slides7 - Lecture Stat 302 Introduction to Probability -...

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Unformatted text preview: Lecture Stat 302 Introduction to Probability - Slides 7 AD Feb. 2010 AD () Feb. 2010 1 / 16 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 = Admitted, B = Be a woman, B c = Be a man, we have P ( A j B ) & P ( A j B c ) . Was Berkeley really biased? AD () Feb. 2010 2 16 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 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 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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This note was uploaded on 10/21/2010 for the course STAT Stat302 taught by Professor 222 during the Spring '10 term at The University of British Columbia.

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slides7 - Lecture Stat 302 Introduction to Probability -...

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