by Robert Lerner, Ph.D. and Althea K. Nagai, Ph.D.
Lerner & Nagai Quantitative Consulting
Prepared for the Center for Equal Opportunity

This report presents selected preliminary findings for the Center for Equal Opportunity's undergraduate admissions project for the University of California, Berkeley, 1993-1995. It describes the racial and ethnic composition of Berkeley applicants and enrollees, and racial and ethnic differences in SAT scores and grade point averages. The report also describes in detail the procedures used to generate these results. There is a greater degree of racial preference in the admissions process at Berkeley than is usually assumed.

Part I. Procedures for Analysis
A. Type of Data Used for Analysis.

As of now, we have obtained from the University of California, Berkeley two kinds of usable information (income data was sent to us in an unusable form). The first type of data set consists of applicant files. There is one data set for each of the years 1993, 1994 and 1995. Each applicant data set contains information regarding each individual applicant for the following seven variables: the applicant’s ethnic group; high school grade-point average; SAT math score; SAT verbal score; best math achievement test score; best English achievement test score; and best third achievement test score.

The second type of usable information consists of three enrollee data set, with information for each individual enrollee for the same seven variables listed above: the applicant’s racial and ethnic group; high school grade-point average; SAT math score; SAT verbal score; best math achievement test score; best English achievement test score; and best third achievement test score.

B. Admission Status of Individual Applicants.

The data files sent by Berkeley, however, lack critical information on the admission status of individual applicants. That is, we do not know if an individual applicant was accepted and eventually enrolled, accepted but declined admission, or was rejected. Without these codes, there is no way of studying acceptances, nor is there any way to link individual applicants to their final enrollment status. Despite these limitations, much can be learned from the data at hand.

C. Technical Procedures for Statistical Analysis.

The data consists of separate files of applicants and enrollees, for each of the years 1993, 1994, and 1995, which we have transformed into SPSS-PCTM for Windows 3.1TM system files. We created composite SAT indexes, ethnic group frequencies, and average scores of applicants and enrollees for each variable for all three years of data as well as other variables for the admissions simulations.

Part II. Results.
A. Racial and Ethnic Composition of the Applicant Pool.

The applicant pool increased in size from 9,949 in 1993 to 10,830 in 1995. The racial and ethnic composition of the applicant pool for all three years was nearly identical. No single racial or ethnic group comprised a majority of applicants. For 1995, Asian Americans were 45 percent of the applicants. Whites were 39 percent, while Hispanics were 10 percent of the applicants. African Americans comprised 5 percent, and American Indians, 1 percent.

B. Racial and Ethnic Composition: Enrollees.

The racial and ethnic composition of the entering freshman class at Berkeley remained nearly identical for all three years. No single racial or ethnic group was a majority of enrollees.

In 1995, Asian Americans were 41 percent of the entering class. Thirty-three percent were white and 17 percent were Hispanics. African Americans comprised seven percent of the enrollees, and American Indians, two percent.

The proportions were roughly the same in 1993 and 1994. For 1993, Asian Americans were 43 percent of the entering class. Thirty-two percent of the freshman class were white, while 18 percent were Hispanic, 6 percent African-American, and 1 percent American Indian. For 1994, Asian Americans were 44 percent and whites were 32 percent of enrollees. Sixteen percent of enrollees were Hispanic, seven percent were African American, and one percent was American Indian.

C. Enrollees as Proportion of Applicants.

The proportion of enrollees to applicants declined from 29.8 percent in 1993 to 25.4 percent in 1995.

It is much easier for African Americans, Hispanics, and American Indians to enroll at Berkeley than it is for whites and Asian Americans. We arrive at this conclusion in the following manner.

For each racial or ethnic group, we computed the proportion of applicants who enrolled. White and Asian American enrollees made up considerably smaller percentages of white and Asian American applicants, than did Hispanics, African Americans, and American Indians. This pattern holds true for all three years.

In 1995, roughly one in five white applicants and one in four Asian American applicants enrolled at Berkeley. In contrast, two in five Hispanic applicants, more than one in three African American applicants, and practically all American Indian applicants enrolled.

