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Unformatted text preview: Outline The Statistical Model and Hypothesis The ContrastBased Approach The RankBased Approach Lecture 30 Chapter 11: Comparing k( > 2) Populations Michael Akritas Michael Akritas Lecture 30 Chapter 11: Comparing k( > 2 ) Populations Outline The Statistical Model and Hypothesis The ContrastBased Approach The RankBased Approach The Statistical Model and Hypothesis The ContrastBased Approach Comparing k( > 2) Means Comparing k ( > 2) Proportions The RankBased Approach The KruskalWallis Test Procedures Using Contrasts on the Average Ranks Michael Akritas Lecture 30 Chapter 11: Comparing k( > 2 ) Populations Outline The Statistical Model and Hypothesis The ContrastBased Approach The RankBased Approach Michael Akritas Lecture 30 Chapter 11: Comparing k( > 2 ) Populations Outline The Statistical Model and Hypothesis The ContrastBased Approach The RankBased Approach I Let μ i , σ 2 i , denote the mean and variance of population (or factor level) i , i = 1 ,..., k . Michael Akritas Lecture 30 Chapter 11: Comparing k( > 2 ) Populations Outline The Statistical Model and Hypothesis The ContrastBased Approach The RankBased Approach I Let μ i , σ 2 i , denote the mean and variance of population (or factor level) i , i = 1 ,..., k . I Write μ i = μ + α i , where μ = k 1 ∑ n i =1 μ i is the overall mean, and α i = μ i μ is the effect of population i . Michael Akritas Lecture 30 Chapter 11: Comparing k( > 2 ) Populations Outline The Statistical Model and Hypothesis The ContrastBased Approach The RankBased Approach I Let μ i , σ 2 i , denote the mean and variance of population (or factor level) i , i = 1 ,..., k . I Write μ i = μ + α i , where μ = k 1 ∑ n i =1 μ i is the overall mean, and α i = μ i μ is the effect of population i . I Of interest is the testing of zero effects ( α i = 0 for all i ), or H : μ 1 = μ 2 = ··· = μ k vs H a : H is false . Michael Akritas Lecture 30 Chapter 11: Comparing k( > 2 ) Populations Outline The Statistical Model and Hypothesis The ContrastBased Approach The RankBased Approach I Let μ i , σ 2 i , denote the mean and variance of population (or factor level) i , i = 1 ,..., k . I Write μ i = μ + α i , where μ = k 1 ∑ n i =1 μ i is the overall mean, and α i = μ i μ is the effect of population i . I Of interest is the testing of zero effects ( α i = 0 for all i ), or H : μ 1 = μ 2 = ··· = μ k vs H a : H is false . I H can also be described in terms of k 1 contrasts: H : μ 1 μ 2 = 0 ,μ 1 μ 3 = 0 ,...,μ 1 μ k = 0 . Michael Akritas Lecture 30 Chapter 11: Comparing k( > 2 ) Populations Outline The Statistical Model and Hypothesis The ContrastBased Approach The RankBased Approach I Let μ i , σ 2 i , denote the mean and variance of population (or factor level) i , i = 1 ,..., k ....
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 Spring '00
 Akritas
 Variance, statistical model, Michael Akritas, contrastbased approach

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