A COMPARISON OF AMERICAN COLLEGE TEST (ACT) SCORES AND
COLLEGE CUMULATIVE GRADE POINT AVERAGES
by
Bruce C. Rowe
A thesis submitted to the
Department of Education at
Western Montana College
in partial fulfillment of the requirements
for the degree of
Master of Science in Education
Western Montana College
Dillon, Montana 59725
April, 1988
SIGNATURES AND APPROVALS
This thesis has been examined and approved for acceptance by the
Department of Education, Western Montana College, Dillon, Montana,
on this 29th day of April, 1988.
Graduate Committee:
Dr. Nyles Humphrey, Chair 4u~,
Dr. John Rogan, Member 1 .-vi i2 ~, '==
Graduate Council: r
Dr. Henry Worrest, Chair
STATEMENT OF PERMISSION TO COpy
In presenting this thesis in partial fulfillment of the requirements
for an advanced degree at the Western Montana College, I agree that the
library shall make it freely availble for inspection. I further agree that
permission for extensive copying of this thesis for scholarly purposes may
be granted by my major professor or, in his absence, by the head librarian.
It is understood that any copying or publication of this thesis for finan-cial
gain shall not be allowed without my written permission.
ABSTRACT
"A Comparison of American College Test (ACT) Scores and College Cumulative
Grade Point Averages," by Bruce C. Rowe (Western Montana College, Dillon,
Montana, April, 1988).
This study addresses the question: Can the American College Test (ACT)
be used to predict a Montana college student's cumulative grade point
average?
Considered in the study are first-time freshmen who graduated with a
baccalaureate degree from either Western Montana College or the Montana
College of Mineral Science and Technology in 1985, 1986 or 1987. Analyses
of statistical data yield interpretations of measures of central tendency,
measures of variability, simple regression and multiple regression.
Focus of the conclusions is the statistical fact that the ACT composite
score accounts for 25% of the variance in a student's cumulative grade point
average on completion of his baccalaureate requirements. The composite
score is a significant statistical factor in projecting the cumulative grade
point average.
Specific recommendations are offered for use of the report's findings
in determining admission standards. Based as it is on actual student
records from two heterogeneous institutions in the same state, the study is
a statistically reliable analysis with applicability beyond the two colleges
studied--almost certainly to other Montana colleges and universities, and
quite possibly to other Northwest institutions. However, cautions should be
exercised against using the ACT composite score as the sole criterion in
establishing admission standards. Employed within the limits suggested, the
conclusions offer a new measuring tool sufficiently significant to demand
consideration in discussions of college admission standards.
Acknowledgements
Chapter One--Research Problem
Introduction
Statement of the Problem
Delimitations
Hypothesis
Assumptions
Definitions
Justification •
Chapter Two--Research Process
Review of Existing Studies
Research Design •
Sample
Methods
Procedures
Chapter Three--Results
Montana Tech
Table of Contents
Measures of Central Tendency for Montana Tech
All Montana Tech Majors
All Montana Tech Engineering Majors
All Montana Tech Engineering and Science Majors
All Montana Tech Arts and Sciences Majors
Page
i
1
1
2
2
3
3
3
4
5
5
6
6
7
8
10
10
12
12
17
18
19
All Montana Tech Non-Engineering and
Non-Science Majors ••••• . . . . . . .
Measure of Central Tendency (Mean) with the Measure of
Variability (Standard Deviation) for Montana Tech
All Montana Tech Majors ••••••• . . . .
All Montana Tech Engineering Majors •
All Montana Tech Engineering and Science Majors •
All Montana Tech Arts and Sciences Majors
All Montana Tech Non-Engineering and
Non-Science Majors
Simple Regression
Multiple Regression
Western Montana College •
Measures of Central Tendency for Western
Montana College
. . .
Measure of Central Tendency (Mean) with the Measure
of Variability (Standard Deviation) for Western
Montana College •
Simple Regression
Page
20
21
21
24
26
28
30
32
38
44
44
45
47
Multiple Regression • • • • 51
Chapter Four--Summary, Conclusions, and Recommendations • • • • 53
Montana Tech
Western Montana College • •
Conclusions and Recommendations • •
Bibliography •• • • • • • • •
. . . . 55
66
71
74
Table 3.1
Table 3.2
Table 3.3
Table 3.4
Table 3.5
Table 3.6
Table 3.7
Table 3.8
Table 3.9
List of Tables
English ACT measures of central tendency for
all Montana Tech majors . . . . . . . .
Mathematics ACT measures of central tendency for
all Montana Tech majors . . . .
Social Science ACT measures of central tendency for
all Montana Tech majors . . . . . . . . .
Natural Science ACT measures of central tendency for
all Montana Tech majors . . . . . . .
Composite ACT measures of central tendency
all Montana Tech majors •••••••••
Composite ACT measures of central tendency
all Montana Tech engineering majors
for
for
Composite ACT measures of central tendency
Montana Tech engineering and science majors
Composite ACT measures of central tendency for
all Montana Tech arts and sciences majors
Composite ACT measures of central tendency for
all Montana Tech non-engineering and non-science
for all
. . .
majors ••••• . . . . .
.
Table 3.10 The means and standard deviations for all Montana Tech
majors in each of the ACT score categories and in
cumulative grade point averages • • • • •
Page
12
13
14
15
16
17
18
19
20
21
Table 3.11 Norms profile based on ACT test scores and high
school grade averages of college-bound high school
Page
graduating seniors 1984-85-86 •••• •• • • • 22
Table 3.12 A comparison of the mean ACT scores of all Montana
Tech majors (1985-87) and their estimated percentile
ranks based on ACT's normed group (1984-86)
Table 3.13 The means and standard deviations for all Montana Tech
engineering majors in each of the ACT score categories
and in cumulative grade point averages
Table 3.14 A comparison of the mean ACT scores of all Montana
Tech engineering majors (1985-87) and their estimated
percentile ranks based on ACT's normed group
(1984-86)
Table 3.15 The means and standard deviations for all Montana Tech
engineering and science majors in each of the ACT
score categories and in cumulative grade point
averages • •
Table 3.16 A comparison of the mean ACT scores of all Montana
Tech engineering and science majors (1985-87) and
their estimated percentile ranks based on ACT's
normed group (1984-86) • • . . . . .
Table 3.17 The means and standard deviations for all Montana
Tech arts and sciences majors in each of the ACT
score categories and in cumulative grade point
averages • • • • . . . . . . .
23
24
25
26
27
28
Table 3.18 A comparison of the mean ACT scores of all Montana
Tech arts and sciences majors (1985-87) and their
estimated percentile ranks based on ACT's normed
group (1984-86) . . . . . . . . . .
Table 3.19 The means and standard deviations for all Montana Tech
non-engineering and non-science majors in each of
the ACT score categories and in cumulative grade
point averages • • • • •
Table 3.20 A comparison of the mean ACT scores of all Montana
Tech non-engineering and non-science majors (1985-87)
and their estimated percentile ranks based on ACT's
normed group (1984-86) ••••
Table 3.21 Simple regression statistics based on the English
ACT score for all Montana Tech majors . . . . . . .
Table 3.22 Simple regression statistics based on the Mathematics
ACT score for all Montana Tech majors
Table 3.23 Simple regression statistics based on the Social
Science ACT score for all Montana Tech majors
Table 3.24 Simple regression statistics based on the Natural
Science ACT score for all Montana Tech majors
Table 3.25 Simple regression statistics based on the Composite
ACT score for all Montana Tech majors •••••
Table 3.26 Multiple regression equation statistics for all
Montana Tech maj ors •••• • • • • • • • • • •
Page
29
30
31
33
34
35
36
37
39
Table 3.27 Multiple regression equation statistics for all
Montana Tech engineering majors . . . . . . . .
Table 3.28 Multiple regression equation statistics for all
Montana Tech engineering and science majors
Table 3.29 Multiple regression equation statistics for all
Montana Tech non-engineering majors
Table 3.30 Multiple regression equation statistics for all
Montana Tech non-science and non-engineering
majors •
Table 3.31 The five ACT scores and their measures of central
tendency for Western Montana College • . . . . . . .
Table 3.32 The means and standard deviations for Western Montana
College in each of the ACT categories and in cumulative
grade point averages • • • • • • • • • • • • •
Table 3.33 A comparison of the mean ACT scores at Western Montana
College (1985-87) and estimated percentile ranks based
Page
40
41
42
43
44
45
on ACT's normed group (1984-86) ••••• 46
Table 3.34 Simple regression statistics based on the five ACT
scores at Western Montana College
Table 3.35 Multiple regression equation statistics for Western
Table 4.1
Montana College . . . . . . . . . . . . . .
