Powers and Xie give us an example of graduate admissions at UC Berkeley by gender and major. This can be modeled as a three-way table of sex by admissions outcome by major (2x2x8). The overall table of sex by admissions indicates a serious sex imbalance.
| Sex |
No Admit |
Admit |
| Men |
1480 |
1211 |
| Women |
1285 |
551 |
But, does this finding hold conditional on differences in major choice between men and women? Is there an association between sex and admittance once major is accounted for? To answer this question, Powers and Xie fit the conditional independence model (RL, CL).
This model had a
and
. It did not fit by
standards, although
liked it well enough (
).
By examining the actual admission rates by major, Xie and Powers noted that the admission rate only seemed to differ by gender for Major A. Therefore they fit the following model:
Where
was equal to one if i=female, j=admitted, and k=major A, and o otherwise. This model is the same as the conditional independence model, except that it does allow for gender differences in admission rates for major A.
This model fits the data well (
,
) indicating that except for Major A, there is no difference in admission rates by gender, once the association between major choice and gender (RL) and admission rates and major (CL) are accounted for. Furthermore, the difference by Major A actually favored women (
).