12.13. More Perils of Aggregation: Berkeley Admission Data. Examination of aggre
ID: 3362543 • Letter: 1
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12.13. More Perils of Aggregation: Berkeley Admission Data. Examination of aggregate data on graduate admissions to the University of Califor- nia, Berkeley, for fall 1973 shows a clear but misleading pattern of bias against female applicants (Bickel et al., 1975). For the six major graduate programs denoted here as A-F, a total of 4,526 students applied, 2,691 males and 1,835 females. Among 1,755 admitted students, 1,198 were males and 557 females (a) Using a 2 × 2 contingency table show that gender and admission are dependent. Also, show that the population proportions are significantly different (test for two proportions on page 465).Explanation / Answer
1) chi square test for 2*2 contingency table
Null hypothesis: There is no association between gender and admition process
Alternative hypothesis : There is an association between gender and admition process.
perform chi square test for checking dependancy between gender and admition in r gives followimg result,
Pearson's Chi-squared test with Yates' continuity correction
data: m
X-squared = 91.61, df = 1, p-value < 2.2e-16
you con see that p-valueis less than 0.05 that means,there is dependency between gender and admition process.
2)Mantel-Haenszel test
Null hypothesis: There is no association between gender and admition process
Alternative hypothesis : There is an association between gender and admition process.
to perform Mantel-Haenszel test in r ,gets following result,
Mantel-Haenszel X-squared = 1.4269, df = 1, p-value = 0.2323
alternative hypothesis: true common odds ratio is not equal to 1
95 percent confidence interval:
0.7719074 1.0603298
sample estimates:
common odds ratio
0.9046968
Result :using p-value it is conclude that ,there is no association between gender and admition process
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