Sex Bias in Graduate Admissions? ^*
Interpreting the Data

	Men		Women
Dept	Numb. Applicants	Admitted	Numb. Applicants	Admitted
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	2,691	45%	1,835	30%

Observe:

The first two majors were easy to get into. Over 50% of the men applied to these two majors -- but less than 10% of the women.
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.

How can one compute fair numbers that summarize the admision rates? One approach is to calculate the admission rates assuming that for each department the same number of men and women applied -- but use the admission rates from the above table. This will give a weighted average of the admissions rates.
Here are the details: For each of these six departments we will compute the total number of men and women who applied.

A: 825 + 108 = 933, B: 560 + 25 = 585, . . . , F: 373 + 341 = 714. In total there were 4,526 applicants. Use this data 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. Only the admission rates change. 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.

Sex Bias in Graduate Admissions? * Interpreting the Data

Sex Bias in Graduate Admissions? ^*
Interpreting the Data