An Analysis of the UPCAT Admission Equations
There are two main equations that are being used at present in selecting campus
qualifiers through the University of the Philippines College Admission Test (UPCAT). These
are the University Predicted Grade (UPG) and the UP Admission Index (UPAI).
1. The UPG equation
The UPG is an equation that predicts a student’s academic performance in the
University on the basis of his/her High School Weighted Average (HSWA) and UPCAT
scores. It was introduced in 1976 and first used in AY 1978-79 as the sole admission criterion
into each U.P. campus. The basis of the equation was 4,978 random samples of students who
were admitted through the 1973 UPCAT.
The UPG is computed using the following equation:
UPG = 2.8101 - 0.047147*ZMA – 0.046402*ZRC - 0.1381*ZLP
- 0.15531*ZHSWA - 0.025178*ZSC*ZLP*ZHSWA
There are four UPCAT subtests that go into the equation: Mathematics (MA), Reading
Comprehension (RC), Language Proficiency (LP), and Science (SC). The other component is
the HSWA. It is the standardized Z scores in these components that go into the UPG equation.
The intercept and coefficients were the values derived when the high school grades and
UPCAT scores of the 1973 sample were regressed to their subsequent UP grades. A statistical
analysis of the coefficients gives the basis for the approximate 60% UPCAT and 40% HSWA
distribution.
2. The UPAI equation
On the other hand, the UPAI was introduced in 2005 by a U.P. Diliman committee
created by then Chancellor Emerlinda R. Roman to replace the UPG. Since AY 2006-2007, it
has been used as the admission criterion for selecting UPCAT qualifiers to U.P. Diliman and
UP Extension Program in Pampanga. The UPAI is not a regression equation like the UPG.
But it implements in a straightforward manner the 60:40 ratio between the UPCAT and the
HSWA.
The UPAI is computed using the following equation:
UPAI = 0.6*(AVE_T) + 0.4*(HSWA_T)
AVE_T is the Average T-score of the 4 UPCAT subtests, and HSWA_T is the
Adjusted HSWA. T scores are also standardized scores.
3. UPG and UPAI comparison
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Since the UPG and the UPAI use different standardized scores – Z-scores for the
UPG and T-scores for the UPAI – their respective ranges differ. Theoretically, the UPG
ranges from 1.0 to 5.0 while the UPAI ranges from 100 to 0. Moreover, the two equations are
not comparable since they assign different weights to the UPCAT subtests. The following
table indicates the weights of the components.
Subtest
Language
Proficiency
Mathematics
Reading
Comprehension
Science
HSWA
UPG
UPAI
(%)
(%)
33.5
15
±2
11.4
15
11.3
15
±2
37.7
15
40
±2
As can be seen from the table, the UPAI assigns equal weights to the UPCAT subtests
whereas the UPG assigns the highest weight, among the subtests, to Language Proficiency.
Science’s contribution to the UPG is minuscule. Moreover, as will be explained later, the
weights of three components, viz., Language Proficiency, Science and HSWA, each vary
within a 2% value for the UPG. So, the UPAI appears to be a simpler formula than the UPG.
Indeed, the UPAI was developed primarily to address certain problems with the UPG. One
point made against the UPG is that it is antiquated. It was based on 1970’s data and there is a
feeling that it does not apply anymore at present. The relationship modelled by the regression
in the 1970’s could have already undergone structural changes through the years. For one, the
UPCAT itself has changed a lot since then. To appreciate how wide the gap is between the
basis of the UPG and its intended application, consider that it is quite possible that those who
took the UPCAT in 1973 are now the grandparents of those who took the UPCAT this year.
However, the more serious argument against the UPG is the undesirable effect of its socalled “interaction term.” In its last term, three variables interact, viz., SC, LP and HSWA.
Since the SC score occurs only in this part of the equation, it can sometimes have an
unexpected effect. When both LP and HSWA scores lead to a negative score, SC yields a
negative effect. The negative score obtains when either ZHSWA > 0 and ZLP < 0, or ZHSWA < 0
and ZLP > 0. In both cases, a higher SC score will result to a lower UPG (higher numerically)
while a lower SC score will result to a higher UPG (lower numerically). Since with the UPG,
the lower the score the better, the applicants are penalized if they get high science scores, and
rewarded if they get low science scores.
To address this seeming flaw in the UPG equation, the Presidential Advisory Council
approved in 2006 a “win-win” scheme whereby the UPG is computed as is and computed
without the interaction term, and whichever of the two is lower, is chosen as the actual value
of the UPG. This is intended to mitigate the perverse effect of the UPG’s interaction term.
