP=B EIMCAT=C NC0E = D HIYRED=E SEX=F
OAFQT=G GTSCR=H PQSCR=I CMF = J PAYGD=K RACETH=L
1
Figure
The results
appear to
significant factor is
a
measures:
AFQTP
OAFQTP,
HIYRED.
.
quite reasonable,
composite of all the
factor consists primarily
EDLVL and
6
of
academic
The fourth
factor is
SEX and two other nominal
fifth,
sixth
and seventh
by single variables,
The second
performance measures
The third factor is composed of NCOE and
PAYGD and reflects two closely related
paygrade.
mental aptitude
EIMCAT.
and
GTSCR,
where the most
measures dominated by
predominantly
variables,
CMF
and
a
measure of
PAYGD.
The
factors all appear to be dominated
PQSCR, RACE, and CMF respectively.
115
.
In short,
each of the
twelve
variables
is in
represented in the five factors, the first five
some measure
factors accounting
seventy
over
for
five
percent
of the
By observing the entry for PROPORTION one can see
variance.
that the subsequent seven
.0668
original
.0028
to
of
the
factors
each
contributed between
variance and as such are not major
contributors
Using the results of the first solution
was conducted
each of the
having the
of
solution
factors
the
In
single variable
largest loading factor was selected and the other
related variables
results
second analysis
reduced number of input variables.
with a
initial
a
that
were
eliminated.
solution,
Table
XXI
shows the
and Figure 6.2 shows the Factor
Plot.
116
TABLE XXV
Reduced Principal Components Tabular Results
PRIOR COMMUNALITY ESTIMATES: ONE
Input Matrix of correlation coefficients
EIGENVALUE
DIFFERENCE
PROPORTION
CUMULATIVE
7
2.1666
0.9602
0.3095
0.3095
1.2063 1.0019 0.8703 0.8049 0.7081 0.2416
0.2044 0.1315 0.06540.09670.4665
0.1723 0.1431 0.1243 0.1150 0.10120.0345
0.4819 0.6250 0.7493 0.8643 0.96551.0000
FACTORS WILL BE RETAINED BY THE NFACTOR CRITERION
FACTOR PATTERN
FACTl
FACT2
FACT3
FACT4
FACT5
FACT6
-.5422
.0221
-.3801 -.1071
NCOE
,6941
.2656
-.5162
-.2443 -.4001
HIYRED
.3659
.5302
.3135
SEX
.1803
.6532
1514
.6993
.0899 -.1346
-.0412
-.0668
OAFQT
.0404
.8945
.0502
.2462
-.0374
-.0492
-.1259
.8592
GTSCR
.0154
.3664
- .0613
-.3707
5069
.2537
.7141 -.2648
PQSCR
-.1589
RACETH -.4521
.3275
.5799
.2487
.5031
.
.
Intell
Tests
Acad
NCOE
SEX
FINAL COMMUNALITY ESTIMATES: TOTAL
NCOE
HIYRED
1.0000 1.0000
SEX
1.0000
NOAFQT
1.0000
117
GTSCR
1.0000
PQSCR
=
FACT7
.018
-.004
-.051
-.328
-.328
-.022
.037
Race
7.000000
PQSCR
1.0000
RACETH
1.0000
.
PLOT OF FACTOR PATTERN FOR FACTORl AND FACT0R2
FACTORl
1
E.9D
.8
.7
.6
F
.5
B
.4
.3
.2
F
A
C
.1
.9-
.8-.7-.6A.5-.4-.3-.2-.
.2
.1
1
.3
.4
.5
.6
.7
.8
C
.9 T
-.1
-.2
-.3
-
-
R
2
.2
.4
G
-.5
-.6
-.7
-
.8
-.9
-1
NCOE=A
OAFQT-D
HIYRED=B SEX=C
Figure
Restricting the
6.2
input to
GTSCR-E
PQSCR^F RACETH-G
Factor Plot
the strongest unique variables
results in an almost complete separation into single factors.
The only exception is the grouping of GTSCR and OAFQT,
D)
.
This is not
both scores
the
decision
models makes
suprising
from the
to
considering
the
sense from
GTSCR
the Factor
well
118
from
and
composition of
same set of tests in the ASVAB.
eliminate
(E
Thus,
earlier regression
Analysis perspective as
.
E.
