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Unformatted text preview: Chapter 2: TwoSample Methods 6 Scoring Systems • Different scoring systems: to come up with ones that are effective in re vealing difference that exist among treatments • Which one to choose? – depends on the distribution of population • Whatever scoring system we use, a permutation test is applied to the scores • Scores (a) Rank W 1 ,...,W N ∼ iid f ( w ) = 1 N + 1 w = 0 , 1 ,...,N + 1 (b) van der Waerden Scores (quantile normal scores) V ( i ) = Φ 1 parenleftbigg i N + 1 parenrightbigg (c) Exponential or Savage Scores E ( i ) = i summationdisplay j =1 1 N + 1 − j – powerful for comparing scale differences in exponential distribution or location shifts in extreme value distributions. 1 Example The mouse data (Efron). 16 mice divided assigned to a treat ment group (7) or a control group (9). Survival in days following a test surgery. Did the treatment prolong survival ? Ordered Data Group Rank VW Scores Savage Scores 10 C 11.565 0.063 16 T 21.187 0.129 23 T 30.929 0.201 27 C 40.722 0.278 30 C 50.541 0.361 38 T 60.377 0.452 40 C 70.223 0.552 46 C 80.074 0.663 51 C 9 0.074 0.788 52 C 10 0.223 0.931 94 T 11 0.377 1.097 99 T 12 0.541 1.297 104 C 13 0.722 1.547 141 T 14 0.929 1.881 146 C 15 1.1871....
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 Spring '08
 Staff
 Normal Distribution, Null hypothesis, yj, permutation test, RMD, van der Waerden

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