The ethnic group proportions were approximately the same in 1993 and 1994. For 1993 and 1994, white and Asian American enrollees were roughly one in four white and Asian American applicants. In contrast, for 1993 African American enrollees were 39 percent of their respective applicant pool, while Hispanic enrollees were two-thirds of applicants. Lastly, American Indians enrollees were 100 percent of applicants. For 1994, while one in four white and Asian American applicants enrolled, enrollees were almost half of all Hispanic applicants; along with 39 percent of African-American applicants, and almost all American Indians who applied.

Anomalies of the American Indian data.

The American Indian data show some discrepancies, however, and need to be treated with caution. In 1993 and in 1995, a slightly larger number of American Indians were reported as having enrolled than who actually applied.

There are several possible explanations for this discrepancy. First, there may be coding errors in the data, either for applicants, enrollees, or both. Second, there may be enrollees who "discover" their American Indian heritage upon enrollment and seek to utilize it to their advantage. Third, selected individuals may be granted special admission outside of the regular admissions process. Determining which of these explanations is true requires more information.

D. RACIAL AND ETHNIC DIFFERENCES IN ENROLLEE SCORES

These differences in enrollment are accompanied by substantial differences in enrollee qualifications among ethnic groups, including differences in SAT verbal scores, SAT math scores, and in high school grade-point averages (GPAs).

Method of Statistical Analysis. Ordinary statistical analysis rests on the normal bell-shaped curve. In the Berkeley enrollee data sets, the distributions of SAT math and verbal scores and of GPAs are so asymmetrical (i.e., skewed) as to be significantly different from the standard bell-shaped curve.

Because of the asymmetry of the data, reporting means for SAT math and verbal scores and GPAs places greater weight on extreme values than is warranted. A few unusually high or low scores can have a substantial effect on the value of the mean. Standard deviations, which are based on squared deviations from the mean, are even more useless for describing the spread of cases for asymmetrical, badly skewed distributions, because they reflect the (mathematical) square of these extreme values (e.g., Hartwig and Dearing, 1979).

We describe the Berkeley data using medians and interquartile ranges for each racial and ethnic group. The median represents the middle of the distribution. At the median, 50 percent of all cases have greater scores, and 50 percent have lesser scores. The median is not affected by the values of extreme cases.

Instead of means and standard deviations, then, we report scores at the medians (50th percentiles) and the interquartile ranges (25th and 75th percentiles) to describe the distribution of scores. These are less susceptible to the influence of extreme values and more adequately represent the properties of the bulk of the cases (e.g., Hartwig and Dearing, 1979).

We computed medians and interquartile ranges for each of the ethnic groups on the following variables: SAT Verbal Scores, SAT Math Scores, and high school GPAs. Scores at the 25th percentile mean that 75 percent of the group had scores higher than that score, while 25 percent had lower scores. The 75th percentile score is the point at which 25 percent of the group had higher scores, and 75 percent had lower scores.

SAT Math Scores

Math SAT scores at the 25th, 50th, and 75 percentiles are displayed for each racial and ethnic group, for 1993, 1994, and 1995 respectively. The median is the 50th percentile for each racial and ethnic group.

For every year, the rank-order of racial and ethnic groups from highest to lowest percentile scores is the same. Asian Americans have the highest scores at the 25th, 50th and 75th percentile, followed by whites, American Indians, Hispanics, and African Americans. In addition, the SAT math score differences between African Americans and Hispanics as compared to Asian Americans and whites were substantial. They were so large that for all three years, the 75th percentile scores for African Americans were less than the 25th percentile scores for Asian Americans and whites (See Charts 4a, 4b, and 4c). They form two separate and distinct populations, with little overlap in scores. The Hispanic scores differ only slightly less.

SAT Verbal Scores

SAT verbal scores follow a pattern similar to that of SAT math scores, but the differences among the racial and ethnic groups are somewhat more modest. Nevertheless, there are differences among whites and Asian Americans versus African Americans and Hispanics, for all three years.

The highest quartile, or 75th percentile score for African Americans is almost equal to the lowest quartile, or 25th percentile score for whites and Asian Americans. In 1995, the score for the top quartile among African Americans fell between the 25th and 50th percentile score for Asian Americans; it is almost equal to the score at the lowest quartile (25 percentile) for whites. In 1994, the 75th percentile score for African Americans is slightly less than or equal to the 25th percentile score for Asian Americans and whites respectively. In 1993, the scores at the 75 percentile for African Americans are equal to or greater than the 25th percentile scores for Asian Americans and whites respectively.

