What does STAT400 Cover?Chapter 1–5: ProbabilityProbabilityExpectation, mean, varianceDistributions (discrete, continuous)IndependenceNormal distributionCentral limit theorem, ...Chapter 6–8: StatisticsMaximum likelihood estimatesConfidence intervalsHypothesis testing2/7STAT400 / MATH 463, Spring 2017ImportanceTwo famous examples:Simpson’s paradoxThe case of Sally Clark3/7STAT400 / MATH 463, Spring 2017Simpson’s Paradox: A Gender Bias StudyUC Berkeley was sued for bias against female applicants for admissionto graduate school.Admission figures of Fall 1973 (two departments):# applicants % admittedMen 1242 52.26%Women 483 45.51%Take a closer lookMajor Men Women# applicants % admitted # applicants % admittedA 825 62% 108 82%B 417 33% 375 35%Combining different departments reverses the admission rate!825 ⇥ 0.62 + 417 ⇥ 0.331242= 0.5226;108 ⇥ 0.82 + 375 ⇥ 0.35483= 0.45514/7STAT400 / MATH 463, Spring 2017Simpson’s Paradox: A Gender Bias StudyUC Berkeley was sued for bias against female applicants for admissionto graduate school.Admission figures of Fall 1973 (two departments):# applicants % admittedMen 1242 52.26%Women 483 45.51%Take a closer lookMajor Men Women# applicants % admitted # applicants % admittedA 825 62% 108 82%B 417 33% 375 35%Combining different departments reverses the admission rate!825 ⇥ 0.62 + 417 ⇥ 0.331242= 0.5226;108 ⇥ 0.82 + 375 ⇥ 0.35483= 0.45514/7STAT400 / MATH 463, Spring 2017Simpson’s Paradox: A Gender Bias StudyUC Berkeley was sued for bias against female applicants for admissionto graduate school.Admission figures of Fall 1973 (two departments):# applicants % admittedMen 1242 52.26%Women 483 45.51%Take a closer lookMajor Men Women# applicants % admitted # applicants % admittedA 825 62% 108 82%B 417 33% 375 35%Combining different departments reverses the admission rate!825 ⇥ 0.62 + 417 ⇥ 0.331242= 0.5226;108 ⇥ 0.82 + 375 ⇥ 0.35483= 0.45514/7STAT400 / MATH 463, Spring 2017Simpson’s Paradox: A Gender Bias StudyUC Berkeley was sued for bias against female applicants for admissionto graduate school.Admission figures of Fall 1973 (two departments):# applicants % admittedMen 1242 52.26%Women 483 45.51%Take a closer lookMajor Men Women# applicants % admitted # applicants % admittedA 825 62% 108 82%B 417 33% 375 35%Combining different departments reverses the admission rate!825 ⇥ 0.62 + 417 ⇥ 0.331242= 0.5226;108 ⇥ 0.82 + 375 ⇥ 0.35483= 0.45514/7STAT400 / MATH 463, Spring 2017What Happened?Two reasons for Simpson’s paradox1Admission rate is quite different2Gender preference for departmentsMen:825 ⇥ 0.62 + 417 ⇥ 0.33825 + 417= 0.5226Women:108 ⇥ 0.82 + 375 ⇥ 0.35108 + 375= 0.4551Major Men Women# applicants % admitted # applicants % admittedA 825 62% 108 82%B 417 33% 375 35%5/7STAT400 / MATH 463, Spring 2017What Happened?Two reasons for Simpson’s paradox1Admission rate is quite different2Gender preference for departmentsMen:825 ⇥ 0.62 + 417 ⇥ 0.33825 + 417= 0.5226Women:108 ⇥ 0.82 + 375 ⇥ 0.35108 + 375= 0.4551Major Men Women# applicants % admitted # applicants % admittedA 825 62% 108 82%B 417 33% 375 35%5/7STAT400 / MATH 463, Spring 2017What Happened?Two reasons for Simpson’s paradox1Admission rate is quite different2Gender preference for departmentsMen:825 ⇥ 0.62 + 417 ⇥ 0.33825 + 417= 0.5226Women:108 ⇥ 0.82 + 375 ⇥ 0.35108 + 375= 0.4551Major Men Women# applicants % admitted # applicants % admittedA 825 62% 108 82%B 417 33% 375 35%5/7STAT400 / MATH 463, Spring 2017The Case of Sally ClarkSally Clark, a British woman who wasaccused in 1998 of having killed herfirst child at 11 weeks of age, thenconceived another child and allegedlykilled it at 8 weeks of age.According to the expert witness, for anaffluent non-smoking family like theClarks, the probability of a single cotdeath was 1 in 8543, so the probabilityof two cot deaths in the same familywas around “1 in 73 million"(8543 ⇥ 8543).Sally Clark (1964–2007).The case was widely criticizedbecause of the way statisticalevidence was misrepresented inthe original trial.6/7STAT400 / MATH 463, Spring 2017The Case of Sally ClarkSally Clark, a British woman who wasaccused in 1998 of having killed herfirst child at 11 weeks of age, thenconceived another child and allegedlykilled it at 8 weeks of age.According to the expert witness, for anaffluent non-smoking family like theClarks, the probability of a single cotdeath was 1 in 8543, so the probabilityof two cot deaths in the same familywas around “1 in 73 million"(8543 ⇥ 8543).Sally Clark (1964–2007).The case was widely criticizedbecause of the way statisticalevidence was misrepresented inthe original trial.6/7STAT400 / MATH 463, Spring 2017What’s Wrong Here?8543 ⇥ 8543 = assuming independence of the cot death eventsUnknown genetic/environmental factors that dispose the family to thecot death=) the 2nd death event becomes much more likely if the 1st eventoccurredEven accept the independence assumption(??) “1 in 73 million" = Prob(Sally is innocent | 2 babies died)Correct interpretation:“1 in 73 million" = Prob(2 babies died | Sally is innocent)If the prior probability of her innocence is high, thenProb(Sally is innocent | 2 babies died) “1 in 73 million" !!7/7STAT400 / MATH 463, Spring 2017What’s Wrong Here?8543 ⇥ 8543 = assuming independence of the cot death eventsUnknown genetic/environmental factors that dispose the family to thecot death=) the 2nd death event becomes much more likely if the 1st eventoccurredEven accept the independence assumption(??) “1 in 73 million" = Prob(Sally is innocent | 2 babies died)Correct interpretation:“1 in 73 million" = Prob(2 babies died | Sally is innocent)If the prior probability of her innocence is high, thenProb(Sally is innocent | 2 babies died) “1 in 73 million" !!7/7STAT400 / MATH 463, Spring 2017What’s Wrong Here?8543 ⇥ 8543 = assuming independence of the cot death eventsUnknown genetic/environmental factors that dispose the family to thecot death=) the 2nd death event becomes much more likely if the 1st eventoccurredEven accept the independence assumption(??) “1 in 73 million" = Prob(Sally is innocent | 2 babies died)Correct interpretation:“1 in 73 million" = Prob(2 babies died | Sally is innocent)If the prior probability of her innocence is high, thenProb(Sally is innocent | 2 babies died) “1 in 73 million" !!7/7STAT400 / MATH 463, Spring 2017What’s Wrong Here?8543 ⇥ 8543 = assuming independence of
View Full Document
Unlocking...