Question

Consider the following table of counts, based on data from the University of California at Berkeley's graduate admissions process in 1973. School officials, who feared bias and potentially being sued, asked a statistician to examine the data. Men Accepted 533 Denied 665 Total 1198 Women Total 113 646 336 1001 449 a) Why is it not reasonable to simply consider the counts 533 and 113 in order to compare admissions decisions of men and women? b) Calculate the proportion of male applicants who were accepted. Also calculate the proportion of female applicants who were accepted. Comment on how these proportions compare. The counts in the previous table came from combining data from two different programs. Men Women Accepted Denied Accepted Denied Program N 511 89 19 Program E 22 351 24 317 Total 533 665 113 336 314 c) Within each program, calculate the proportion of male applicants who were accepted and the proportion of female applicants who were accepted. Comment on how the proportions compare within each program d) You should have noticed that women have a higher acceptance rate than men in both programs, but men have a higher acceptance rate than women when examined together. Explain, based on the data provided, how this oddity occurs – hint-think about two ways in which programs N and E differ from each other, with regards to applicant's sex and acceptance rates.

Answer 1

a) As the number of men and women applied for the admission is not equal simply considering the number of men and women applied cannot be considered for comparing the admission decision of men and women in this question. Percentage rate must be considered for each gender for the comparison

b) proportionate calculation of male applicant

533/1198*100= 44.49%

Proportionate calculation of female applicant

113/449*100 = 25.16%

This data can be compared by considering the percentage of the acceptance rate and can conclude that 44.49% of men have been selected where as only 25.16 female candidates have been selected. Thus can create a gender bias.

c) Programme wise calculation of proportionate male and female applicant

Programme M :

Male.   :511/825*100 = 61.94%

Female : 89/108*100 = 82.41%

Programme F

Male. : 22/373*100 = 5.90%

Female : 24/341*100 = 7.04%

If we compare on gender wise selected candites for each programme, percentage of female candidates selected is higher than that of male candidates. That is in case of programme N only 61.94% of men where selected where as 82.41% of female where selected and 7.04% where selected for programme F but from male candidates only 5.90% where selected.

d) If we consider the programme wise acceptance rate we can see that percentage of women selected out of total applications made by women will be more than the case of men. This is because of the total number of male and female applied for each programme is different.

In case of programme N

Percentage of male applicant out of total male applicant = 825/1195*100 = 68.86% out of which 61.94% have been selected, that is 511 male candidates

Where as female = out of 449 female candidates only 108 applied, ie.,24.05% and 89 females have been selected.

Same in the case of programme M. So that gender wise proportion rate of selected applicant for each programme shows a higher rate of selection for female