Composite score ranges with equivalent percentile
rank for Montana Tech majors when compared with
scores and ranks of the ACT-normed group
48
52
57
Table 4.2
Table 4.3
Table 4.4
Table 4.5
Standard deviation and ACT-normed group percentile
rank comparisons among the all-majors group, the
engineering subgroup, and the arts and sciences
subgroup • • • •
All Montana Tech majors' ACT scores with their
correlations, correlations squared, and standard
errors • • • • • • • •
Composite score ranges with equivalent percentile
rank for Western Montana College majors when
compared with scores and ranks of the ACT-normed
group •••••••
All Western Montana College majors' ACT scores
with their correlations, correlations squared,
and standard errors . . . . . . . . . . .
Page
59
60
67
69
Figure 4.1
Figure 4.2
Figure 4.3
Figure 4.4
Figure 4.5
Figure 4.6
Figure 4.7
Figure 4.8
List of Figures
The ACT Composite score standard deviations for
all Montana Tech majors (1985-87)
The cumulative grade point average standard
deviations of all Montana Tech majors (1985-87)
Band of confidence for a predicted grade point
average in cases wherein the student scored 25
on the MACT •
A 68% band of confidence built around a predicted
grade point average of no less than 2.00
Band of confidence for a predicted grade point
average when the student scored 25 on the MACT
and 21 on the EACT
The ACT Composite score standard deviations for
all Western Montana College majors (1985-87)
The cumulative grade point average standard
deviations of all Western Montana College majors
(1985-87) •• . . . . . .
Band of confidence for a predicted grade point
average in cases wherein the student has scored
25 on the NACT •••••• • • • • • • • • • •
Page
56
58
62
63
65
66
68
70
****************************************
DEDICATION
I dedicate this document to Warren Barnes from the Montana Tech
graduating class of 1987 in gratitude for his unwavering support
and for his confidence in my ability to make a contribution to
the field of education.
****************************************
ACKNOWLEDGEMENTS
Special thanks to Dr. Nyles Humphrey and Dr. John Rogan at Western
Montana College for their encouragement and enthusiasm throughout my work on
this project. To my mother, family, and friends, I would like to acknowledge
my appreciation for continuous support throughout this study. Also, I
wish to thank those who allowed me to access needed records: at Montana
College of Mineral Science and Technology, Chuck Nelson and Arlene Holland;
and at Western Montana College, Larry Hickethier and Betty Hanson. I appreciate
the special help and attention provided me by Bill Schmidt and Jim
Michelotti, at Montana Tech, who assisted me with SPSS-X and with the generation
of statistics. To Sister Ann Delores Ybarrola and Sister Maryann
Benoit of the College of Great Falls, Montana, I wish to extend my gratitude
for structural suggestions and for proof-reading expertise.
A very special thanks to my sister, Betty McManus of Butte, Montana,
who typed this thesis; and to my niece, Kim McManus, who worked diligently
in assisting me with computer work on statistics.
I also appreciate the support and information provided to me by the
personnel at the American College Testing Program, Iowa City, Iowa: Maureen
Farmer, John Maxey, and Mark Ruger.
In advance, I salute those who will use this study's information with
good judgment and integrity.
CHAPTER ONE
RESEARCH PROBLEM
I. INTRODUCTION
Studies to determine how well the American College Test (ACT) can
predict college success continuously engage scholars throughout the United
States of America. Most studies address correlations of college freshman
ACT scores with first year college grade point averages. However, the
present study examines the academic records of only those students who
successfully completed the course work for baccalaureate degrees either at
Montana College of Mineral Science and Technology (Montana Tech) or at
Western Montana College. Those students' cumulative grade point averages at
college level are correlated with their ACT scores. Success is therefore
defined in this study as the completion of a group of required subjects at
an institution and the consequent earning of a baccalaureate degree. In
both Colleges, the minimum acceptable cumulative grade point average for a
baccalaureate degree is a 2.00 on a 4.00 scale.
The value of such a study may be helpful to those in higher education
at these Colleges who may use the ACT test results as a predictor of
academic achievement at the College. As with all studies of this nature,
comparisons between these two institutions should not be made on the basis
of the findings presented here, since many factors unrelated to this study
contribute to the differences at each school. Examples may include differences
in student body composition, in mean ACT score, in type of faculty,
and in standards for grading.
-1-
Western Montana College is one of six units of higher education in the
Montana University System. Its emphasis is on a liberal arts-based education.
The school has had a long history of excellence in the granting of
degrees in education and related fields.
The Montana College of Mineral Science and Technology (Montana Tech) is
also one of the six units composing the Montana University System. The
emphasis of Montana Tech is in the engineering and science-related fields.
It has been recognized for many years as a reputable minerals engineering
school.
II. STATEMENT OF THE PROBLEM
The problem was to determine if a significant correlation exists
between ACT scores of entering students and their cumulative grade point
averages upon completion of baccalaureate degrees at selected Montana
colleges.
III. DELIMITATIONS
This study was delimited to the following:
(1) Montana Tech and Western Montana College.
(2) ACT scores.
(3) Cumulative grade point averages.
(4) Entering first-time freshmen who graduated in May 1985,
1986, 1987.
-2-
IV. HYPOTHESIS
There will be no significant correlation between the students' performance
on the ACT test and the students' cumulative grade point averages at
either institution.
V. ASSUMPTIONS
The following assumptions were made:
(1) All students performed to the best of their ability on the
ACT and in course work at the College.
(2) The information obtained from the College records was
accurate, reliable, and complete.
(3) The claimed validity and reliability of the ACT test were
accurate.
VI. DEFINITIONS
(1) AMERICAN COLLEGE TEST (ACT)--a norm-referenced test which is composed
of four test modules: English (EACT), Mathematics (MACT), Natural
Science (NACT), and Social Science (SACT). This test, widely
accepted by colleges and universities for admission to their
institutions, claims to predict academic success.
(2) College--Montana Tech, Western Montana College
(3) Composite score (CACT)--the average of the four test modules on the
ACT.
(4) cumulative grade point average (cgpa)--the average of all grades (A, B,
C, D, or F) earned at the College based on a 4.00 scale.
-3-
(5) first-time freshmen--students who entered the College without prior
course work from another post-secondary institution.
(6) transfer student--a student who has transferred from another postsecondary
institution after having accrued 15 or more semester
credits.
VII. JUSTIFICATION
The Board of Regents for the State of Montana is considering changing
the minimum ACT composite score for first-time freshmen entering the Montana
University System. This study will adhere to guidelines for pursuit of a
baccalaureate degree as outlined by the College catalogs specified by the
Board of Regents. The information in this report may be used to enhance the
board's efforts in establishing College admission standards.
-4-
CHAPTER TWO
RESEARCH PROCESS
I. REVIEW OF EXISTING STUDIES
The writer solicited information from American College Test officials
in Iowa City, Iowa. ACT personnel do not research possible correlations
between ACT scores and graduating cumulative grade point averages. Among
reasons cited for not attempting the research was the difficulty in gathering
the information needed from colleges and universities. Officials of ACT
expressed an interest in this study and offered help should the writer
encounter problems compiling the statistics.
ACT officials referred the writer to the University of Utah where they
thought a related study might have been completed. Contact with the
University, first by telephone and then in person, revealed that no such
attempt has been made by the Department of Institutional Research.
The only material available from ACT was correlation studies which had
used ACT scores along with high school grade point averages to predict
college freshmen's grade point averages. A limited number of papers on
juniors showed the same results as did the study of freshmen.
An ERIC search determined that no pertinent literature existed regarding
a comparison of ACT scores and college graduates' cumulative grade point
averages.
The writer arranged an appointment with the registrar at each College
to determine a time when the needed information for this study could be
obtained.
-5-
II. RESEARCH DESIGN
An ex post facto design was used in this study. All students had
already taken the ACT test and are graduates of either the Montana College
of Mineral Science and Technology or Western Montana College with baccalaureate
degrees. Data including ACT scores and college cumulative grade point
averages were gathered from the historical records located in the respective
registrar's offices.
III. SAMPLE
(1) The sample includes all students who began at the College as
first-time freshmen and who graduated in 1985, 1986, or 1987 with
fewer than 12 semester credits of transfer credit from another
institution. All cases are included from all years of the study.
(2) The information regarding each individual includes the following
data: College I.D., last name, first name, sex, birth year, date
of graduation, College class rank, high school class rank, English
ACT, Math ACT, Social Science ACT, Natural Science ACT, Composite
ACT, credits attempted, credits earned, grade points, cumulative
grade point average, date of entry to College, College, major,
minor, dual degrees.