SUMMARY OF FINDINGS
The
application
principal
of
analysis confirmed many of
redundancy
with
the
the
study
choices for unique variables
in Chapter
IV,
and
gave
a
components
patterns
variables.
in the
of
It
and
factor
dependency and
confirmed the
regression as developed
good second opinion for deciding
which variables could be set aside with little
model
119
effect on the
CONCLUSION
VII.
OVERALL FINDINGS
A.
There
proposition
success
that
promotion rate
,
scores
test
statistical
strong
is
is related
the
in
Army,
academic
the most
important
measure,
OAFQT
is
not
nearly
independently affect
as
its
in
substantial changes
represents very
AFQT score
The
and the
time of entry is the more
changes
but
by
future promotion rate.
for a
education at
year of
measured
education at time of entry are
year of
important indicators
The highest
as
background.
explanatory variables of the 1980 normed
individual's highest
support the
to
individual's intelligence
to the
previous
and
evidence
discrete
scale
in academic background.
important
as
HIYRED
and
can
the predicted promotion rate only up to
ten percent.
individual scores
While in service, how well the
Performance Qualification
The statistical evidence
argued by
promotion
explanatory
showing the
measures
for
a
faster promotion rate.
these
observations
can be
existence of significantly increasing
averages
rate
and his attendance at
Test Scores
NCO schooling will be indicative of
on his
in
across
ANOVA
and
ascending
levels
ANCOVA analysis.
of
This
argument can be supplemented, and those differences seen more
concretely, by
a
simpler comparison of top performers verses
120
.
the sample averages
Considerable variance of promotion rate exists across any
of
the
levels
discrete explanatory variables, and
the
of
within any of the categorical variables.
in
designing
effective
an
dependent
controlling categorical variables such
the effects
significant.
There
is a dilemma
While
variable.
as CMF
and Paygrade,
other variables become more apparent and
of the
ability of
However, the
the model
to explain
variance is significantly diminished.
Selecting
explanatory
set
a
variables
important
most
the
of
achieved
was
via
methods.
two
successive, increasing dimension procedure distilled
explanatory
unique
variables.
developing detailed
process
familiarity with
hypothesis
insignificant
variable from
testing
contributors
and
used
principal components,
was confirmed
method
a
set of
relied
to
A
upon
In
the
eliminate
identify the most important
group of related variables.
a
a
each variable.
was
explanatory variables
set of
method
This
unique
and
which
uses
This restricted
with the use of
a
mathematical
approach to identify orthogonal and unique variables.
When
met
inferential
using
assumptions,
regression
nonparametrically
procedures
.
Further,
the resulting model
parametrically
both
model
the
estimates
and
are
reproducable with an alternate data set.
Although the model is technically acceptable,
accurate
in
predicting
promotion
121
values
for
it is only
population
The low R2 value
subcategories.
found
terms
and high
regression
during
were
manifested
predictions
making
mean square error
based
in
model
incremental
testing.
When
changes in
AFQT the sample data values were close, but upper
and lower bounds were
large
so
on
resulting predictions
that
were not usefull.
The
performance
poor
predictive
the
of
attributed to two possible reasons.
some unspecified
better account
significant
First, that there exists
predictor variable
variance.
for
inexplicable
model can be
which could
chance
there exists
secondly,
Or
occurance
the
in
be used to
of
a
promotion rate for any given individual.
In the case of
that
number
the
the first
available
of
entries
were
felt
variable.
expressing the
variables
entries
held
on
a
is limited.
given
Of the
and forty data fields, this study considered all
which
explanatory
should be observed
it
or MILPERCEN
individual at either DMDC
one hundred
reason,
considered
variables was reduced to
and
predictors.
To
only six.
measures
unique
discover
additional
merit
Of
number
of
Overall,
available
as an
versions
several
quality.
final
the
potential
included
This
fundamental
same
significant
have
to
the twelve
significant
there are few
to
use
as
explanatory variables
would require establishment of new personnel data elements in
those data bases.
report averages,
candidates
Pot ntial
or
p'
sibly,
122
the results
include evaluation
of a personality
composite test.
Alternatively, the quality of information on
performance
academic
inclusion
grade
of
periods.
could
increased,
be
averages
from
such
as
the
school attendance
high
The utility of this additional data would then have
to be evaluated in a manner similar to this thesis.
The second reason given
explanation, for
and
not
resolution of
deterministic
even
a
more probable
a
physical
phenomenon.
