Performance on the Pharmacy College Admission Test: An
Exploratory Analysis
Notes
Nancy E. Kawahara
College of Pharmacy, University of Illinois at Chicago, 833 S. Wood Street (M/C 886), Chicago IL 60612
Corinna Ethington
Educational Psychology, College of Education, University of Illinois at Chicago, Chicago IL 60612
The exploratory data analysis technique known as median polishing was used in this study to examine
performance on the Pharmacy College Admission Test (PCAT) over a six year period of time. Performance
across years was variable with 1984 and 1985 showing the best overall performance on all seven sections
of the exam. The data illustrate a declining trend in performance for the six years which were evaluated. Since
the demographics of the pharmacy applicant pool have shifted to included more women than men, evaluation
by gender was also performed. Across all seven PCAT sections males performed better than females with
the largest differences seen in chemistry and biology. On the basis of gender alone, one would expect about
an eight percentage point difference in performance on the chemistry and biology sections.
INTRODUCTION
The Pharmacy College Admission Test (PCAT) is a standardized test of academic ability used as a screening tool for
admission to Schools and Colleges of Pharmacy. Currently,
22 programs require the PCAT and an additional 14 programs recommend the PCAT as one component in their
admissions process(1). The PCAT contains five content
areas: verbal ability, quantitative ability, biology, chemistry,
and reading comprehension. The quantitative ability content area can be further sub-divided into a section on basic
arithmetic skills and a section on mathematical problem
solving. Students who complete the PCAT receive a total of
seven separate scores which are reported as percentile
ranks.
Published literature investigating the utility of the PCAT
has focused on the exam’s ability to predict students’ academic success within pharmacy educational programs. Studies have shown that various scores from the PCAT along
with other variables (e.g., pre-pharmacy grade point average) can serve as reliable predictors of students’ academic
success(2-9). Academic success is typically defined as the
student’s grade point average (GPA) at the completion of
their first year in the pharmacy program. Since the first year
of the pharmacy curriculum is composed primarily of basic
science courses, we would expect those PCAT sections
which measure scientific and quantitative performance to
appear in the predictive equations most often. Review of the
literature supports this phenomenon and most studies have
shown the chemistry, biology, and quantitative sections to
be most useful in predicting first year academic performance.
The University of Illinois at Chicago (UIC) requires
that all students who apply to the College of Pharmacy take
the PCAT as part of their admissions requirements. The
College uses each student’s PCAT chemistry score, prepharmacy science GPA (composed of college level math
and science grades), and a feeder school index (based on the
average Medical College Admissions Test scores) in a regression statement to produce what is internally known as
the predictive index. The predictive index is our best estimate of what the student’s GPA will be at the completion of
their first year of pharmacy studies. Historically, the predictive index has accounted for between 30 and 40 percent of
the variance in the students’ actual GPAs at the completion
of their first year in the program. Recently, faculty have
shared their perception that the academic quality of students applying to our College has declined over the years
and as a result have also expressed concern about the
validity of this predictive index.
In an attempt to investigate whether the faculty’s perception of a decline in the academic quality of students
entering the College might be accurate, this study using an
exploratory data analysis technique was designed. Since
there has been a significant shift in the UIC College of
Pharmacy applicant pool to include more women than men,
performance by gender was also investigated. The purpose
of this study was twofold: (i) to evaluate the performance of
students, in general, across a six year time period; and (ii) to
determine whether gender differences in performance on
the seven sections of the PCAT were present.