(3) Not all information was available for each individual. However,
no person is excluded from the study if his/her record contained
the cumulative grade point average and ACT raw scores.
-6-
(4) If ACT scores were not available or if the student was a transfer
student as defined, no data were collected on that individual.
IV. METHODS
(1) With permission of the College, in each of the two registrars'
offices the hard copy permanent academic record was accessed. The
information obtained from the transcript was student data pertaining
to the work accomplished at the College. This information
included the College I.D., student last and first names, birth
year, entry date, graduation date, major, minor, sex, cumulative
credits attempted, cumulative credits earned, cumulative grade
points, cumulative grade point average, College class rank, dual
degrees.
(2) Additionally, in the registrars' offices, the hard copy admission
information was obtained from the entry records. The information
gathered from the files included ACT scores and high school class
rank.
(3) Personally identifiable information was collected initially to
proof the records and to provide ready access in case of need to
correct any improperly recorded information. No personally
identifiable information is reported in the study.
(4) All data were transferred by data entry into a main frame DEC VAX
11/782. The material was proofed by two individuals to reduce
potential errors in data entry.
-7-
(5) The SPSS-X software package was used to process all data and to
generate the statistics needed for the analyses that follow.
V. PROCEDURES
(1) A VAX 11/782 was used for data storage and processing. SPSS-X was
used for the statistical analyses. Included in the study were a
spreadsheet, graphs, correlations, and regression analysis and
other appropriate treatments of the data.
(2) An analysis of the results determined if there were significant
correlations between the variables.
(3) Using SPSS-X, the following data were generated for both ACT
scores and College grade point averages:
(a) measures of central tendency (mean, median, mode).
(b) measures of variability (range, variance, standard
deviation).
(4) The Pearson Product-Moment formula was used to determine the
following correlations:
(1) ACT English: cgpa
(2) ACT Mathematics : cgpa
(3) ACT Social Studies : cgpa
(4) ACT Natural Science : cgpa
(5) ACT Composite : cgpa
-8-
(5) A stepwise multiple regression was used in a prediction formula,
wherein the four (4) ACT raw scores served as criteria to predict
the cumulative grade point average. The model used was as
follows:
cgpa Constant + ACT (ENG) + ACT (MATH) + ACT (SS) + ACT (NS)
A simple regression was used in a prediction formula wherein the
ACT Composite score was used to predict the cumulative grade point
average. The model used was as follows:
cgpa Constant + ACT (COMP)
-9-
CHAPTER THREE
RESULTS
Since the two Colleges are different in role and scope, the data and
the analyses provided in this section are separated into two distinct
groups. The first section deals with the data from Montana Tech and the
second deals with the data from Western Montana College.
I. Montana Tech
For Montana Tech, the data are separated into three subgroups: data
for 1985, for 1986, and for 1987. The three years are then studied as a
group. ACT uses at least 100 scores as a sample to obtain an adequate
number for a valid study. Montana Tech data are as follows:
1985 93
1986 110
1987 118
Total 321
The only year below the accepted 100 sample is 1985 (-7%). Since all
other enrollments are above the accepted sample size of 100 used by ACT, the
three are treated separately.
Additionally, Montana Tech subgroups are shown according to academic
major within the institution. The subgroups consist of the following:
-10-
All Majors--engineering degrees: engineering science, environmental,
geological, geophysical, metallurgical, mineral processing,
mining, and petroleum.
arts and sciences degrees: business administration, chemistry,
computer science, mathematics, occupational safety and health,
and society and technology.
Engineering majors--engineering science, environmental, geological,
geophysical, metallurgical, mineral processing, mining, and
petroleum.
Arts and Sciences majors--business administration, chemistry, computer
science, mathematics, occupational safety and health, and
society and technology.
Engineering and Science majors--engineering science, environmental,
geological, geophysical, metallurgical, mineral processing,
mining, petroleum, chemistry, computer science, mathematics,
and occupational safety and health.
Non-engineering and non-science majors--business administration and society
and technology.
-11-
A. Measures of Central Tendency for Montana Tech
1. All Montana Tech Majors.
In measuring central tendency, all majors are included in each of the
five ACT scores. Table 3.1 shows how the English ACT scores compare in each
of the three years and in the total of the three years.
N
93 (1985)
110 (1986)
118 (1987)
321 (1985-86-87)
Table 3.1
English ACT measures of central tendency
for all Montana Tech majors.
MEAN
19.53
20.04
20.03
19.89
-12-
MEDIAN
20.00
20.00
20.00
20.00
MODE
21.00
18.00
22.00
22.00
In Table 3.2, when the Mathematics ACT scores are compared, it can be
noted in all cases that the mean is slightly smaller than the median, but
this deviation represents a normal distribution of scores. The total group
shows a negative skew.
N
93 (1985)
110 (1986)
118 (1987)
321 (1985-86-87)
Table 3.2
Mathematics ACT measures of central tendency
for all Montana Tech majors.
MEAN
22.85
23.75
23.50
23.40
-13-
MEDIAN
23.00
24.00
24.00
24.00
MODE
20.00
27.00
24.00
27.00
In Table 3.3, the Social Science ACT scores are compared. The
variation between measures of central tendency indicates a normal
distribution. The total again shows a slightly negative skew.
N
93 (1985)
110 (1986)
118 (1987)
Table 3.3
Social Science ACT measures of central tendency
for all Montana Tech majors.
321 (1985-86-87)
MEAN
21.53
22.35
21.59
21.83
MEDIAN
22.00
24.00
22.00
23.00
-14-
MODE
21.00
20.00
18.00
27.00
Table 3.4 illustrates the measures of central tendency for the Natural
Science ACT scores. In each case, the mean is lower than the median by a
small amount, indicating a normal distribution of scores in each case. All
cases, except those in 1986, show a slight negative skew.
N
93 (1985)
110 (1986)
118 (1987)
Table 3.4
Natural Science ACT measures of central tendency
for all Montana Tech majors.
321 (1985-86-87)
MEAN
25.96
25.83
26.20
26.00
MEDIAN
28.00
26.00
27.00
27.00
-15-
MODE
31.00
24.00
31.00
31.00
In Table 3.5, the Composite ACT score measures of central tendency are
compared. All three measures of central tendency are numerically similar,
indicating a normal distribution.
N
93 (1985)
110 (1986)
118 (1987)
321 (1985-86-87)
Table 3.5
Composite ACT measures of central tendency
for all Montana Tech majors.
MEAN
22.60
23.15
22.99
22.93
-16-
MEDIAN
23.00
23.00
23.50
23.00
MODE
25.00
20.00
24.00
21.00
2. All Montana Tech Engineering Majors
The measures of central tendency for all engineering majors at Montana
Tech include only the Composite ACT score. The mean in all years is numerically
similar to the median and mode, indicating that normal distribution
is present. (See Table 3.6.) When compared with Table 3.5, the engineering
majors' mean scores differ from those of all other majors by +.70 when the
totals (1985-87) are compared; therefore, the difference between these two
subgroups is negligible.
N
63 (1985)
70 (1986)
65 (1987)
198 (1985-86-87)
Table 3.6
Composite ACT measures of central tendency
for all Montana Tech engineering majors.
MEAN
23.29
24.17
23.39
23.63
-17-
MEDIAN
23.00
24.00
24.00
24.00
MODE
23.00
20.00
21.00
21.00
3. All Montana Tech Engineering and Science Majors
The Composite ACT score is again used to compute the measures of
central tendency for the engineering and science majors. In all years, a
slight variation between the measures of central tendency indicates a normal
distribution. The difference between the scores of all the engineering and
science majors and all majors group in Table 3.5 is +.84 between means.
This group is approximately one raw score above the mean of the all-major
group.
Table 3.7
Composite ACT measures of central tendency
for all Montana Tech engineering and science majors.
N
82 (1985)
81 (1986)
93 (1987)
256 (1985-86-87)
MEAN
23.21
24.41
23.70
23.77
-18-
MEDIAN
23.50
25.00
24.00
24.00
MODE
25.00
20.00
24.00
25.00
4. All Montana Tech Arts and Sciences Majors
Fewer student scores are available for the arts and sciences majors.
Therefore, no interpretation of this subgroup is given. The data are
provided as information only and are available for use should the enrollment
in these areas increase at a later date.
N
30 (1985)
40 (1986)
53 (1987)
Table 3.8
Composite ACT measures of central tendency
for all Montana Tech arts and sciences majors.
123 (1985-86-87)
MEAN
21.17
21.35
22.51
21.81
MEDIAN
21.50
21.00
23.00
22.00
-19-
MODE
26.00
17.00
24.00
20.00
s. All Montana Tech Non-Engineering and Non-Science Majors.
