August 30, 2017

Question

In the Fall of 1973, an observational study on possible gender bias was conducted at the University of California, Berkeley. In that year, there were 12,763 applicants for graduate admission; the following is a two-way table that gives the data according to the variable’soutcome (admitted or denied) andgender (male or female).

Denied

Male

3738

4704

Female

1494

2827

Of course, it’s hard to draw any conclusions about the question of gender bias from this table because different numbers of men and women applied for graduate admission. Clearly, we should work with percentages instead.

Construct a two-way table that gives the percentages of men admitted and denied, and the percentages of women admitted and denied.
Percentage

Denied

Male

Female

From your table in Exercise 1, you should have observed that approximately 44% of men were admitted, but only about 35% of women were admitted.

Do you believe that there was gender bias in graduate admissions at UC Berkeley in 1973?
Can you think of possible causes for the discrepancy in admission rates other than gender bias?
One factor that you probably thought of in the last exercise was thequalification of the applicants. Naturally, a discrepancy in admission rates could result if the women, as a group, were less qualified than the men, in terms of college grades or standardized tests. In fact, however, there was no significant difference between the qualifications of the men and the women, as groups.

In light of this information, answer questions b and c again.
Let us now introduce a new variable that may help explain the data. At UC Berkeley, as in most universities, decisions about graduate admission are made at thedepartment level. In 1973, UC Berkeley had 101 different graduate departments, but for simplicity, we will consider only the six largest departments (which collectively account for 4486 of the applicants). The following table is athree-way table that presents the admissions data according to the variablesdepartment (A, B, C, D, E, F),gender (male, female), andoutcome (admitted, denied). The table is adapted from data in reference [2].

Male

Female

Denied

Denied

A

512

313

89

19

B

313

207

17

8

C

120

205

202

391

D

138

279

131

244

E

53

138

94

299

F

22

351

24

317

Once again, construct the three-way table that gives the percentages of men admitted and denied, and the percentages of women admitted and denied for each department.

Male

Female

Denied

Denied

A

B

C

D

E

F

Construct the two way table (both with counts and percentages) for the variablesoutcome andgender. Sketch the corresponding histogram.
Count

Denied

Male

Female

Percentage

Denied

Male

Female

Construct the two way table (both with counts and percentages) for the variable’soutcome anddepartment. Sketch the corresponding histogram.
Count

Denied

A

B

C

D

E

F

Percentage

Denied

A

B

C

D

E

F

Construct the two-way table (both with counts and percentages) for the variablesgender anddepartment. Sketch the corresponding histogram.
Count

Male

Female

A

B

C

D

E

F

Percentage

Male

Female

A

B

C

D

E

F

Based on your analysis, do you now believe that there was gender bias in graduate admissions at the University of California at Berkeley in 1973?

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Identify the lurking variables and explain what they may have accounted for in the observed association.
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