In other words, the groups overlap somewhat. The top 25 percent of African American enrollees performed the same or better than 25 percent of whites and Asian Americans on the SAT Verbal test. However, 50 percent of white and Asian American enrollees still did better than 75 percent of African Americans on the SAT verbal test.

Hispanic SAT Verbal Scores are somewhat higher. The gap between their SAT Verbal Scores and whites and Asian American scores are smaller than that between African Americans and these same groups. In all three years, the top quartile (i.e., the 75th percentile) of Hispanic scores fall between 25th and 50th percentiles of Asian Americans and whites. That is, the top 25 percent of Hispanic enrollees perform somewhere between the lowest 25 percent and 50 percent of Asian American and white enrollees on the Verbal SAT.

High-School Grade-Point Averages (GPAs)

Similar racial and ethnic group differences are found for high school GPAs. The bottom quartile (25th percentile) GPA for Asian American enrollees for 1993, 1994, and 1995 was 4.00. This means that at least three out of four Asian American enrollees have a 4.00 GPA. White scores are slightly lower. Between 50 and 75 percent of whites also have GPAs of 4.00, while the lowest quartile GPA was about 3.8.

There is little overlap in GPAs between African Americans and whites and Asian Americans respectively. The 75 percentile GPA for African Americans in the same years is less than the lowest quartile score for Asian Americans and whites. African American GPAs at the 75th percentile were 3.77 in 1993, 3.78 in 1994, and 3.76 in 1995.

There is considerably more overlap between GPAs of Asian Americans and whites compared to Hispanics. The 75th percentile of Hispanic enrollees was 4.00 in 1994 and 1995, and 3.96 in 1993, which was the same as the interquartile range (25th through 75th percentile) for Asian Americans, and the median and top quartile (50th and 75 percentile) of whites. In other words, 25 percent of Hispanic enrollees did as well as 75 percent of Asian Americans and 50 percent of whites.

Half the Hispanic enrollees, however, did more poorly in high school than 75 percent of Asian Americans and whites -- Hispanic scores at the median and lowest quartile are lower than the scores for Asian Americans and whites at the 25th percentile.

Racial and ethnic group differences on all three measures of academic performance -- the SAT Math scores, the SAT Verbal scores, and high school GPAs, show similar kinds of differences among enrollees. There are small differences between Asian Americans and white enrollees. In contrast, the differences in prior academic performances between either whites or Asian Americans, and African Americans are so substantial as to suggest that these groups of enrollees are selected from entirely distinct academic populations. The gaps between white and Asian American enrollees and Hispanic enrollees are smaller, although they are still substantial.

For every variable in every year, a distinct rank order of ethnic group performance emerges. Asian Americans or whites are at the top, with Asian Americans scoring higher than whites in SAT math tests and high school GPAs, and whites scoring higher than Asian Americans in SAT verbal tests. These two groups are always followed by American Indians who generally score higher than Hispanics, except for GPAs. African Americans consistently have the lowest scores.

Part III. Creating a Simulated Meritocratic Admissions Process
A. Procedure

Although we are unable to link Berkeley's official admissions status to the admissions data sets, we created a simulated admissions process which provides additional insight into the results of a perfectly meritocratic selection process using Berkeley's applicant data. By comparing these results to the actual enrollment figures, we can gauge the extent to which Berkeley's actual admissions procedure exhibits racial preference, where selection based on perfect racial preference is a quota and selection based on perfect merit is equal to the absence of any racial preference.

The simulation of a race-blind, merit admissions process was carried out as follows. Selecting such a class requires two assumptions to be made for the calculations to be carried out. These are 1) a definition of merit and 2) a desired class size or a desired proportion of applicants to be admitted.

Our definition of academic merit is partly a function of available information and partly a function of reasonable assumptions. We have no information from personal interviews, individual essays, or kinds of courses taken in high-school. We omitted achievement test scores for simplicity, although in view of the high correlations between these and SAT verbal and math scores (not shown here), it is doubtful that including them would make much difference.