Again, in the non-engineering and non-science majors subgroup the
sample size is too small to permit a valid prediction. Therefore, the data
are provided for information only, and no interpretation is provided.
Should the size of this group increase in the years ahead, these data may
then be of value.
Table 3.9
Composite ACT measures of central tendency
for all Montana Tech non-engineering and non-science majors.
N
11 (1985)
29 (1986)
25 (1987)
65 (1985-86-87)
MEAN
18.09
19.62
20.36
19.65
-20-
MEDIAN
15.00
20.00
21.00
20.00
MODE
12.00
13.00
22.00
23.00
B. Measure of Central Tendency (Mean) with the Measure of Variability
(Standard Deviation) for Montana Tech
1. All Montana Tech Majors
In Table 3.10 below, the means and their corresponding standard
deviations are given.
Table 3.10
The means and standard deviations for all Montana Tech majors
TOTAL
93
(1985)
110
(1986)
118
(1987)
321
(1985-
86-87)
in each of the ACT score categories
and in cumulative grade point averages.
EACT MACT SACT NACT CACT
19.53 22.85 21.53 25.96 22.60
4.77 6.34 6.62 5.59 5.17
20.04 23.75 22.35 25 .. 83 23.15
4.53 6.10 6 .. 54 5.49 4.82
20.03 23.50 21.59 26.20 22.99
4.14 5.65 6.09 4.88 4.25
19.89 23.40 21.83 26.00 22.93
4.46 6.00 6.39 5.29 4.71
CGPA
2.88
.. 47
2 .. 86
.49
2.97
.48
2.90
.48
Table 3.10 represents the mean for each category of the ACT test and
for the cumulative grade point average. ACT has reported a normed group
profile of college-bound high school seniors who graduated in 1984, 1985,
and 1986. (See Table 3.11.)
-21-
Upper
25%
Middle
50%
Lower
25%
Percentile
Rank
99
98
95
90
80
70
60
40
30
20
10
5
2
Table 3.11
Norms Profile Based on ACT Test Scores and
High School Grade Averages of
College-bound High School Graduating Seniors
1984-85-86
ACT Test Scores Average
r-------,-~~---.--~~--~~--~_r------~HS Grades
Mathe- Social Natural (self-
English
Usage
29-33
28
27
26
25
24
23
22.
14
13
12
11
10
9
8
7
6
1-5
matlcs Studies SCiences Composite reported)
Usage Reading Readrng Score
34·36 32.34
32·33
31
30
29
28
27
26
25
24
31
30
29
28
27
26
25
24
33-35
32
31
30
29
28
27
: ":~~ ,,:;::~:~~~
10
9
8
7
6
5
4
3
2
10
9
8
7
6
5
4
1-3
16
15
14
13
12
11
10
9
8
1·7
31·35
30
29 400
28
27
26
25
24
13
12
11
10
9
8
7
1·6
233
2.25
200
175
166
150
133
Mean 182 17.1 17.4 211 186 2.90
Standard DeViation 5.4 81 73 64 60 7
Percentile
Rank
99
98
95
90
80
70
60
40
30
20
10
5
2
Note: The test score data are based on the 2,215,161 college-bound high school graduating semors who completed the
ACT Assessment from 1984-86
Norms Profile Showing AAP Standard Score Scales.
(taken from ACT Assessment Technical ~~ua1, 7)
-22-
The standard deviations at Montana Tech are lower than those of the
normed group in all areas. [Note that Table 3.11 reports high school grade
point averages, whereas Table 3.10 represents the College grade point
averages.] The smaller standard deviation indicates that the data in the
sample are more homogeneous than those in the normed group.
Comparison of all majors at Montana Tech (1985-87) with the normed
group yields the following approximations:
Table 3.12
A comparison of the mean ACT scores of all
Montana Tech majors (1985-87) and their
estimated percentile ranks based on ACT's
normed group (1984-86).
Test Score Percentile
EACT 19.89 59
MACT 23.40 75
SACT 21.83 68
NACT 26.00 75
CACT 22.93 73
The mean of the all-major group at Montana Tech ranks students within
the top 27% as compared with those normed by ACT during approximately the
same years as those in this study if the Composite score is used.
-23-
2. All Montana Tech Engineering Majors
From Table 3.13 and Table 3.11, a comparison can be made to determine
the approximate percentile ranks of engineering majors compared to ranks of
the group normed.
Table 3.13
The means and standard deviations for all Montana Tech engineering majors
in each of the ACT score categories
and in cumulative grade point averages.
TOTAL EACT MACT SACT NACT CACT CGPA
19.97 23.71 21.68 27.35 23.29 2.88
63
(1985) 4.44 5.74 6.13 4.39 4.34 .43
20.11 25.00 23.71 27.30 24.17 2.83
70
(1986) 4.34 5.42 5.40 4.45 4.14 .51
19.49 24.26 22.03 27.12 23.85 2.97
65
(1987) 4.04 5.46 6.28 4.60 4.25 .50
19.86 24.35 22.52 27.26 23.63 2.89
198
(1985-
86-87) 4.26 5.53 5.97 4.46 4.24 .48
-24-
The following comparison is estimated with regard to each test:
Table 3.14
A comparison of the mean ACT scores of all
Montana Tech engineering majors (1985-87)
and their estimated percentile ranks based on
ACT's normed group (1984-86).
Test
EACT
MACT
SACT
NACT
CACT
Score
19.86
24.35
22.52
27.26
23.63
Percentile
59
79
72
82
78
The engineering students, based on the Composite score and the national
norm, would rank within the top 22%. All standard deviations are smaller
than those of the normed group; additionally, in all years, they are
smaller than those at Montana Tech as a group.
-25-
3. All Montana Tech Engineering and Science Majors
From Table 3.15, the engineering and science majors have standard
deviations below those of the normed group in all years when compared with
data in Table 3.11.
Table 3.15
The means and standard deviations for all Montana Tech
engineering and science majors in each of the ACT score categories
and in cumulative grade point averages.
TOTAL EACT MACT SACT NACT CACT CGPA
19.23 23.70 22.00 26.72 23.21 2.90
82
(1985) 4.40 5.81 6.18 4.94 4.58 .48
20.32 25.58 23.68 27.48 24.41 2.88
81
(1986) 4.70 5.54 5.96 4.62 4.43 .52
20.36 24.41 22.14 27.23 23.70 2.97
93
(1987) 4.03 5.34 6.13 4.24 4.00 .50
20.21 24.55 22.58 27.15 23.77 2.92
256
(1985-
86-87) 4.36 5.59 6.12 4.59 4.34 .50
-26-
The following percentile ranks are estimated with regard to each test:
Table 3.16
A comparison of the mean ACT scores of all
Montana Tech engineering and science majors
(1985-87) and their estimated percentile
ranks based on ACT's normed group (1984-86).
Test
EACT
MACT
SACT
NACT
CACT
Score
20.21
24.55
22.58
27.15
23.77
Percentile
61
80
72
82
78
A variation exists in the standard deviations of this subgroup when
compared with Montana Tech majors as a group. The scores show more variability
in the Composite comparison.
-27-
4. All Montana Tech Arts and Sciences Majors
In.a comparison of the arts and sciences majors (See Table 3.17.) with
the normed group in Table 3.11, all arts and sciences majors rank above the
normed group in standard deviation.
Table 3.17
The means and standard deviations for all Montana Tech
arts and sciences majors in each of the ACT score categories
and in cumulative grade point averages.
TOTAL EACT MACT SACT NACT CACT CGPA
18.60 21.03 21.20 23.03 21.17 2.88
30
(1985) 5.35 7.23 7.64 6.70 6.42 .55
19.90 21.55 19.95 23.25 21.35 2.89
40
(1986) 4.92 6.66 7.67 6.19 5.42 .47
20.68 22.57 21.04 25.06 21.51 2.96
53
(1987) 4.20 5.78 5.86 5.01 4.21 .47
19.92 21.86 20.72 23.98 21.81 2.92
123
(1985-
86-87) 4.77 6.42 6.90 5.88 5.21 .49
-28-
From the above, the following is estimated with regard to each test:
Table 3.18
A comparison of the mean ACT scores of all
Montana Tech arts and sciences majors
(1985-87) and their estimated percentile
ranks based on ACT's normed group (1984-86).
Test
EACT
MACT
SACT
NACT
CACT
Score
19.92
21.86
20.72
23.98
21.81
Percentile
59
67
64
65
68
The arts and sciences majors' data are too limited to justify comparisons.
The data provided are for general information only.
-29-
5. All Montana Tech Non-Engineering and Non-Science Majors
In Table 3.19 the ACT score means are compared with those in Table
3.11.
