Simpson’s Paradox – Berkeley data

We have seen Simpson’s paradox in one of the earlier posts. A famous one was the discrepancy in observed admission rates of men and women from six departments at Berkeley. Here is what the data shows; the dataset is available on GitHub.

Admit	Gender	Dept	Frequency
Admitted	Male	A	512
Rejected	Male	A	313
Admitted	Female	A	89
Rejected	Female	A	19
Admitted	Male	B	353
Rejected	Male	B	207
Admitted	Female	B	17
Rejected	Female	B	8
Admitted	Male	C	120
Rejected	Male	C	205
Admitted	Female	C	202
Rejected	Female	C	391
Admitted	Male	D	138
Rejected	Male	D	279
Admitted	Female	D	131
Rejected	Female	D	244
Admitted	Male	E	53
Rejected	Male	E	138
Admitted	Female	E	94
Rejected	Female	E	299
Admitted	Male	F	22
Rejected	Male	F	351
Admitted	Female	F	24
Rejected	Female	F	317

The paradox

If one considers the university as a whole, here is the summary

Admit	Gender	#
Admitted	Male	1198
Rejected	Male	1493
Admitted	Female	557
Rejected	Female	1278
Total		4526

Proportion of Male admitted = 1198 /(1198+1493) = 0.45

Proportion of female admitted = 557/(557 + 1278) = 0.30

There is a difference in success rates for men and women. But what about department-wise ‘discrimination’? Here are the success rates of males and females in each department.

Department	Male	Female
A	0.62	0.82
B	0.63	0.68
C	0.37	0.34
D	0.33	0.35
E	0.28	0.24
F	0.06	0.07

Success rates of females are at par or even higher in every department! Let’s probe further and check where they applied against the success rates.

Department	% Male Applied	% Female Applied	Admission Rate (%)
A	30	6	64
B	21	1	63
C	12	32	35
D	15	20	34
E	7	21	25
F	14	19	6
Total	100	100

Women preferred more competitive departments with lower acceptance rates, whereas more men opted for departments with better acceptance rates.