But the undesirable effect for many applicants is that the science score gets cancelled out. For
these applicants, it would not matter if they sleep through the entire Science test.
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The science subtest was not included in the original UPCAT developed in 1967; it was
introduced only in 1970. Perhaps, with the 1973 batch, the effect of the science score was
indeed negligible. That is why it did not have its own coefficient but instead interacted only
with other variables. Indeed, the reliability of a test usually takes some time to develop.
However, recent regression analyses have shown that science can be predictive and therefore
assigned its own weight.
Another issue that the UPAI is supposed to address is the difference in the grading
practices of schools. The transmuted high school grades are not deemed comparable since
some schools are strict in grading while others are lenient. So the same numerical grade will
not have the same significance in these schools. The UPAI uses the UPCAT itself to adjust
the raw HSWA’s. An adjustment factor (AF) is computed for each school based on the past
performance of its students. This factor is intended essentially to address the problem of
grade inflation and deflation. Its value may range from around 1.3 for the strictest and 0.7 for
the most lenient. This number is then multiplied against the HSWA to get the 40% of the
UPAI score.
4. Correlation analysis
Naturally, the question arises which of the two equations is a better selection criterion.
Data was collected in the form of UPCAT enrolees’ General Weighted Averages (GWA) from
the various units of the University. Initial GWA’s, that is, first year and second year GWA’s,
of the 2008, 2009, 2011 batches were gathered and correlated with their UPCAT performance.
Older data sets, specifically for 2006 and 2007, were also analyzed. The specific type of
correlation used is the Pearson Product Moment Correlation.
The results show that the composite scores, meaning UPCAT scores combined with HSWA,
correlate better with college grades than the individual subtest scores. Moreover, the best
correlations are with the first-year grades. Indeed, studies have shown that the predictive
value of admission tests like SAT and UPCAT with high school grades extend only up to 2
years of college. It is admitted that beyond that, there are simply too many factors outside the
test scores and high school grades that determine graduation. Recent studies have shown that
even the percentage of part-time faculty in a university can affect the rate of its graduation.
For the two equations, the correlation coefficients with the 2008, 2009, and 2011 initial
GWA’s are the following:
UPGGWA
UPAIGWA
0.
448
0.
483
Of course, the possible values range from 1.0 (perfect correlation) to 0 (no correlation).
The values show that there is a moderate positive linear relationship between the variables,
with the UPAI-GWA correlation being stronger than the UPG-GWA correlation.
5. Regression analysis
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In developing a GWA predictor, it is best to use grades earned during the first two years at
the most. While it may be pointed out that first-year grades only include basic courses and do
not contain grades from major subjects, performance in the latter should be predictable from
the former since the basic subjects are supposed to prepare a student for the higher courses. It
stands to reason that in predicting the GWA, we try to account for as much variability as can
be explained by the independent variables available. Given that the first two years of college
are preparations for the succeeding years, success in the former should ensure success in the
latter ceteris paribus. Anyway, if a student does not get good grades in the first-year, the
chances that he will finish in four or five years is greatly diminished. Even if he does
eventually finish, it will be at a much greater cost.
Recent studies have been made to regress the GWA’s of students from their
UPCAT scores and high school grades to come out with a more up-to-date UPG. The
problem generally has been the low r squared rating of the models developed. UPAI was
introduced instead by UP Diliman because the r squared ratings of the resulting models were
not high enough. To get a moderately good fit, it was necessary to introduce very
complicated equations, with additional variables like campus and high school type variables.
But at some point, the gain in predictive power might not be worth the complexity.
Still, the best regressions on recent data (with r squared = 0.236) show close
correlation with the UPAI, particularly on the UPCAT subtest weights. Mathematics, for
instance, has a 15% weight, like in the UPAI. Language Proficiency has around 17% and
Reading Comprehension 12%. Science is lower at 8%; but more importantly, it has its own
weight. In sum, the values are closer to the UPAI values than to the UPG weights.
So the correlation and regression analyses appear to favour the UPAI over the UPG. But
one problem with the UPAI is that it was not intended as a GWA predictor. This explains
why its range is not the same as the GWA and UPG values. This makes it difficult to evaluate
UPAI scores. Just what does a UPAI score of 60 mean for instance? I can say that it means
that the score is 1 standard deviation higher than the mean score. But unless you are familiar
with statistics, it would not mean anything. It does not say anything about how the student
will do in college. This appears to be the reason why even in UP Diliman and UPEPP, the
UPG is still used to evaluate walk-ins, and applicants for athletic and financial scholarships.