In a comparison of the non-engineering and non-science majors (See
Table 3.19.) with the normed group in Table 3.11, all non-engineering and
non-science majors rank above the normed group.
Table 3.19
The means and standard deviations for all Montana Tech
non-engineering and non-science majors in each of the ACT score categories
and in cumulative grade point averages.
TOTAL EACT MACT SACT NACT CACT CGPA
16.55 16.55 18.00 20.27 18.09 2.72
11
(1985) 6.44 6.85 8.82 7.00 7.11 .33
19.24 18.62 18.62 21.21 19.62 2.77
29
(1986) 4.03 4.50 6.75 5.10 4.12 .42
18.80 20.12 19.52 22.36 20.36 2.94
25
(1987) 4.36 5.59 5.58 5.26 4.12 .42
18.62 18.85 18.86 21.49 19.65 2.82
65
(1985-
86-87) 4.65 5.43 6.64 5.48 4.72 .41
-30-
From the above, the following is estimated with regard to each test:
Table 3.20
A comparison of the mean ACT scores of all
Montana Tech non-engineering and non-science
majors (1985-87) and their estimated percentile
ranks based on ACT's normed group (1984-86).
Test
EACT
MACT
SACT
NACT
CACT
Score
18.62
18.85
18.86
21.49
19.65
Percentile
49
54
56
51
54
In all years (except 1985) the standard deviations are below those of
the normed group. The sample size is small. The data provided are for
general information only and would not be considered valid indicators of
possible correlation between ACT scores and academic performance.
-31-
C. Simple Regression
Simple regression statistics have been generated using the Composite
ACT and each of the subscores to predict the cumulative grade point average
for the Montana Tech group. Some general guidelines (Your College Freshmen,
113) regarding interpretation of correlation statistics from ACT are these:
(1) ".30 to .40: A low correlation. A definite but small
relationship exists. Grade predictions based on these
predictors will be useful, but greater than normal thought
should be given to the consequences of prediction errors."
(2) ".40 to .70: A typical correlation in testing applications.
A marked relationship exists. Grade predictions based on
these predictors will be useful in most educational programs,
such as guidance, admissions, class sectioning, or advising.
Normally, multiple correlations between ACT data and college
grades are in this range."
In this section of the report the variables will be defined in the
equations as follows:
b weight assigned as a regression coefficient
xl English ACT raw score
x
2 = Mathematics ACT raw score
x3 = Social Science ACT raw score
x
4 Natural Science ACT raw score
Xs = Composite ACT raw score
y predicted cumulative grade point average
-32-
The general prediction equation for the group with respect to the
English score is as shown below.
Y bO + bl xl
Based on the English ACT regression data listed in Table 3.21, the
following is the regression equation for Montana Tech.
93
110
118
321
(1985)
(1986)
(1987)
Y = 2.01 + .05 xl
Table 3.21
Simple regression statistics based on the
English ACT score for all Montana Tech majors.
2- SE b
r r O
.49 .24 .41 1.94
.44 .19 .46 1.90
.33 .12 .46 2.19
(1985-86-87) .42 .17 .44 2.01
-33-
b
l
.05
.05
.04
.05
93
110
118
321
Regression data for the Mathematics score are as listed in Table 3.22.
(1985)
(1986)
(1987)
Table 3.22
Simple regression statistics based on the
Mathematics ACT score for all Montana Tech majors.
2 r r SE bO
.54 .30 .40 1.96
.52 .27 .42 1.86
.36 .13 .45 2.24
(1985-86-87) .47 .22 .43 2.02
b2
.04
.04
.03
.04
The general prediction equation for the group with respect to the
Mathematics score is shown below.
Based on the Mathematics ACT score regression data in Table 3.22, the
following is the regression equation for Montana Tech.
Y = 2.02 + .04 x2
-34-
Regression data for the Social Science score are as listed in Table
3.23.
Table 3.23
Simple regression statistics based on the
Social Science ACT score for all Montana Tech majors.
2 r r SE bO b3
93 (1985) .38 .14 .44 2.31 .03
110 (1986) .38 .15 .46 2.21 .03
118 (1987) .36 .13 .45 2.34 .03
321 (1985-86-87) .37 .13 .45 2.30 .03
The general prediction equation for the group with respect to the
Social Science score is shown below.
Y = bO + b3 x3
Based on the Social Science ACT score regression data in Table 3.23,
the following is the regression equation for Montana Tech.
Y = 2.30 + .03 x3
-35-
Regression data for the Natural Science score are as listed in Table
3.24.
93 (1985)
110 (1986)
118 (1987)
Table 3.24
Simple regression statistics based on the
Natural Science ACT score for all Montana Tech majors.
r r 2 SE bO
.41 .17 .43 1.98
.34 .12 .47 2.06
.26 .07 .47 2.28
321 (1985-86-87) .34 .12 .46 2.10
b4
.03
.03
.03
.03
The general prediction equation for the group with respect to the
Natural Science score is shown below.
Based on the Natural Science ACT score regression data from Table 3.24,
the following is the regression equation for Montana Tech.
Y = 2.10 + .03 x4
Considering the information provided, the Mathematics score is the best
predictor of cumulative grade point average when compared with the other
three subscores.
-36-
93
110
118
321
Regression data for the Composite score are as listed in Table 3.25.
(1985)
(1986)
(1987)
Table 3.25
Simple regression statistics based on the
Composite ACT score for all Montana Tech majors.
2 - - - - - - SE - - - . - - . b
O r r
.51 .26 .40 1.83
.48 .23 .43 1.72
.41 .17 .44 1.88
(1985-86-87) .46 .22 .43 1.81
b
S
.05
.05
.05
.05
The general prediction equation for the group with respect to the
Composite score is shown below.
Based on the Composite ACT score regression data from Table 3.25, the
following is the regression equation for Montana Tech.
Y = 1.81 + .05 Xs
-37-
D. Multiple Regression
A stepwise multiple regression has been used to determine the extent to
which ACT raw scores playa role in predicting the cumulative grade point
average.
By use of multiple regression, the following equation can be generated.
Y bO + bl Xl + b2 x2 + b3 x3 + b4 x4
Since the multiple regression is stepwise with a probability to enter
the equation at .05, then those variables that have a smaller probability
will be entered provided they pass this tolerance level. Only those
variables will be considered in the prediction equation.
-38-
Table 3.26
Multiple regression equation statistics
for all Montana Tech majors.
VAR r r 2 ADJ r2 F SIG F B SE
93 STEP 1 MACT .54 .30 .29 38.42 0.000 .040
(1985)
CONSTANT 1.961 .40
110 STEP 1 MACT .52 .27 .26 39.15 0.000 .032
(1986)
STEP 2 EACT .54 .30 .28 22.69 0.000 .023
CONSTANT 1.628 .42
118 STEP 1 SACT .36 .13 .13 17.76 0.000 .019
(1987)
STEP 2 MACT .42 .17 .16 12.01 0.000 .020
CONSTANT 2.082 .44
321 STEP 1 MACT .47 .22 .22 89.16 0.000 .027
(1985-
86-87) STEP 2 EACT .50 .25 .25 53.01 0.000 .024
CONSTANT 1.790 .42
From Table 3.26 the following general multiple prediction equation can
be generated for the total group 1985-87.
Based on the data from Table 3.26, the following is the multiple
regression equation for Montana Tech.
Y = 1.790 + .024 Xl + .027 x2
-39-
Table 3.27
Multiple regression equation statistics
for all Montana Tech engineering majors.
VAR r r 2 -- -ADJ r2 F SIG F B SE
63 STEP 1 MACT .49 .24 .23 19.76 0.000 .025
(1985)
STEP 2 NACT .55 .30 .28 12.86 0.000 .028
CONSTANT 1.524 .37
70 STEP 1 MACT .58 .34 .33 34.31 0.000 .054
(1986)
CONSTANT 1.481 .42
65 STEP 1 MACT .45 .20 .19 16.11 0.000 .041
(1987)
CONSTANT 1.973 .45
198 STEP 1 MACT .50 .25 .24 64.62 0.000 .033
(1985-
86-87) STEP 2 EACT .53 .28 .27 37.89 0.000 .024
CONSTANT 1.614 .41
From Table 3.27 the following general multiple prediction equation can
be generated for the total group 1985-87.
Based on the data from Table 3.27, the following is the multiple
regression equation for Montana Tech.
Y = 1.614 + .024 xl + .033 x2
-40-
Table 3.28
Multiple regression equation statistics
for all Montana Tech engineering and science majors.