METHODOLOGY
Sample
Data for this study were drawn from application records
for all students applying to the UIC, College of Pharmacy
for classes entering in the years 1984 through 1989. The UIC
program is a 2-4 program leading to a Doctor of Pharmacy
degree. Therefore, all individuals included in this study had
completed a minimum of one year college level coursework
before taking the PCAT (see above for description of the
components of the test). Only those records with complete
data were used in the analysis. Complete records accounted
American Journal of Pharmaceutical Education Vol. 58, Summer 1994
145
Table I. PCAT percentage score means by gender
PCAT section
1984
1985
1986
Verbal
Males
Females
Reading Comprehension
Males
Females
Biology
Males
Females
Chemistry
Males
Females
Quantitative
Males
Females
Arithmetic
Males
Females
Math
Males
Females
1988
1989
44.73
42.54
44.50
44.90
39.07
34.57
34.40
35.37
38.94
35.09
35.91
32.17
51.96
42.82
49.10
50.18
46.51
40.29
41.29
45.48
45.28
41.67
43.04
39.48
62.33
54.72
61.67
53.40
58.56
45.08
53.14
45.71
59.04
46.13
50.39
46.42
59.50
48.57
58.75
50.15
52.27
44.13
50.37
44.84
48.82
41.44
45.51
43.42
45.25
40.60
52.41
45.86
35.84
38.14
41.41
38.52
38.80
36.35
39.61
34.85
43.29
39.94
52.28
44.97
33.59
38.83
42.59
37.26
37.49
34.52
38.98
35.95
49.50
44.10
54.75
49.72
41.61
41.32
44.93
43.71
44.89
42.93
44.81
38.88
Table II. Polished table for PCAT verbal through matha
PCAT section
1984
1985
1986
Verbal
Male
Female
Year effect
Reading Comprehension
Male
Female
Year effect
Biology
Male
Female
Year effect
Chemistry
Male
Female
Year effect
Quantitative
Male
Female
Year effect
Arithmetic
Male
Female
Year effect
Math
Male
Female
Year effect
1987
1987
1988
1989
Gender effect
-0.59
0.59
6.52
-1.88
1.88
7.58
0.57
-0.57
-0.30
-2.17
2.17
-2.23
0.24
-0.24
-0.10
0.19
-0.19
-3.08
1.68
-1.68
Common effect 37.12
2.78
-2.78
3.95
-2.33
2.33
6.20
1.32
-1.32
-0.04
-3.89
3.89
-0.05
0.01
-0.01
0.04
-0.01
0.01
-2.18
1.79
-1.79
Common effect 43.44
-0.11
0.11
6.32
0.11
-0.11
5.43
2.82
-2.82
-0.38
-0.20
0.20
-2.78
2.53
-2.53
0.38
-1.93
1.93
-3.80
3.92
-3.92
Common effect 52.20
1.59
-1.59
6.13
0.42
-0.42
6.55
0.19
-0.19
0.30
-1.12
1.12
-0.30
-0.19
0.19
-2.77
-2.84
2.84
-3.44
3.88
-3.88
Common effect 47.90
0.44
-0.44
4.15
1.39
-1.39
10.37
-3.03
3.03
-1.78
-0.44
0.44
1.20
-0.66
0.66
-1.20
0.50
-0.50
-1.54
1.89
-1.89
Common effect 38.77
0.08
-0.08
2.92
2.06
-2.06
9.93
-4.22
4.22
-2.48
1.07
-1.07
1.23
-0.11
0.11
-2.69
-0.08
0.08
-1.23
1.60
-1.60
Common effect 38.70
0.95
-0.95
2.68
0.77
-0.77
8.12
-1.60
1.60
-2.65
-1.14
1.14
0.20
-0.77
0.77
-0.20
1.22
-1.22
-2.27
1.75
-1.75
Common effect 44.11
a
All values reported as percentage points.
for 99 percent of the total number of records available. The
sample consisted of 408 men and 748 women.
Analyses
In order to look at the trend in performance over time
146
as well as whether sex-related difference in performance
were present, an exploratory data analysis technique known
as median polishing was employed(10, 11). This technique
was chosen because unlike standard inferential statistical
American Journal of Pharmaceutical Education Vol. 58, Summer 1994
Fig. 1. Plot of relative performance on the PCAT verbal and
PCAT reading comprehension sections for 1984 through 1989.