6. UPAI as GWA predictor
But with the better correlations with GWA’s, I think that the UPAI can be now considered
as a true GWA predictor. Based on statistical analysis, it should be a better predictor than the
UPG. So what is needed is a way of converting the UPAI in GWA or UPG terms so that it is
easier to evaluate. That can now be done using the following conversion:
PG = 2.8101-(((UPAI-50)/10)*0.5)
The UPAI is standardized using 50 as mean and 10 as standard deviation. 2.8101, the UPG
intercept, is retained to make the converted UPAI comparable to the UPG.
Here are some examples of converted UPAI scores:
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U P
PAI G
82 1
.21
62 2
.21
50 2
.81
30 3
.81
Comparing the GWA’s of 26,516 UPCAT takers in 2006, 2007, 2008, 2009, and
2011, and who subsequently enrolled in UP with their UPG scores and PG (converted UPAI)
scores, we get the mean absolute percentage error for both equations.
U 22.
PG 7 %
P 18.
G 6%
On average, the UPG over- or under-estimates the GWA by 22.7 %. The conclusion we
get from this analysis is that the PG (converted UPAI) is a better approximation of GWA than
UPG since the percentage of prediction error is less.
7. Proposal for one equation
Given that we are one University, we should only have one admission criterion for
admitting students through the UPCAT. Whether it be in UP Diliman or UP Mindanao, we
should be using the same equation. There may be differences in the degree programs offered
and the enrolment quotas, but the treatment of the UPCAT subtests and HSWA should be
uniform across CU’s to say that there is really just one UP standard.
If the difference between the UPG and UPAI is deemed significant, then UPAI can
be considered as being superior to the UPG. On the other hand, if the difference is not
deemed significant enough, then perhaps it would not really matter which equation we use. In
this case, the argument would be to just come up with one equation to standardize admission
into the University. Given the antiquity of the UPG, its structural shortcoming, and its
different weights for the UPCAT subtests, we should perhaps be better off adopting the PG or
converted UPAI. Different weights for the UPCAT subtests should be associated with degree
program predictors and not with the campus selection equation.
8. UPAI as UPG
Adopting the converted UPAI as the new UPG is the best option as its effect on
UPCAT processing is very minimal. Only the computation of the UPG will change. The
absolute cut-offs (2.8), “palugit” (0.05), “pabigat” (0.1), and the EEAS procedure are retained.
Assessments (for walk-ins, scholarships, etc.) will still be in GWA terms. Higher actual cutoffs would be expected in some cases, but these are the effect too of an increase in the number
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of applicants and the retention of quotas. Equity issues can then be better addressed once we
have a unified admission equation.
9. Course predictors
Finally, assigning campus qualifiers to the various degree programs is usually done
using course predictors. When the UPG was first used in 1977, there were other predictors
that were introduced, namely, MPG (Mathematics Predicted Grade), BSPG (Biological
Science Predicted Grade), and PSPG (Physical Science Predicted Grade).
The UPAI might not be an appropriate degree program predictor in some cases
since it simply averages the UPCAT scores. An applicant who does very well in mathematics
but not so well in the remaining subtests would not fare as well as an applicant who does not
do well in mathematics but does very well in the other subtests. With simple averaging of
scores in different subtests, an applicant who is not so good in mathematics has a better
chance of getting into a mathematics program than someone who is very good in mathematics.
So these predictors likewise need to be updated. The grades of UP Diliman students in
specific subjects were regressed to develop course-specific equations. Among the various
equations generated, two with the best r squared ratings were used to derive the equations
below.
MPG = MA_T*.6 + HSWA_T*.25 + SC_T*.1 + LP_T*.05
SPG = SC_T*.35 + HSWA_T*.3 + MA_T*.15 + LP_T *.1 + RC_T*.1
SPG replaces the two science predictors, since one, BSPG, is based on the other. Both
MPG and SPG will likewise be converted using the same formula with different intercepts:
3.2 for MPG and 3.0 for SPG -- such values being based on the initial regressions. It is safe to
say that the two equations, together with the converted UPAI, can be used to select qualifiers
to the various degree programs.
Proposal:
In sum, these are the proposals based on the analysis of the UPCAT equations.
1.
The UPG will be updated by computing it in terms of the converted UPAI.
The UPAI itself is computed based on the UPCAT subtests and all the academic grades during
the first three years of high school adjusted for grade inflation or deflation.
2.
The degree program predictors: MPG, BSPG and PSPG, will also be updated
using the two new formulas: the updated MPG and SPG. Both BSPG and PSPG will be
replaced by one formula: SPG. They are similarly converted but with different intercepts.
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