An observational study on sex bias in graduate admissions was done at the University of California, Berkeley. During the study period there were 8,442 men and 4,321 women who applied for admission to graduate school. About 44% of the men and 35% of the women were admitted.

Assuming that the men and women were on the whole equally well qualified (and there is no evidence to the contrary), the difference in admission rates looks like a strong piece of evidence to show that men and women are treated differently in the admissions procedure. The university seemed to prefer men, 44 to 35.

Each major did its own admissions to graduate work. They looked at the data for each major separately to identify the departments that discriminated against women. A puzzle appeared. Major by major there did not seem to be any general bias against women. On the whole, if there was any bias it ran against the men.

Here is the data for the six largest departments. These accounted for over one-third of the total number of applicants. The data was typical of the whole campus -- except that the bias looks worse.

Men Women
A 825 62% 108 82%
B 560 63% 25 68%
C 325 37% 593 34%
D 417 33% 375 35%
E 191 28% 393 24%
F 373 6% 341 7%
Total 2,69145% 1,83530%

Observe:

• The first two majors were easy to get into. Over 50% of the men applied to these two majors.
• The other four majors were much harder to get into. Over 90% of the women applied to these four majors.
Moral: There was an effect due to the choice of the major that confounded the effect due to sex.

The above table compares 12 admissions rates. One way to understand this data better is to use a weighted average of the admissions rates, the weights being the total number of applicants (male and female) to each department. To compute this we first compute the total number of applicants for each of these six departments:

A: 825 + 108 = 933,   B: 560 + 25 = 585, . . . , F: 373 + 341 = 714
and use these to compute the weighted average admission rate for men:

(.62×933 + .63×585 + .37×918 + .33×792 + .28×584 + .06×714) / 4,526 = 39%

Similarly, the weighted average admission rate for the women works out to be 43%:

(.82×933 + .68×585 + .34×918 + .35×792 + .24×584 + .07×714) / 4,526 = 43%

In these computations, the weights are the same for the men and women. These averages suggest that if anything, the admissions processed against the men.

*From Chapter 2 of Statistics, 3rd. ed., by D. Freedman, R. Pisani, & R. Purves, published by W. W. Norton, 1998.

This was based on the article:
B. Bickel, E. Hammel, & J.W. O'Connell, "Is there a sex bias in graduate admissions?", Science, Vol. 187 (1975), pp.398--404.