A 1975 study on graduate admissions at Berkeley found that male applicants had a substantially higher likelihood of being admitted, compared to women. However, upon closer examination the presence of aggregation paradoxes do not legitimize the conclusion that women were discriminated against.
In an attempt to study whether or not sex inequalities in higher education are due to discrimination, one may want to study individual admissions, and compare whether a man and a woman on average has an equal opportunity of being admitted, after applying for a graduate education. Sure, we need to take into account all possibly relevant differences between the candidates, such as prior academic performance, motivation, experience, and whatever other aspects may be relevant in the admission procedure. But then, when comparing (statistically) identical men and women, finding that men have a higher likelihood to be admitted to a graduate program compared to women, would lead many to the conclusion that this university discriminates against women. Right?
I believe that when such a research finding was published regarding a university, a great many of us would indeed suspect, or even believe, that women are discriminated on this university. And, in public opinion, the news, talkshows, and the blogosphere, I can easily imagine this university being accused of sex discrimination. And possibly Bickel, Hammel, and O’Connell did so as well, initially, when they indeed found that women actually had a substantially smaller chance of being admitted to a graduate program on Berkely university (the study was carried out during the fall of 1973 and published in 1975).
After having determined that 44% of all male applicants were admitted to Berkeley, but only 35% of all female applicants, the authors decided to find out which departments were the culprits. Perhaps some departments discriminated against women more strongly than other departments? Fortunately, the data on Berkeley allowed the authors to study the likelihood of being admitted for each department separately. Much to their surprise, however, they found only a few departments to be biased, and the number of departments biased towards men equalled the number biased towards women!
The paradox is clear: at the level of the departments men and women had about an equal chance of being admitted to a graduate programme, but still this resulted in the finding that in this university as a whole, a man had a substantially higher likelihood of being admitted than a woman.
A solution to this paradox lies in the aggregation: at different level of aggregation (university as a whole vs. individual departments) the association between an applicants’ sex and their likelihood of being admitted is of a different sign. This is an example of Simpson’s Paradox. As I illustrated in an earlier post, this paradox can occur when two or more sub-populations are aggregated, and if one or more of the associated characteristics is not equally prevalent amongst sub-populations.
As it turned out, Bickel, Hammel, and O’Connell indeed found that women applied relatively frequently to departments that reject more applicants in general. So, even while these departments did not have a bias towards either men, nor women, because they rejected a great number of applicants, they also rejected a proportionally large number of women. Therefore, while none of the departments discriminated against women, the selection of women towards specific departments resulted in a lower overall likelihood for women of being admitted to Berkeley.
Is this to say that no discrimination of women takes place? No, for as the authors conclude: “Women are shunted by their socialization and education towards fields of graduate study that are generally more crowded, less productive of completed degrees, and less wel funded, and that frequently offer poorer professional employment prospects” (p. 403). So, inequality and possibly discrimination remained, but this analysis showed that the unequal likelihood of a woman being admitted to Berkeley could not legitimize the conclusion that the departments, on average, showed a bias towards men. If there was discrimination, it was somewhere else.
Bickel PJ, Hammel EA, & O’connell JW (1975). Sex Bias in Graduate Admissions: Data from Berkeley. Science (New York, N.Y.), 187 (4175), 398-404 PMID: 17835295