Although
mathematical remedy,
this condition
with the
does not
the judgement of whether or not
small, highly variable measure of trend
still lies
The
cause effect relationship is more subtle and
a
more difficult to verify.
have a
is
the subject matter of this study is people,
more
a
error
for
is sufficient
analyst and his ability to present that
judgement to decision makers.
B.
POLICY RECOMMENDATIONS
The first question that must be answered in
is whether
or not
having a predictive model is necessary to
make policy decisions regarding promotion or
answer offered
and
accession.
in this document is that it is not.
sufficiently reliable information
testing
this section
subpopulation
resulting
analysis
to
The
There is
from hypothesis
make
cogent
observations and decisions with.
From the results of this investigation,
makers should
HIYRED.
than
a
accession policy
closely manage the two attributes of OAFQT and
This recommendation
proposal.
is more
a
confirmation, rather
The 1984 Defense Authorization Act already
123
.
.
category and
places constraints on AFQT
high school diploma
status
in-service attributes that should be managed are
The two
the Performance Qualification Score,
form of promotion points or
NCO's of less potential
aggressiveness
and
more competent
lessening of
minimum threshold
a
scale would
Unfortunately, this may artificially force
approach.
with the
at NCO
To directly tie scores on these attributes in the
schooling.
be one
attendance
and
individuals.
discriminatory
the
into categories
The result
effectiveness
of
may be a
the two
measures
If
score
the
and
promotion
individual
policy,
directly
should not mean that
promotion
either
of
variables
to
not
tying these
values or thresholds
points
measure
independent
these
of
However,
better.
be
to
ability
the
to achieve his or her
education
in-service
pursue
discriminate would
scores
allowed
were
would
be
unused.
A
policy where promotion boards were still instructed to review
an individual's scores,
inclusive
with notification
of this
review policy to the NCO population allows for self selection
by the more ambitious individuals.
C.
SUGGESTIONS FOR FURTHER RESEARCH
One disturbing observation of this study was the apparent
disparity among
promotion
race and
rates.
explanation of
As
ethnic groups in terms of AFQT and
pointed
out
by
Daula
(1985)
the
this disparity cannot be seen in an aggregate
124
promotion
approach
approach,
data
with
time.CRef. 11 pp
:
is
a
result
subcategory
set
a
.
7-9]
of
group
of
duration
a
individual
soldiers
model
over
His paper reports that this disparity
Specifically, the shifting of
attrition.
promotion
retention patterns
rather,
but
averages
is
a
result
of different
among race and ethnic groups, and not due
to a racialy sensitive promotion system.
A
for
study to determine the magnitude and underlying reasons
the
different
retention
patterns,
hypothesis, would have considerable merit.
125
and
to
test this
APPENDIX
A
CAREER MANAGEMENT FIELDS AND FREQUENCIES
MOSNAME
Infantry
Cbt Engineer
Artillery
Air Defense
Special Ops
Armor
Hawk Missile
Nike Missile
Tac Radar
Tac Radar
Communication
Elect Warfare
Tech Drafter
Chem Warfare
Explosive Ord
Repair
Cargo Spec
A/C Repair
Admin Spec
Programmer
Supply
Recruiter
Topo Eng
AV Spec
Medical
Lab Spec
Air Traffic
Food SVC
Mil Police
Intelligence
Musician
EW/SIGINT
CMF
11
12
13
16
18
19
23
27
28
29
31
33
51
54
55
63
64
67
71
74
76
79
81
84
91
92
93
94
95
96
97
98
FREQUENCY
4320
1030
2780
851
244
2434
187
352
40
625
3265
PERCENT
11.4
2.7
7.3
2.2
0.6
6.4
0.5
0.9
0.1
1
.7
8.6
0.1
1.6
1.4
30
619
529
400
3766
1041
1090
3020
423
2677
106
65
157
2498
444
175
919
1674
789
176
1125
1.1
9.9
2.8
2.9
8.0
1.1
7.1
0.3
0.2
0.4
6.6
1.2
0.5
2.4
4.4
2.1
0.5
3.0
126
CUMULATIVE CUMULATIVE
FREQUENCY PERCENT
4320
5350
8130
8981
9225
11659
11846
12198
12238
12863
16128
16158
16777
17306
17706
21472
22513
23603
26623
27046
29723
29829
29894
30051
32549
32993
33168
34087
35761
36550
36726
37851
11 .4
14.1
21.5
23.7
24.4
30.8
31 .3
32.2
32.3
34.0
42.6
42.7
44.3
45.7
46.8
56.7
59.5
62.4
70.3
71.4
78.5
78.8
79.0
79.4
86.0
87.2
87.6
90.0
94.5
96.6
97.0
100.0
APPENDIX
B
AFQT TRANSFORMATION EQUIVALENT SCORES
Armed Forces Qualification Test (AFQT)
Equivalent Percentile Scores for 1944
Mobilization Population and 1980 Youth Population
1944
1980
1
1
2
3
1
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
2
2
3
4
5
6
6
8
8
10
11
12
14
15
16
17
18
19
21
22
23
24
25
26
26
27
28
29
30
31
32
1944
1980
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
33
34
35
35
36
37
38
38
39
40
41
42
42
43
44
46
47
48
49
49
50
51
52
53
54
56
57
58
59
60
62
63
65
127
1944 980
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
83
84
85
87
89
91
92
93
94
95
95
97
98
98
99
99
99
D
.
