What does STAT400 Cover Chapter 1 5 Probability Probability Expectation mean variance Distributions discrete continuous Independence Normal distribution Central limit theorem Chapter 6 8 Statistics Maximum likelihood estimates Confidence intervals Hypothesis testing STAT400 MATH 463 Spring 2017 2 7 Importance Two famous examples Simpson s paradox The case of Sally Clark STAT400 MATH 463 Spring 2017 3 7 Simpson s Paradox A Gender Bias Study UC Berkeley was sued for bias against female applicants for admission to graduate school STAT400 MATH 463 Spring 2017 4 7 Simpson s Paradox A Gender Bias Study UC Berkeley was sued for bias against female applicants for admission to graduate school Admission figures of Fall 1973 two departments Men Women applicants 1242 483 admitted 52 26 45 51 STAT400 MATH 463 Spring 2017 4 7 Simpson s Paradox A Gender Bias Study UC Berkeley was sued for bias against female applicants for admission to graduate school Admission figures of Fall 1973 two departments Men Women applicants 1242 483 admitted 52 26 45 51 Take a closer look Major A B Men applicants admitted 825 62 417 33 Women applicants admitted 108 82 375 35 STAT400 MATH 463 Spring 2017 4 7 Simpson s Paradox A Gender Bias Study UC Berkeley was sued for bias against female applicants for admission to graduate school Admission figures of Fall 1973 two departments Men Women applicants 1242 483 admitted 52 26 45 51 Take a closer look Major A B Men applicants admitted 825 62 417 33 Women applicants admitted 108 82 375 35 Combining different departments reverses the admission rate 825 0 62 417 0 33 0 5226 1242 108 0 82 375 0 35 0 4551 483 STAT400 MATH 463 Spring 2017 4 7 What Happened Two reasons for Simpson s paradox STAT400 MATH 463 Spring 2017 5 7 What Happened Two reasons for Simpson s paradox 1 Admission rate is quite different Men Women Major A B 825 0 62 417 0 33 0 5226 825 417 108 0 82 375 0 35 0 4551 108 375 Men applicants admitted 825 62 417 33 Women applicants admitted 108 82 375 35 STAT400 MATH 463 Spring 2017 5 7 What Happened Two reasons for Simpson s paradox 1 Admission rate is quite different 2 Gender preference for departments Men Women Major A B 825 0 62 417 0 33 0 5226 825 417 108 0 82 375 0 35 0 4551 108 375 Men applicants admitted 825 62 417 33 Women applicants admitted 108 82 375 35 STAT400 MATH 463 Spring 2017 5 7 The Case of Sally Clark Sally Clark a British woman who was accused in 1998 of having killed her first child at 11 weeks of age then conceived another child and allegedly killed it at 8 weeks of age Sally Clark 1964 2007 The case was widely criticized because of the way statistical evidence was misrepresented in the original trial STAT400 MATH 463 Spring 2017 6 7 The Case of Sally Clark Sally Clark a British woman who was accused in 1998 of having killed her first child at 11 weeks of age then conceived another child and allegedly killed it at 8 weeks of age According to the expert witness for an affluent non smoking family like the Clarks the probability of a single cot death was 1 in 8543 so the probability of two cot deaths in the same family was around 1 in 73 million 8543 8543 Sally Clark 1964 2007 The case was widely criticized because of the way statistical evidence was misrepresented in the original trial STAT400 MATH 463 Spring 2017 6 7 What s Wrong Here 8543 8543 assuming independence of the cot death events STAT400 MATH 463 Spring 2017 7 7 What s Wrong Here 8543 8543 assuming independence of the cot death events Unknown genetic environmental factors that dispose the family to the cot death STAT400 MATH 463 Spring 2017 7 7 What s Wrong Here 8543 8543 assuming independence of the cot death events Unknown genetic environmental factors that dispose the family to the cot death the 2nd death event becomes much more likely if the 1st event occurred STAT400 MATH 463 Spring 2017 7 7 What s Wrong Here 8543 8543 assuming independence of the cot death events Unknown genetic environmental factors that dispose the family to the cot death the 2nd death event becomes much more likely if the 1st event occurred Even accept the independence assumption STAT400 MATH 463 Spring 2017 7 7 What s Wrong Here 8543 8543 assuming independence of the cot death events Unknown genetic environmental factors that dispose the family to the cot death the 2nd death event becomes much more likely if the 1st event occurred Even accept the independence assumption 1 in 73 million Prob Sally is innocent 2 babies died STAT400 MATH 463 Spring 2017 7 7 What s Wrong Here 8543 8543 assuming independence of the cot death events Unknown genetic environmental factors that dispose the family to the cot death the 2nd death event becomes much more likely if the 1st event occurred Even 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 STAT400 MATH 463 Spring 2017 7 7
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