Fig. 2. Plot of relative performance on the PCAT biology and PCAT
chemistry sections for 1984 through 1989.
tests, such as analysis of variance(ANOVA), it does not
require the formulation of an up-front hypothesis. This
technique entails a decomposition of the data, resulting
in patterns of effects which may not be apparent in the
summary data. The technique- successively sweeps
information from the original data into a common value,
row effects, and column effects. The patterns which
emerge from the summary data may then lead to
formulation of hypotheses which can be tested using more
rigorous statistical methodology, such as ANOVA. The
approach taken here is similar to that of Wainer (10) in
analyses of trends in Scholastic Aptitude Test (SAT)
performance.
The model used in this study is similar to the model
of ANOVA but it uses medians as opposed to means to
describe the common effects, row effects, and column
effects. For the factors involved in this study the model
is the following:
X ij = C + G i + U j + eij
where Xij is the mean PCAT score for gender i in
the entering year j; C is the common effect (median
across entering years); G; is the effect of gender i; U is the
effect of the entering year j; and e- is a residual. The
residual is an indication of how well the model describes
the data. Whenever an individual row or column deviates
from a pattern which is generally followed by the other
rows and columns it will be evident in the residual
pattern for that particular row or column (e.g., the
residual will be large in absolute value).
At the present time, there is no commercially available
statistical package which contains the median polishing
Fig. 3. Plot of relative performance on the PCAT quantitative,
PCAT arithmetic, and PCAT math sections for 1984 through 1989.
American Journal of Pharmaceutical Education Vol. 58, Summer 1994
147
Fig. 4. Plot of performance relative to model prediction for females
on the PCAT verbal and PCAT reading comprehension sections
across years 1984 through 1989.
Fig. 5. Plot of performance relative to model prediction for females
on the PC A T biology and PC A T chemistry sections across years
1984 through 1989.
technique. Therefore, all analyses were done by hand and
confirmed using a program written for a personal computer
by a colleague of one of the authors. The reader is referred
to references 10 and 11 for a detailed description of how to
perform this technique.
The analysis consisted of two components. The first
component was to run the exploratory data analysis. Results
of the analysis were examined for overall trends in performance and for differences in performance by gender. The
second phase consisted of examining the application data
base for other variables that may offer an explanation for
gender differences in performance, if any, identified in the
exploratory analysis.
RESULTS
Table I shows the percentage score means by gender on each
PCAT section for the six years of the analysis. Table II shows
the completed polished tables for each of the seven reported
scores from the PCAT.
The common effect can be interpreted as the typical
score for this group of men and women, while the gender and
year effects are incremental changes in performance as a
result of membership in a particular category. The cell
residuals indicate the portion of the score not explained by
the common value, gender, and year of application. For
example, the mean performance score on the PCAT verbal
for men in the application year 1989 can be expressed as:
37.12 + 1.68 + (-3.08) + 0.19 = 35.91
where 37.12 represents the common value (typical score for
148
Fig. 6. Plot of performance relative to model prediction for females
on the PC AT quantitative, PC AT arithmetic, and PC AT math
sections across years 1984 through 1989.
American Journal of Pharmaceutical Education Vol. 58, Summer 1994
Table III. Mean and standard deviationa for quantitative college level quarter hours in math and science
completed by gender
1984
1985
1986
1987
1988
1989
Male
84.27 ± 43.45
83.49 ± 35.04
92.73 ± 36.35
82.08 ± 39.39
86.30 ± 62.93
84.65 ± 39.30
Female
76.17 ± 35.34
71.50 ± 27.92
76.26 ± 32.97
72.67 ± 24.92
79.84 ± 31.09
77.89 ± 67.28
a
Large standard deviations attributable to variation in the number of college years completed (e.g., minimum 2 year pre-pharmacy requirement to
completion of a baccalaureate or masters degree in a quantitative field).
