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The document discusses non-parametric statistical tests for comparing distributions that are not normally distributed or that involve ordinal data. It specifically describes the Wilcoxon Rank-Sum test for comparing two independent samples, and provides an example comparing the medians of two emergency room operating rates. It also describes the Kruskal-Wallis test for comparing three or more independent samples, and provides an example comparing the medians of filling times across three machines.

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Ordinal Dependent Variable or Non-normal Continuous Variable Week 14 4/6/09 Comparing non-parametric statistics Final due 4/12/09
Wilcoxon Rank-Sum Test for Differences in 2 Medians ,[object Object],[object Object],[object Object],[object Object]
Wilcoxon Rank-Sum Test ,[object Object],[object Object],[object Object],[object Object],[object Object]
Wilcoxon Rank-Sum Test ,[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],Wilcoxon Rank-Sum Test:
Wilcoxon Rank-Sum Test: Tie in 3 rd and 4 th places Ranked Capacity values: Capacity Rank Hosp A Hosp B Hosp A Hosp B 71 1 77 2 82 3.5 82 3.5 85 5 88 6 92 7 94 8 97 9 Rank Sums: 20.5 24.5
Wilcoxon Rank-Sum Test: ,[object Object],[object Object]
Wilcoxon Rank-Sum Test: ,[object Object],[object Object]
Kruskal-Wallis Rank Test for c Medians ,[object Object],[object Object],[object Object]
Kruskal-Wallis Rank Test ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Kruskal-Wallis Rank Test: ,[object Object],Machine1 Machine2 Machine3 25.40 23.40 20.00 26.31 21.80 22.20 24.10 23.50 19.75 23.74 22.75 20.60 25.10 21.60 20.40
Obtaining a Ranking Machine1 Machine2 Machine3 14 9 2 15 6 7 12 10 1 11 8 4 13 5 3 Raw Data Ranks 65 38 17 Machine1 Machine2 Machine3 25.40 23.40 20.00 26.31 21.80 22.20 24.10 23.50 19.75 23.74 22.75 20.60 25.10 21.60 20.40
Kruskal-Wallis Test Procedure ,[object Object],[object Object],where: n = sum of sample sizes in all samples c = Number of samples T j = Sum of ranks in the j th sample n j = Size of the j th sample
Kruskal-Wallis Test Example Solution ,[object Object],[object Object],[object Object],[object Object],[object Object],Decision: Conclusion:  = .05 H = 11.58
Nonparametric Equivalents ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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Hph7300week14winter2009narr

  • 1. Ordinal Dependent Variable or Non-normal Continuous Variable Week 14 4/6/09 Comparing non-parametric statistics Final due 4/12/09
  • 2.
  • 3.
  • 4.
  • 5.
  • 6. Wilcoxon Rank-Sum Test: Tie in 3 rd and 4 th places Ranked Capacity values: Capacity Rank Hosp A Hosp B Hosp A Hosp B 71 1 77 2 82 3.5 82 3.5 85 5 88 6 92 7 94 8 97 9 Rank Sums: 20.5 24.5
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12. Obtaining a Ranking Machine1 Machine2 Machine3 14 9 2 15 6 7 12 10 1 11 8 4 13 5 3 Raw Data Ranks 65 38 17 Machine1 Machine2 Machine3 25.40 23.40 20.00 26.31 21.80 22.20 24.10 23.50 19.75 23.74 22.75 20.60 25.10 21.60 20.40
  • 13.
  • 14.
  • 15.