We decided to define "merit" as the sum of verbal and math SAT scores and high school GPAs, as combined into a single index. This reflects our belief in the intuitive appeal of combining somewhat different types of information into a single score. It also reflects the common view that such an index is the best predictor of college performance (e.g., Anastasi, 1976, p. 320).

Once the academic index is created, the higher a student's score on the index, the greater the merit of the student's application. A cut-off point is selected so that students scoring above the cut-off point are automatically admitted and students scoring below are automatically rejected. The level at which this is set can be determined either by the desired class size or the desired proportion of admittees. We decided to admit 1/3 of each class, which yielded a class size somewhat larger than the number of enrollees for each year. This is realistic on the assumption that not all admittees actually enroll, which is at least sometimes the case.

B. Creating the Merit Index.

First, the variable SUM_SAT was created, which added verbal and math SAT score for all applicants. While it would be desirable to simply add GPAs and SATs together, this cannot be meaningful done because they are measured on different scales - grades from 1.00 to 4.00 and SATs from 400 to 1600. To combine them into a unitary index, SAT_SAT and GPA were each transformed into standard-score variables. This means that each was transformed to create a new variable with a mean of 0, and a SD of 1. This was done for each variable by subtracting each score from its mean and dividing it by its standard deviation (e.g., Anastasi, 1976, pp. 78-84).

The index of academic merit is simply the sum of the two normalized variables. This procedure allows the normalized variables to be added together so that equal weight is given to SAT scores and high-school grades. This was the simplest assumption, but the relative weights of grades and SATs can be varied without affecting the results in any material way (of course, the results for particular individuals will vary somewhat).

C. Estimating Desired Class Size.

We decided to admit one-third of all the applicants in all three years. Each applicant was assigned a percentile rank based on his or her merit score. We split the index into thirds, admitted the top third, and rejected the rest. It should be clear to the reader that the only way any kind of racial preference can enter into the process is if the admissions committee so desires it.

D. Simulation Results

The synthetic acceptances contain far fewer Hispanics, African Americans, and American Indians and more whites and Asian Americans (See Chart 7a). For 1993, 0.3 percent of the class are African American (n=11), 0.2 percent are American Indian (n=5), 50.3 percent are Asian American (n=1,581), 1.3 percent are Hispanic (n=41), and 47.9 percent are white (n=1,505). Total class size is 3,143.

For 1994, African Americans are 0.1 percent (n=2), American Indians are 0.1 percent (n=4), Asian Americans are 51.9 percent (n=1,762), Hispanics are 1.2 percent (n=42), and whites are 46.7 percent (n=1,585). Total class size is 3,395.

For 1995, African Americans are 0.2 percent (n=8), American Indians are less than 0.01 percent (n=1), Asian Americans are 48.2 percent (n=1,836), Hispanics are 1.6 percent (n=62), and whites are 50.0 percent (n=1,906). Total class size is 3,813.

Next, the SATs and GPAs results of the synthetic process were computed by ethnicity and compared them with average scores of the actual enrollees.

The differences between racial and ethnic groups in the synthetic admissions group are non-existent. In other words, under the simulated admissions process, all admitted persons are - because they were selected to be - equal in their academic qualifications, regardless of their race or ethnicity. As we have seen above, in the case of actual enrollees, they are not all selected equal. Some are selected to be more equal than others.

PART IV. DISCUSSION

Based on our analysis, we conclude that a massive degree of racial preference in admissions policy exists at Berkeley for the for which we have data.

A consequence of the enrollment process as it actually exists has the potential to reinforce stereotypes. When students actually meet each other, they may know that the average minority student is less qualified than is the average non-minority student. Moreover, the probability of encountering such a student is high, creating a class-wide heterogeneity. Under our synthetic, meritocratic process, the average student of a different ethnicity is likely to be as equally likely to be qualified as they are, creating class-wide homogeneity.

REFERENCES

Anastasi, Anne. 1976. Psychological Testing. 4th Edition. New York: Macmillan Publishing Co., Inc.

Hartwig, Frederick with Brian E. Dearing. 1979. Exploratory Data Analysis. Beverly Hills: Sage Publications.