Table IV. Mean and standard deviation for pre-pharmacy science grade point average by gender
1984
1985
1986
1987
1988
1989
Male
3.96 ± 0.57
3.83 ± 0.55
3.79 ± 0.51
3.87 ± 0.63
3.88 ± 0.57
3.68 ± 0.74
Female
3.81 ± 0.62
3.82 ± 0.53
3.86 ± 0.57
3.81 ± 0.54
3.84 ± 0.60
3.79 ± 0.61
men and women in this group); 1.68 represents the incremental increase in performance attributed to being a male;
-3.08 represents the incremental decrease in performance
attributed to the application year 1989; and 0.19 is the
residual (portion of the score not accounted for by the
common value, gender, and application year).
Figures 1-3 are plots of the year effects which illustrate
the relative performance across the six year time period.
Figures 4-6 are graphic representations of the model residuals for the females in this study. Graphs are grouped according to similarity of subject matter for ease of comparison.
The residual graphic representations for males would be the
mirror image of that illustrated for females.
Table III shows by gender the breakdown for total
number of quantitative college level quarter hours (includes
science and math courses) completed for each of the six
years. Table IV illustrates by gender the pre-pharmacy
science GPA for each of the six years evaluated.
DISCUSSION
Effects attributable to year of application are in many cases
quite large. On the basis of application year alone, we would
expect a difference in performance as high as 12.62 percentage points (e.g., arithmetic score between years 1985 and
1988). For all seven sections of the PCAT this data shows a
trend towards declining performance. Suggesting that, in
general, the faculty perception that academic quality of
students applying to the UIC program over the time period
for this study appears to be accurate.
The effects seen as a result of gender are small. The
largest gender effects are present in the performance on the
PCAT biology and PCAT chemistry sections. On the basis
of gender alone, one would expect about an eight percentage point difference in both PCAT biology and chemistry
scores, while the difference in scores for all other PCAT
sections would be less than four percentage points. While
the gender effects are relatively small, they consistently
favor performance for males. On the basis of gender alone,
we would expect males to perform better on all seven
sections of the PCAT.
Examination of the cell residuals suggests that for most
PCAT sections there is no consistent pattern across time for
either men or women. However, the residual plot for female
performance on the chemistry section demonstrates that
female performance improved relative to what the model
would predict across the six-year study period (see Figure
5). While overall performance on the chemistry section for
this group of applicants declined over the six year study
period, female applicants, in general, improved their performance.
Most residuals are comparatively small indicating that,
in general, the model describes the mean scores fairly well.
However, there are three instances where the residual exceeds the effect which can be attributed to both gender and
year of application (reading comprehension 1987; arithmetic skills 1986; quantitative ability 1986). In each of these
instances the residual is in favor of females. This indicates
that female performance in these years is better than what
we would have expected. The large residuals indicate that
there are interactive effects between gender and year of
application.
The Psychological Corporation, administrators of the
PCAT, suggest that the scores received for performance on
the chemistry and biology sections are most sensitive to the
amount of previous relevant coursework the student has
completed(12). It is well documented in the educational
literature that males, in general, perform higher than females on test of quantitative ability. A variety of explanations for these gender difference in performance have been
studied(13). One such theory is the differential coursework
hypothesis(14-16). This hypothesis proposes that these differences are a function of the variations in the number of
mathematical and scientific courses each sex completes.
Males typically take more elective math and science courses,
whereas, females tend to complete only those courses necessary for graduation. In an attempt to determine whether
this hypothesis may explain the gender effects in performance on the PCAT chemistry and PCAT biology sections,
we examined the data base for an indicator of science
focused coursework. Our data base contained a variable
which consisted of the total number of quarter hours each
applicant had completed in college level science and math
courses. While this is not a precise indicator of exposure to
chemistry and biology, it does provide information regarding the potential exposure each applicant may have received.