VAR r r 2 ADJ r2 F SIG F B SE
82 STEP 1 MACT .59 .34 .34 42.54 0.000 .049
(1985)
CONSTANT 1.745 .39
81 STEP 1 MACT .59 .35 .34 42.57 0.000 .038
(1986)
STEP 2 EACT .64 .41 .39 26.57 0.000 .033
CONSTANT 1.251 .40
93 STEP 1 SACT .38 .14 .13 14.95 0.000 .021
(1987)
STEP 2 MACT .42 .18 .16 9.76 0.000 .021
CONSTANT 1.994 .46
256 STEP 1 MACT .50 .25 .25 84.81 0.000 .032
(1985-
86-87) STEP 2 EACT .54 .29 .29 52.05 0.000 .028
CONSTANT 1.563 .42
From Table 3.28 the following general multiple prediction equation can
be generated for the total group 1985-87.
Based on the data from Table 3.28, the following is the multiple
regression equation for Montana Tech.
Y = 1.563 + .028 xl + .032 x2
-41-
Table 3.29
Multiple regression equation statistics
for all Montana Tech non-engineering majors.
VAR - r r 2 ADJ r2 F SIG F B SE
STEP 1 MACT .63 .40 .38 18.78 0.000 .048
30
(1985) CONSTANT 1.863 .43
STEP 1 SACT .56 .31 .30 17.38 0.000 .024
40
(1986) STEP 2 MACT .62 .38 .35 11.47 0.000 .022
CONSTANT 1.931 .38
STEP 1 SACT .49 .24 .23 16.30 0.000 .040
53
(1987) CONSTANT 2.133 .41
STEP 1 SACT .49 .24 .23 37.74 0.000 .023
123
(1985- STEP 2 MACT .53 .28 .27 23.81 0.000 .020
86-87)
CONSTANT 1.991 .42
From Table 3.29 the following general multiple prediction equation can
be generated for the total group 1985-87.
Based on the data from Table 3.29, the following is the multiple
regression equation from Montana Tech.
Y = 1.991 + .020 x2 + .023 x3
-42-
Table 3.30
Multiple regression equation statistics
for all Montana Tech non-science and non-engineering majors.
VAR r r 2- ADJ r 2 F SIG F B SE
[NONE AT PIN = .050]
11
(1985)
STEP 1 SACT .43 .19 .16 6.19 0.019 .027
29
(1986) CONSTANT 2.270 .39
STEP 1 EACT .53 .28 .25 8.88 0.007 .051
25
(1987) CONSTANT 1.977 .37
STEP 1 MACT .35 .12 .11 8.97 0.004 .027
65
(1985-86-87) CONSTANT 2.322 .39
From Table 3.30 the following general multiple prediction equation can
be generated for the total group 1985-87.
Based on the data from Table 3.30, the following is the mUltiple
regression equation for Montana Tech.
Y = 2.322 + .027 x2
-43-
II. Western Montana College
At Western Montana College, the numbers of students per year would not
meet the minimum sample size of 100 used by ACT. Therefore, all data for
the three years are treated as one group. This treatment does not allow for
a year-by-year comparison. The total number of students included at Western
Montana College is 147.
Because of the smaller group and the diversity of majors at Western
Montana College, no subgroups are considered separately.
A. Measures of Central Tendency for Western Montana College
The measures of central tendency for all five ACT scores are recorded
in Table 3.31.
N
147
147
147
147
147
Table 3.31
The five ACT scores and their measures of
central tendency for Western Montana College.
TEST MEAN MEDIAN MODE
EACT 16.81 17.00 20.00
MACT 16.61 17.00 18.00
SACT 16.89 17.00 17.00
NACT 21.27 21.00 22.00
CACT 18.01 18.00 18.00
-44-
The Composite score at Western Montana College is consistent, showing the
same value of 18.00 for all three measures of central tendency and thus
indicating a normal distribution.
B. Measure of Central Tendency (Mean) with the Measure of Variability
(Standard Deviation) for Western Montana College
In Table 3.32 below, the means and their corresponding standard
deviations are given.
TOTAL
147
Table 3.32
The means and standard deviations for Western Montana College
in each of the ACT categories
and in cumulative grade point averages.
EACT
16.81
4.67
MACT
16.61
6.26
SACT
16.89
6.49
NACT
21.27
5.94
CACT
18.01
4.67
CGPA
3.10
.41
Table 3.32 represents the mean from each category of the ACT test and
the cumulative grade point averages of those in the sample from 1985-87.
ACT has reported the information on the normed group of high school seniors
from 1984-86. (See Table 3.11.)
-45-
Western Montana College ACT standard deviations are lower than those of
the normed group. The Western Montana College group appears more homogeneous
than the normed group. [Note that Table 3.11 reports high school grade
point averages, whereas Table 3.32 presents College cumulative grade point
averages.]
Comparing the mean scores of students at Western Montana College
(1985-87) with those of the normed group, the following approximations are
estimated for each test.
Table 3.33
A comparison of the mean ACT scores at
Western Montana College (1985-87) and
estimated percentile ranks based on ACT's
normed group (1984-86).
Test Score Percentile
EACT 16.81 38
MACT 16.61 47
SACT 16.89 48
NACT 21.27 50
CACT 18.01 48
-46-
This ranking places Western Montana College at the top 52% of those
normed during approximately the same years as those in this study if the
Composite score is used.
c. Simple Regression
Simple regression statistics have been generated using the five ACT
scores to predict the cumulative grade point average at Western Montana
College. Some general guidelines (Your College Freshmen, 113) regarding
correlation statistics from ACT are these:
(1) ".30 to .40: A low correlation. A definite but small
relationship exists. Grade predictions based on these
predictors will be useful, but greater than normal thought
should be given to the consequences of prediction errors."
(2) ".40 to .70: A typical correlation in testing applications.
A marked relationship exists. Grade predictions based on
these predictors will be useful in most educational programs,
such as guidance, admissions, class sectioning, or advising.
Normally, multiple correlations between ACT data and college
grades are in this range."
-47-
In this section of the report the variables will be defined in the
equations as follows:
b weight assigned as a regression
xl English ACT raw score
x2
Mathematics ACT raw score
x3 Social Science ACT raw score
X4 = Natural Science ACT raw score
x5 = Composite ACT raw score
coefficient
Y = predicted cumulative grade point average
General prediction equations can be given from the above equation.
From the regression data in Table 3.34, specific regression equations can be
given on each test for Western Montana College.
EACT
MACT
SACT
NACT
CACT
Table 3.34
Simple regression statistics based on the
five ACT scores at Western Montana College.
2 SE b
r r O
.46 .21 .37 2.42
.38 .15 .38 2.68
.50 .25 .36 2.57
.35 .13 .39 2.54
.51 .26 .36 2.29
-48-
b
1
.04
.03
.03
.03
.04
The general prediction equation based on the English score is shown
below.
Based on the English ACT regression data listed in Table 3.34, the
following is the regression equation for Western Montana College.
Y = 2.42 + .04x1
The general prediction equation based on the Mathematics score is shown
below.
Based on the Mathematics ACT regression data listed in Table 3.34, the
following is the regression equation for Western Montana College.
Y = 2.68 + .03x2
The general prediction equation based on the Social Studies score is
shown below.
Based on the the Social Studies ACT regression data listed in Table
3.34, the following is the regression equation for Western Montana College.
Y = 2.57 + .03x3
-49-
The general prediction equation based on the Natural Science score is
shown below.
Based on the Natural Science ACT regression data listed in Table 3.34,
the following is the regression equation for Western Montana College.
Y = 2.54 + .03x4
The general prediction equation based on the Composite score is shown
below.
Based on the Composite ACT regression data listed in Table 3.34, the
following is the regression equation for Western Montana College.
Y = 2.29 + .04x5
-50-
D. Multiple Regression
A stepwise multiple regression has been used to determine the extent to
which the ACT raw scores playa role in predicting the cumulative grade
point average.
Using multiple regression, the following equation can be generated.
Y = bO + bl xl + b2 x2 + b3 x3 + b4 x4
Since the multiple regression is stepwise with a probability to enter
the equation at .05, then those variables that have a smaller probability
are entered provided they pass this tolerance level. Only those variables
are considered in the prediction equation.
-51-
Table 3.35
Multiple regression equation statistics
for Western Montana College.
TOTAL Vll r r2 ADJ r F SIG F B SE
------~~--~------~~~--~------~~---
147 STEP 1
STEP 2
SACT
EACT
CONSTANT
.50
.53
.25 .24 47.19 0.000 .022
.28 .27 27.56 0.000 .021
2.386
From Table 3.35 the following general multiple regression prediction
equation can be generated for 1985-87.
Y = bO + b 1x1 + b3x3
Based on the data from Table 3.35, the following is the multiple
regression equation for Western Montana College.
