LectureNov12

LectureNov12 - BME 423 Lecture Notes - Nov. 12, 2008...

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Methods Based on Ranks – Nonparameteric Methods BME 423 Lecture Notes - Nov. 12, 2008 I Parametric versus Nonparameteric Methods II. Mann-Whitney Rank-Sum – Two Different Groups A. Idea B. Mann-Whitney Test C. Example III. Wilcoxon Signed-Rank – Same Subject, Two Treatments A. Idea B. Wilcoxon Test C. Example Glantz Chapt. 10, pp 363-385
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Normal or Gaussian Density f ( x ) x μ σ 2 ~( , ) XN μσ () 2 2 1 exp 2 2 x x f μ σ σπ ⎛⎞ −− ⎜⎟ ⎝⎠ =
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II. Mann-Whitney Rank-Sum – Two Different Groups A. Idea Make inferences based on Rank T – Sum of Ranks in Smaller Group will be used as the Test Statistics 12 0: H μ =
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Is T=9 sufficiently extreme to justify rejecting the hypothesis that the drug had no effect? (35 possibilities)
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Distribution of T under the Null Hypothesis
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Procedure 1. Rank all observations in ascending order regardless of group (ties ). 2. Compute T – sum of ranks in smaller group. 3. Comparer T to its critical values a. use T statistic table b. use Normal distribution pdf of T 8 B N 8 B N > 2 (, ) TT N μ σ
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LectureNov12 - BME 423 Lecture Notes - Nov. 12, 2008...

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