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Unformatted text preview: Statistics 127A Mrinal Raghupathi Wednesday, September 1st, 2010 Reminder Quiz tomorrow on chapters 1 and 2. You should make sure you know how to do Exercise Set A. The problems listed online are for practice, you do not have to turn them in. Example: Sex bias in Graduate Admissions (Chapter 2.4) UC Berkeley graduate admissions. An observational study. Applied Rate Men 8,442 44% Women 4,321 35% Example continued Graduate admission by top six majors Men Women Major Applications Rate Applications Rate A 825 62 108 82 B 560 63 25 68 C 325 37 593 34 D 417 33 375 35 E 191 28 393 24 F 373 6 341 7 44% of men admitted, 30% of women. Example continued Men admission rate = number of men admitted total applications from men (1) = . 62 × 825 + . 63 × 560 + ··· + . 06 × 373 825 + 560 + 325 + 417 + 191 + 373 (2) ≈ . 445 = 44 . 5 % (3) Women Same idea with the totals for women. Example continued Why? Example continued Why? I The rst two majors were easy to get into. Over 50% (825 + 560 = 1,385 out of a total of 2,691) of the men applied to these two majors. I The other four majors are much harder to get into. Over 90% (1,702 out of 1,835) of the women applied to these four majors. Example continued This is called Simpson's paradox : Percentages can be reversed when subgroups are combined. If we look at the success rates for men and women and adjust for the sex di erence then we get 39% and 43%. [This is the technical note on page 19]. A calculation The total number of applicants for each major are as follows: Major Applications A 933 B 585 C 918 D 792 E 584 F 714 4,526 men = . 62 × 933 + ··· . 06 × 714 4 , 526 ≈ . 39 women = . 82 × 933 + ··· . 07 × 714 4 , 526 ≈ . 43 Reducing confounding This can be very hard, especially in an observational study. Looking at smaller groups that are more homogeneous with respect to that factor. Problem (2.A.1)Problem (2....
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 Fall '10
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 Statistics, Polio vaccine, Poliomyelitis, Jonas Salk, University of Pittsburgh, Albert Sabin, Tra1Ec Safety Administration

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