LIST OF REFERENCES
Theory
Torgerson, W.S.,
1.
Wiley & Sons, Inc., 1958.
and
Methods
of
Scaling
,
John
Douglas, B.A., An Analysis of the Academic Composites of
Apritude Battery
(ASVAB) and
the Armed Services Vocational
Sections of the Preliminary Scholastic
the Math
and Verbal
Aptitude Test (PSAT), the Scholastic Aptitude Test(SAT), and
(ACT):
the American College Test
A Correlation Study
PH
Southern Illinois University at Carbondale,
Dissertation,
1986.
2.
,
.
Jenson A R
Test Reviews, ASVAB, in Measurement and
Evaluation in Counseling and Development
University of
California, Berkely, April 1985.
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,
,
SAS Institute
Inc., SAS User's Guide:
SAS Institute Inc., 1985.
4.
Edition
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5
Basics Version
5
,
SAS Institute Inc., SAS User's Guide;
Edition SAS Institute Inc., 1985.
Statistics Version
,
Research
June 1986.
6.
IBM
Manual
,
Yorktown Heights,, GRAFSTAT Introductory
Schatzoff,
M.,
and others.
Regression Analysis in
Yorktown
GRAFSTAT IBM
Research Center, June 1986.
7.
,
Scribner, B.L.,
and others.
Are Smart Tankers Better?
Armed Forces &
AFQT and Military Productivity
pp. 193-206,
Winter 1986.
Society, Vol 12 No 2.,
8.
,
9.
Dunbar,
S.B.,
and others.
Training for Males and Females;
Specialties and ASVAB Forms 6 and 7
University of Iowa, February 1985.
On Predicting Success in
,
Marine Corps Clerical
Cada Research Group, The
10.
Department of Defense, Office of the Assistant Secretary
(Manpower, Installations, and Logistics)., Report
of Defense
Services Defense
to the House and Senate Committees on Armed
Manpower Quality, Volume II Army Submission May 1985.
,
11.
Estimating Time to Promotion for Promotion
Daula, T.
Paper presented at The Information
for Enlisted Soldiers
Management/Operations Research Society of America Conference,
Boston, MA., July 1985.
,
Chambers, J.M., and others.. Graphical Methods
Analysis Wadsworth, 1983.
12.
,
128
for Data
Conover W.J.,
Practical Nonparametric Statistics
13.
Wiley & Sons, Inc., 1971
,
John
Baldwin R.H., Documenting Personnel Quality Requirements
14.
United States Military Academy,
with Statistical Analysis
December 1985.
,
and
15.
Berenson,
M.L.
others.
Intermediate Statistical
Methods and
Application,
A
Computer Package Approach
Prentice-Hall, Inc., 1983.
,
129
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Copies
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2.
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2
3.
Superintendent, Code 55Lw
Attn: Prof. P.A.W.
Lewis
Naval Postgraduate School
Monterey, California 93943-5000
1
4.
Superintendent, Code 55La
Attn: Prof. Larson
Naval Postgraduate School
Monterey, California 93943-5000
1
5.
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ATTN:
The Pentagon
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2
6.
Cpt Jim Lewis
SMC 2096
Naval Postgraduate School
Monterey, California 93943-5000
1
7.
Cpt.
Jerry B. Warner
6724 Danforth St.
McLean, Virginia 22101
1
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MOTORS
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Thesis
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Warner
Analysis of intelligence and academic
scores as a predictor o£
promotion rate for U.S.
Army Noncommissioned
Officers.
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