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slides7 - Lecture Stat 302 Introduction to Probability...

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Lecture Stat 302 Introduction to Probability - Slides 7 AD Feb. 2010 AD () Feb. 2010 1 / 16
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Simpson°s Paradox: Sex Bias in Graduate Admissions? The University of California at Berkeley was sued for bias against women who had applied for admission to graduate schools there. The admission ±gures for the fall of 1973 showed that men applying were more likely than women to be admitted, and the di/erence was so large that it was unlikely to be due to chance. The evidence looks really compelling. Applicants % admitted Men 8442 44% Women 4321 35% If we consider the event A = ²Admitted³, B = ²Be a woman³, B c = ²Be a man³, we have P ( A j B ) ° P ( A j B c ) . Was Berkeley really biased? AD () Feb. 2010 2 / 16
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Simpson°s Paradox: Sex Bias in Graduate Admissions? Let us examine more carefully the data by examining admissions in some representative departments Depart. Men Women % in % in 1 63 68 2 33 35 3 6 7 Whatever the department to which they apply, women have an higher probability of getting in than men; i.e. we have for any event C i = f apply to department i g P ( A j B \ C i ) ± P ( A j B c \ C i ) and still overall P ( A j B ) ° P ( A j B c ) AD () Feb. 2010 3 / 16
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Simpson°s Paradox: Sex Bias in Graduate Admissions? Let us examine even more carefully the data Depart. Men Women Appli. % in Appli. % in 1 560 63 25 68 2 417 33 375 35 3 272 6 341 7 AD () Feb. 2010 4 / 16
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Simpson°s Paradox: Sex Bias in Graduate Admissions? The mathematical reason is that P ( A j B \ C i ) ± P ( A j B c \ C i ) does NOT indeed imply P ( A j B ) ± P ( A j B c ) as P ( A j B ) = n i = 1 P ( A j B \ C i ) P ( C i j B ) , P ( A j B c ) = n i = 1 P ( A j B c \ C i ) P ( C i j B c ) , It highly depends on the proba of applying to department i given you are a woman/man . The reason is that women tended to apply to competitive departments with low rates of admission, whereas men tended to apply to less-competitive departments with high rates of admission.
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