Y = 2.386 + .021x1 + .022x3
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.35
CHAPTER FOUR
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
After an analysis of the data, the writer deems it important to
consider what factors may have influenced the data themselves. The American
College Testing program lists some reasons why college grades may be
volatile. According to ACT, some of the most important factors (~
College Freshmen, 82-83) that may affect an accurate prediction of college
grade point averages are those listed below.
"Range of Talent. A relatively small standard deviation
on the ACT Composite is often accompanied by a smaller
than normal correlation. Colleges with policies of
selective admissions, for example, could expect
relatively small ACT Composite standard deviations and
correspondingly smaller correlations between ACT test
scores or high school grades and college GPA."
"Variability of Grades. Colleges that make generous use
of both high and low grades tend to obtain higher
predictive correlations than colleges that give
relatively few extreme grades."
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"Consistency among instructors. If more than one
instructor's grades are included, any differences among
instructors in grading standards, teaching
effectiveness, course objectives, or evaluation
procedures will tend to reduce predictive accuracy."
"Nonacademic Factors. If grades reflect factors other
than academic accomplishment, predictive accuracy will
be reduced. Grades in piano or in sculpture, for
example, may be based on artistic performance, which may
be unrelated to academic performance; predictions based
on academic measures, therefore, may be inaccurate.
Similarly, if nonacademic factors such as attendance,
effort, or dependability are used in assigning grades,
predictive accuracy may be reduced."
Because both schools treated in this study have an open admissions
policy, there is a strong probability of a broad range of talent in
graduates. Therefore, the correlations in both cases are good predictors
based on the "range of talent."
With regard to the "variability of grades," there will be a variation
of grades but this sample is restricted in range. All of the students in
the sample are graduates in areas where the grade point averages are a
subset of the range of grades assigned. Grades assigned range from 0-4,
whereas the graduate grade point averages range from 2-4. This research
at,tempts to study only those students who proved successful--with
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"successful" describing students who completed baccalaureate degrees at
either institution.
In data from both institutions, no differentiation in grading policies
of instructors is considered. The faculty attrition at both institutions
during the 1985-1987 period seemed to be stable.
"Nonacademic factors" could not be controlled in this study. No
attempt is made to consider such information.
Caution should be given to those using ACT test scores as their only
means of predicting college grade point averages. A significant correlation
exists at each College considered in this study. These correlations may be
used to determine "success" as defined in Chapter One, Part VI. In
addition, other factors should be studied to help in the decision process.
Both institutions will now be discussed separately with regard to the
data provided in Chapter Three.
I. Montana Tech
The measures of central tendency and measures of variability have
limited, yet informative, results. The mean, median and mode are similar
for all years indicating a normal distribution of scores. When standard
deviation is considered, variability can also be analyzed. As noted
earlier, the standard deviation in each case indicates that the studied
group is more homogeneous than the ACT-normed group used for comparison.
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Figure 4.1
The ACT Composite score standard deviations
for all Montana Tech majors (1985-87).
SD 4.71
32.35 +2 SD
27.64 +1 SD
22.73 0 SD 68% 95%
18.22 -1 SD
13.51 -2 SD
From the figures presented in Chapter Three, the data given
approximated a normal distribution of ACT scores for Montana Tech. Assuming
a normal distribution of ACT scores, Figure 4.1 shows that 68% of all
composite scores at Montana Tech fall between 18.22 and 27.64.
Additionally, 95% of the scores fall between two standard deviations or
between the raw scores of 13.51 and 32.35.
When these figures are compared with those of the college-bound
ACT-normed group in Table 3.11, the results are as follows:
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Table 4.1
Composite score ranges with equivalent percentile rank
for Montana Tech majors when compared with scores and ranks
of the ACT-normed group.
ACT-Normed Group Composite
Percentile Rank Test Score SD
99 32.35 +2
94 27.64 +1
73 22.73 0
48 18.22 -1
24 13.51 -2
Within two standard deviations, Montana Tech majors rank in the top 76%
of all college-bound students taking the ACT. Additionally, 68% of all
Montana Tech majors rank in the top 52% of all college-bound seniors taking
the ACT.
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From the cumulative grade point averages of this same group, the
following results are shown:
Figure 4.2
The cumulative grade point average standard deviations
of all Montana Tech majors (1985-87).
SD = .48
3.86 +2 SD
3.38 +1 SD
2.90 0 SD 68% 95%
2.42 -1 SD
1.94 -2 SD
At Montana Tech 68% of the students' cumulative grade point averages
fall between 2.42 and 3.38. Based on two standard deviations or 95%
confidence, the cumulative grade point averages range from 1.94 - 3.86.
Since two major subgroups exist at Montana Tech, comparisons among all
majors, the engineering majors, and the arts and sciences majors are shown
in Table 4.2.
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Table 4.2
Standard deviation and ACT-normed group percentile rank comparisons
among the all-majors group, the engineering subgroup, and the
arts and sciences subgroup.
ACT-Normed Group
Percentile Rank
Test Score
All Majors
Test Score
Engineering
Majors
Test Score
Arts & Sciences
Majors
SD
(1) (2) (3) (1) (2) (3)
99 99 99 32.35 32.11 32.23 +2
94 94 92 27.64 27.87 27.02 +1
73 78 68 22.73 23.63 21.81 0
48 53 39 18.22 19.39 16.60 -1
24 32 15 13.51 15.15 11.39 -2
SD 4.24 SD = 4.24 SD 5.21
N 361 N 198 N 123
The standard deviation for engineering majors, smaller than that for
arts and sciences majors, indicates that the engineering subgroup is not as
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diverse in ACT test results as are the arts and sciences majors. Similar
comparisons can be made by means of the data in Chapter Two.
The simple regression statistics indicate the influence that one ACT
score can have on predicting the cumulative grade point average at Montana
Tech. It is important to consider the correlation (r) in each case. Below
is a summary for all majors (1985-87) listing the r, r2, and SEe
Table 4.3
All Montana Tech majors' ACT scores with their
correlations, correlations squared, and standard errors.
EACT
MACT
SACT
NACT
CACT
r
.42
.47
.37
.34
.46
2 r
.17
.22
.13
.11
.22
SE
.44
.43
.45
.46
.43
The correlations when squared indicate what percentage this variance in
cumulative grade point average accounts for in the overall prediction. For
the purposes of this report, this correlation's squared figure is the factor
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that indicates what percentage each ACT score contributes toward predicting
the cumulative grade point average of a student at Montana Tech. The standard
error figure indicates the amount of error that exists in the study's
prediction. It seems obvious that the best predictor from the above list
would be either the MACT or CACT since each independently composes 22% of
the students' cumulative grade point averages. According to the formula
from Chapter Two, the following is the equation arising from use of the MACT
score.
Y 2.02 + .04x2
The equation below represents a cumulative grade point average for a
student who scored 25 on the MACT.
Y 2.02 + .04x2
Y = 2.02 + (.04) (25)
Y 2.02 + 1.00
Y 3.03
The student's predicted cumulative grade point average is, therefore,
3.03. However, the standard error is .43. The standard error builds a band
of confidence around the predicted cumulative grade point average. A
student's true cumulative grade point average is within this band of confi-dence.
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Figure 4.3
Band of confidence for a predicted grade point average in
cases wherein the student scored 25 on the MACT.
SE .43
3.89 +2 SE
3.46 +1 SE
predicted cgpa 3.03 0 SE 68% 95%
2.60 ~1 SE
2.17 -2 SE
With 68% confidence, it can be predicted that the student who scores 25
on the Mathematics ACT will have a cumulative grade point average between
2.60 and 3.46. This assertion means that 2 of every 3 students who score 25
will be in the stated range. If the band of confidence is increased to 95%,
then 19 of every 20 students will have a cumulative grade point average
between 2.17 and 3.89.
Once a cumulative grade point average is selected, the same formula can
be used to determine a band of confidence wherein a student's ACT score will
fall.
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What MACT would be needed to predict a 2.00 cumulative grade point
average? Assuming this grade point average to be in the 68% confidence
band, one adds .43 to the 2.00, the lowest end of the band and tests that
value.
Figure 4.4
A 68% band of confidence built around a predicted
grade point average of no less than 2.00.
SE = .43
predicted cgpa
2.86 +1 SE
2.43 o SE 68%
2.00 -1 SE
2.43 = 2.02 + .04x
2
x2 = 10.25
A student would need to get an eleven (11) on the MACT to achieve a 68%
confidence band when the lower limit is a 2.00 cumulative grade point average
(the minimum for graduation). The smaller the standard error, the
better the prediction.
