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Update:
In 1973 a lawsuit was filed against the University of California at Berkeley, alleging sex discrimination in its
graduate admission policies. The following table pertains to two of the graduate programs at the university.
For each program, it lists the number of males accepted, the number of males denied, the number of
females accepted, and the number of females denied:
Males
Females
Females
Males denied
accepted
accepted
denied
Program A
511
314
89
19
Program B
22
351
24
317
Combined
533
665
113
336
a) Start with the combined data.
1) What proportion of the male applicants were accepted? .445
2) What proportion of the female applicants were accepted? .252
3) Did males or females have a higher proportion of applicants that were accepted overall?
males
??
b) Now consider only Program A.
1) What proportion of the male applicants were accepted?
2) What proportion of the female applicants were accepted?
3) Did males or females have a higher proportion of applicants that were accepted in Program A?
Select an answer X
c) Now consider only Program B.
1) What proportion of the male applicants were accepted?
2) What proportion of the female applicants were accepted?
3) Did males or females have a higher proportion of applicants that were accepted in Program B?
Select an answer
d) This phenomenon is called Simpson's paradox. An association or comparison that holds for all of several
groups can reverse direction when the data are merged to form a single group. Explain how this paradox
happens, based on the data, as if to someone who doesn't know much about statistics.
