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Sex Bias in Graduate Admissions: Data from Berkeley

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Sex Bias in Graduate Admissions: Data from Berkeley by using a familiar statistic, chi-square. As already noted, we are aware of the pitfalls ahead in this naive approach, but we intend to stumble into every Sex Bias in Graduate Admissions: one of them for didactic reasons. We must first make clear two as- Data from Berkeley sumptions that underlie consideration of the data in this contingency table approach. Assumption 1 is that in any Measuring bias is harder than is usually assumed, given discipline male and female ap- do not differ in of their and the evidence is sometimes to plicants respect contrary expectation. intelligence, skill, qualifications,prom- ise, or other attribute deemed legiti- to their as P. J. Bickel, E. A. Hammel, J. W. O'Connell mately pertinent acceptance students. It is precisely this assumption that makes the study of "sex bias" meaningful, for if we did not hold it any differences in acceptance of ap- Determining whether discrimination deceision to admit or to deny admission. plicants by sex could be attributedto because of sex or ethnic identity is be- The questionwe wish to pursueis wheth- differencesin their qualifications,prom- ing practiced against persons seeking er the decision to admit or to deny was ise as scholars, and so on. Theoretical- passage from one social status or locus influenced by the sex of the applicant. ly one could test the assumption, for to another is an important problem in We cannot know with any certainty example, by examining presumablyun- our society today. It is legally impor- the influences on the evaluators in the biased estimatorsof academic qualifica- tant and morally important. It is also Graduate Admissions Office, or on the tion such as Graduate Record Exam- often quite difficult. This article is an faculty reviewing committees, or on ination scores, undergraduate grade exploration of some of the issues of any other administrativepersonnel par- point averages, and so on. There are, measurement and assessment involved ticipating in the chain of actions that however, enormous practical difficul- in one example of the general prob- led to a decision on an individual ap- ties in this. We therefore predicate our lem, by means of which we hope to plication. We can, however, say that discussion on the validity of assump- shed some light on the difficulties.We if the admissions decision and the sex tion 1. will proceed in a straightforwardand of the applicant are statistically asso- Assumption 2 is that the sex ratios indeed naive way, even though we ciated in the results of a series of ap- of applicants to the various fields of know how misleading an unsophisti- plications, we may judge that bias graduate study are not importantlyas- cated approach to the problem is. We existed, and we may then seek to find sociated with any other factors in ad- do this because we think it quite likely whether discrimination existed. By mission. We shall have reason to chal- that other persons interested in ques- "bias" we mean here a pattern of as- lenge this assumption later, but it is tions of bias might proceed in just sociation between a particulardecision crucial in the first step of our explora- the same way, and careful exposure and a particular sex of applicant, of tion, which is the investigationof bias of the mistakes in our discovery pro- sufficient strength to make us con- in the aggregate data. cedure may be instructive. fident that it is unlikely to be the re- sult of chance alone. By "discrimina- tion" we mean the exercise of decision Tests of AggregateData Data and Assumptions influenced by the sex of the applicant when that is immaterial to the quali- We pursue this investigationby com- The particular body of data chosen fications for entry. puting the expected frequenciesof male for examination here consists of ap- The simplest approach (which we and female applicants admitted and plications for admission to graduate shall call approach A) is to examine denied, from the marginal totals of study at the University of California, the aggregate data for the campus. Table 1, on the assumption that men Berkeley, for the fall 1973 quarter. In This approach would surely be taken and women applicants have equal the admissions cycle for that quarter, by many persons interested in whether chances of admission to the university the Graduate Division at Berkeley re- bias in admissions exists on any cam- (that is, on the basis of assumptions ceived approximately 15,000 applica- pus. Table 1 gives the data for all 1 and 2). This computation,also given tions, some of which were later with- 12,763 applications to the 101 grad- in Table 1, shows that 277 fewer wom- drawn or transferred to a different uate departmentsand interdepartmental en and 277 more men were admitted proposed entry quarter by the appli- graduate majors to which application than we would have expected under cants. Of the applications finally re- was made for fall 1973 (we shall refer the assumptionsnoted. That is a large maining for the fall 1973 cycle 12,763 to them all as departments). There number, and it is unlikely that so large were sufficiently complete to permit a were 8442 male applicants and 4321 a bias to the disadvantageof women female applicants. About 44 percent would occur by chance alone. The of the males and about 35 percent of chi-squarevalue for this table is 110.8, Dr. Bickel is professor of statistics, Dr. the females were admitted. Just this and the probability of a chi-square Hammel is professor of anthropology and associ- ate dean of the Graduate Division, and Mr. kind of simple calculation of propor- that large (or larger) under the as- O'Connell is a member of the data processing tions us to examine the data noted is small. staff of the Graduate Division, at the University impels sumptions vanishingly of California, Berkeley 94720. further. We will pursue the question We should on this evidence judge 398 SCIENCE, VOL. 187 that bias existed in the fall 1973 ad- Table 1. Decisions on applications to Graduate Division for fall 1973, by sex of applicant- missions. On that we should naive aggregation. Expected frequencies.are calculated from the marginal totals of the observed account, frequencies under the assumptions (1 and 2) given in the text. N =12,763, 2 = 110.8, look for the responsible parties to see d.f. = 1, P 0 (18). whether they give evidence of dis- Outcome crimination. Now, the outcome of an Difference application for admission to graduate Applicants Observed Expected study is determined mainly by the Admit Deny Admit Deny Admit Deny faculty of the department to which the Men 3738 4704 3460.7 4981.3 277.3 - 277.3 prospective student Let us applies. Women 1494 2827 1771.3 2549.7 - 277.3 277.3 then examine each of the departments for indications of bias. Among the 101 departments we find 16 that either had no women applicants or denied square of 3091 and that the probability deciding therefrom that bias existed admission to no applicants of either of obtaining a chi-square value that in favor of men has now been cast sex. Our computations, therefore, ex- large or larger by chance is about into doubt on at least two grounds. cept where otherwise noted, will be zero. For the 2 X 85 table on the de- First, we could not find many biased based on the remaining 85. For a partments used in most of the analysis, decision-making units by examining start let us identify those of the 85 chi-square is 3027 and the probability them individually. Second, when we with bias sufficiently large to occur by about zero. Thus the sex distribution take account of the differences among chance less than five times in a hun- of applicants is anything but ran- departments in the proportions of men dred. There prove to be four such dom among the departments. In ex- and women applying to them and departments. The deficit in the number amining the data in the aggregate as avoid this problem by computing a of women admitted to these four (un- we did in our initial approach, we statistic on each department separately, der the assumptions for calculating pooled data from these very different, and aggregating those statistics, the expected frequencies as given above) independent decision-making units. Of evidence for campus-wide bias in favor is 26. Looking further, we find six course, such pooling would not nullify of men is extremely weak; on the departments biased in the opposite di- assumption 2 if the different depart- contrary, there is evidence of bias in rection, at the same probability levels; ments were equally difficult to enter. favor of women. these account for a deficit of 64 men. We will address ourselves to that ques- The missing piece of the puzzle is These results are confusing. After tion in a moment. yet another fact: not all departments all, if the campus had a shortfall of Let us first examine an alternative are equally easy to enter. If we cast 277 women in graduate admissions, to aggregating the data across the 85 the data into a 2 X 101 table, distin- and we look to see who is responsible, departments and then computing a guishing department and decision to we ought to find somebody. So large statistic-namely, computing a statistic admit or deny, we find that this table a deficit ought not simply to disappear. on each department first and aggregat- has a chi-square value of 2195, with There is even a suggestion of a sur- ing those.
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