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Multiple regression is the best method of considering the extent to
which selected factors affect the prediction. The data provided have been
handled in a stepwise mUltiple regression process. This process requires
that the factor that most strongly affects the prediction of the cumulative
grade point average be used first. Then, this factor is correlated with the
remaining factors. If there are high correlations with any of those factors,
the first factor considered becomes a lower correlation factor in the
prediction formula. In other words, the two or more factors are predicting
the same thing. The analyst progresses through this process until all
factors have been checked.
In virtually all cases, the F ratio in this study is large and the
probability is zero (0). A significant relationship exists between the
independent and the dependent variables.
The r2 factor has increased in the multiple regression and the standard
error has decreased. To demonstrate the differences between regression
formulas, one can use the formula below to calculate the predicted cumulative
grade point average of a student who scores 25 on the MACT and 21 on
the EACT.
By substitution,
Y = bO + b1x1 + b2x
2
Y = 1.790 + .024x1 + .027x2
Y 1.790 + .024(21) + .027(25)
Y = 1.790 + .504 + .675
Y = 2.97
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Figure 4.5
Band of confidence for a predicted grade point average when the
student scored 25 on the MACT and 21 on the EACT •
SE • 42
~
3.81 +2 SE
3.39 +1 SE
predicted cgpa 2.97 0 SE 68% 95%
2.55 -1 SE
2.13 -2 SE
A simple regression equation satisfies most criteria and is easier to
use than the multiple regression formula.
In Tables 3.26-3.29 on multiple regression statistics in Chapter Three,
the r2 factor runs from 25%-29%. This is a significant r2 factor in educa-tional
statistics. This finding means that ACT selected tests can predict
25%-29% of a student's cumulative grade point average at Montana Tech.
ACT scores may be considered an important factor in admission stan-dards,
but must not be the sole criterion for establishing future admission
standards at Montana Tech. Some questions have arisen regarding increasing
standards at the College. If a score were to be selected on the basis of
the data provided, it would be to the advantage of those setting the stan-dards
to use the simple regression statistics and formula.
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II. Western Montana College
At Western Montana College all three measures of central tendency are
exactly the same--18.00. The standard deviations are smaller than those of
the ACT-normed group, a finding which indicates that the group at Western
Montana College is more homogeneous than is the ACT-normed group. For
Figure 4.6 below, the Composite score is used to determine the distribution
of scores using the standard deviation.
Figure 4.6
The ACT Composite score standard deviations for
all Western Montana College majors (1985-87).
SD 4.67
26.15 +2 SD
21.48 +1 SD
16.81 0 SD 68% 95%
12.14 -1 SD
7.47 -2 SD
From the figures presented in Chapter Three, the data given approximated
a normal distribution of ACT scores for Western Montana College. From
Figure 4.6 it can be seen that 68% of all Composite scores at Western
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Montana College fall between 12.14 and 21.48. Also, it can be seen that 95%
of all scores fall in the range of 7.47 to 26.15.
These figures will now be compared with those of the college-bound
ACT-normed group in Table 4.4.
Table 4.4
Composite score ranges with equivalent percentile
rank for Western Montana College majors when compared
with scores and ranks of the ACT-normed group.
ACT-Normed Group
Percentile Rank
89
68
39
18
3
Composite
Test Score
26.15
21.48
16.81
12.14
7.47
SD
+2
+1
o
1
2
Western Montana College students rank within the top 93% of all
students taking the ACT when two standard deviations are used. Sixty-eight
percent (68%) rank in the top 82% of all college-bound students normed by
ACT.
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Analysis of the cumulative grade point averages of the same group
yields the following results.
Figure 4.7
The cumulative grade point average standard deviations
of all Western Montana College majors (1985-87).
SD = .41
3.92 +2 SD
3.51 +1 SD
3.10 0 SD 68% 95%
2.69 -1 SD
2.28 -2 SD
At Western Montana College 68% of the cumulative grade point
averages are between 2.69 and 3.51. With two standard deviations, or a 95%
confidence band, these cumulative grade point averages rank between 2.28 and
3.92.
The simple regression statistics demonstrate the effect each ACT
score has on the predicted cumulative grade point average. Below is a list
of all Western students' score results with regard to r, r2, and SE.
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Table 4.8
All Western Montana College majors' ACT scores with their
correlations, correlations squared, and standard errors.
r SE
EACT .46 .21 .37
MACT .38 .15 .38
SACT .50 .25 .36
NACT .35 .13 .39
CACT .51 .26 .36
The largest r 2 factor with the smallest SE will be the best regression
equation. From the information above, the CACT will be the best predictor
of cumulative grade point averages for Western Montana College students.
Below is the prediction formula from Chapter Two.
Y = bO + b5xS
Y = 2.29 + .04x5
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Assume that the NACT score is 25.
Y = 2.29 + (.04)(25)
Y 2.29 + 1.00
Y 3.29
When the SE = .36, a band of confidence can be constructed. Below is a
chart demonstrating the band of confidence for a predicted cumulative grade
point average of 3.29.
Figure 4.8
Band of confidence for a predicted grade point average in
cases wherein the student has scored 25 on the NACT.
SE .36
4.01 +2 SE
3.65 +1 SE
predicted cgpa 3.29 0 SE 68% 95%
2.93 -1 SE
2.57 -2 SE
With a composite score of 25 and with 68% confidence, a student at
Western Montana College will achieve a cumulative grade point average
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between 2.93 and 3.65. If the confidence is increased to 95%, then the
cumulative grade point average will fall between 2.57 and 4.00.
When the stepwise multiple regression is used on the data at Western
Montana College, the F ratio is large and the probability is zero (0). A
significant relationship exists between the independent and the dependent
variables.
The r2 factor has increased to 29%. It would be valid for most purposes
to use the simple regression formula with the Composite score.
A factor of 26% of the predicted cumulative grade point average at
Western Montana College is significant. This information should be used in
the determination of significant admission standards. It is doubtful that
any other factor could be isolated that would predict the cumulative grade
point average as well as does the ACT score. In consideration of the ACT
scores as possible admission standards, extreme caution should be used.
Other factors should also be considered when admission standards are set for
this institution.
III. Conclusions and Recommendations
In conclusion, the follow-up findings are important:
(1) The ACT plays a significant role in the prediction of the cumulative
grade point average at both Montana Tech and Western Montana College,
accounting for up to about 25% of the variance.
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(2) Both of the schools can with confidence use the ACT Composite
score ta predict the cumulative grade point average.
(3) Even though the Colleges are different in role and in scope, the
same factor of Composite ACT is evident as the strongest factor for prediction
of cumulative grade point averages at the College level.
(4) The ACT Composite score should be considered when admission standards
are being determined, but in no case should it be the sole determining
factor. Other factors which account for 75% of the variance should be
further researched to determine a better predictive tool than is possible
from sole use of this study's conclusions.
(5) ACT information bulletins outline specific guidelines for using
ACT as a predictive factor and enumerate other factors that may affect this
and other studies with regard to predicting cumulative college grade point
averages. These recommendations by an experienced testing organization
should be heeded by those making critical decisions regarding admission
standards.
(6) The ACT-normed group's correlation factors predicting freshman
grade point averages when compared with correlation factors found in this
study place Montana Tech and Western Montana College within the median (25%
_ 75%) category of colleges included in the normed sample (Research Services
Summary Tables, p. 31). Therefore, the two Montana colleges are properly
compared with the ACT-normed group.
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In applying the conclusions of this paper, the analyst must use caution
in judging the values of the evidence presented. The findings are of
significant value by attesting to the fact that ACT can be a determining
predictive factor regarding success of students in these two Colleges.
Predictive factors at the two institutions are numerically similar; yet the
programs offered at each institution differ. The writer would suggest that
the other colleges in the State of Montana and possibly even colleges elsewhere
in the northwest will also find the ACT Composite score a reliable
predictor of the cumulative grade point average of a baccalaureate candidate.
The value of this study, therefore, potentially affects a broad
population in the northwest.
(7) Future research should focus upon the remaining factors that make
up the 75% of the variance unaccounted for in this study.
**********
This study proves that the ACT Composite score can predict 25% of the
variance of a student's college cumulative grade point average. Such
significant educative data may well furnish a solid base for further studies
calculated to improve the quality and the reliability of existing admissions
standards at higher educational institutions in Montana.
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BIBLIOGRAPHY
Research and Development Division, The American College Testing Program,
Your College Freshmen, (6th ed.) Iowa City: The American College
Testing Program, 1981.
The American College Testing Program, ACT Assessment Program Technical
Manual, Iowa City: The American College Testing Program, 1988.
The American College Testing Program, Research Services Summary Tables,
3-Year Normative Data (based on the Participants in the Standard
Research Service, 1984-89), Iowa City: The American College Testing
Program, 1987.
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