1Chapter 4:Gathering DataRead Chapter 4Simpson’s ParadoxSimpson’s Paradox:When the direction of an association between two variables changes after we include a third variable and analyze the data at separate levels of that variableSimpson’s Paradox ExampleProbability of Death of Smoker = 139/582=24%Probability of Death of Nonsmoker = 230/732=31% Is Smoking Actually Beneficial to Your Health?This can’t be true that smoking improves your chances of living!What’s going on!Simpson’s Paradox ExampleBreak out Data by AgeBerkeley ’73 Admissions Data: Simpson’s ParadoxLet’s settle the law suit regarding under-admission of females to UCB graduate schoolMalesFemalesMajor#App %Admit #App %AdmitA8256210882B560632568C3253759334D4173337535E1912839334F3730634107Listed 44%30%All844244%432135% Women applied to majors with low admission rates (C-F) and men applied to majors with higher admission rates.Perils of AggregationYou win a $1,000,000,000, 000 if you select a red ball! Which urn would you select? Blueor White?Game 1: Blue Urn: 5 Red 6 GreenWhite Urn: 3 Red 4 GreenP(Red in Blue urn)=5/11=.455P(Red in White urn)=3/7=.429 Blue better! Game 2:Blue Urn: 6 Red 3 GreenWhite Urn: 9 Red 5 GreenP(Red in Blue urn)=6/9=.667P(Red in White urn)=9/14=.643Blue better! Combined Game:Blue Urn: 11 Red 9 GreenWhite Urn: 12 Red 9 GreenP(Red in Blue urn)=11/20=.55P(Red in White urn)=12/21=.571White better!
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