For each year of this analysis men completed more
science and math hours than women. This finding does not
allow us to confirm that this difference in the number of
science hours, as we defined it, is the cause of this gender-
American Journal of Pharmaceutical Education Vol. 58, Summer 1994
149
related difference in performance, but it does suggest that
the coursework hypothesis may contribute to this phenomenon.
While males out perform females on standardized tests
of quantitative ability, females obtain higher grades in quantitative courses than males(16). This creates a problematic
relationship between the traditional granting of grades and
the application of standardized tests to evaluate academic
ability. Since the UIC predictive index utilizes the student’s
pre-pharmacy science GPA as well as the PCAT chemistry
score, we were interested in whether the male advantage in
the PCAT chemistry score would be diminished or offset by
the potential female advantage in pre-pharmacy science
GPA. We were unable to show a female advantage in grade
attainment for this group of men and women. The mean prepharmacy science GPA for males and females did not differ
substantively in any of the study years. The pre-pharmacy
science GPA means for men and women within each year
were in the range of 3.68 to 3.96 with similar standard
deviations and ranges.
Factoring in the pre-pharmacy science GPA to the
predictive index would not offset the advantage males have
in the PCAT chemistry score. Unlike other documented
educational research, the grades obtained in college level
math and science course for this group of men and women
did not differ based on gender.
CONCLUSIONS
The results of this analysis are not to be interpreted as
significant differences among the groups described. It is
important to remember that the purpose of exploratory data
analysis is to help researchers highlight patterns of effects
which are not always apparent in summary data. This analysis does demonstrate a declining trend in performance on all
seven sections of the PCAT across the six year study period.
The study supports that men, in general, performed better
than women on all sections of the PCAT.
The patterns uncovered in this analysis suggest future
research questions. Since performance across time appears
highly variable, can a single, valid predictive equation, for
academic success, which includes PCAT scores be developed and effectively employed? Since the literature documents successful application of such a predictive equation,
are faculty grading practices, in particular the curving of
grades, masking the actual utility of such an index? Given
this analysis in which performance declines in the years
following 1985, are we attracting less capable individuals
into our pharmacy curriculum or is this a temporary phenomenon resulting from a decline in the number of students
applying to pharmacy programs seen during the 1980s? If as
these analyses suggest, men score about eight percentage
points higher on the PCAT chemistry section and this
difference may be attributable to variations in coursework
exposure, then is the frequent application of the PCAT
chemistry score as a predictor of student academic success
within pharmacy an issue which needs to be re-examined? In
order to determine whether the variation in performance
across years, the apparent decline in performance, and the
pattern of gender differences, is simply a local trend, a
comparative analysis utilizing a national sample of students
completing the PCAT is underway. Preliminary analyses of
the national data fails to demonstrate the trend in declining
performance across time. However, the national data does
demonstrate a similar pattern of gender differences in per150
formance on all sections of the PCAT.
The PCAT has been available and in use for over a
decade, yet, research has focused only on its utility as a
predictor of students’ academic success. This analysis has
provided the pharmacy education community with a new
way to look at how students perform on the PCAT both as a
function of year of application and gender. While the
number of schools and colleges requiring the PCAT declined as applications to pharmacy educational programs
declined in the 1980s, the increase in applications seen over
the first few years of the 1990s is expected to result in a
refocusing on the development of reliable and valid methods to screen applicants(17). The PCAT exam represents
one mechanism to objectively measure an applicant’s abilities in a variety of subject areas. This report, along with
preliminary analysis of a national data set, suggest that
gender differences in performance are present. This finding
is consistent with the educational literature which demonstrates gender difference in performance on other standardized test of academic ability (e.g., SAT and GRE). Perhaps it
is time for the pharmacy education community to expand its
research on the PCAT to areas other than simply the
prediction of academic success. An issue worth consideration.
Am. J. Pharm. Educ., 58, 145-150(1993); received, 4/22/92, accepted 1/18/94.
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American Journal of Pharmaceutical Education Vol.58, Summer 1994