# 09_07 - STAT 420 Examples for Fall 2010 Kruskal-Wallis test...

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STAT 420 Examples for 09/07/2010 Fall 2010 Kruskal-Wallis test for equivalence of means: Let f ( x ) be a density of a continuous random variable with mean 0. Assume Y i j , i = 1, 2, … , n j , j = 1, 2, … , J , are independent random variables with density f ( x μ j ) . ( The J populations have no parametric assumptions, they are assumed to have densities with a common shape, but perhaps different centers. ) H 0 : μ 1 = μ 2 = … = μ J H 1 : not all of the μ j are equal. μ i μ j for at least one pair i and j . Let r i j be the respective rank of a data point when all the data is ranked from smallest to largest. Let j r be the mean of the ranks for each group. Let r = 2 1 + N be the grand mean of the ranks. Test statistic: K = ( ) ( ) = - + J j j j N N r r n 1 2 1 12 = ( ) = + - + J j N j j N N r n 1 2 2 1 1 12 = ( ) ( ) 1 2 1 3 1 12 + - + = N j j j N N J r n . Reject

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09_07 - STAT 420 Examples for Fall 2010 Kruskal-Wallis test...

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