Chapter 8: Kruskal-Wallis Test Chapter 8: A Non-parametric Alternative to ANOVA The Wilcoxon Rank Sum test can be extended for comparisons of more than two populations where the assumptions of the ANOVA are questionable. Kruskal-Wallis Test Let ni be the size of the ith sample and N be the combined size of all samples, i.e., and let k be the number of populations we have sampled from. iiN=∑n Here the null hypothesis is that all k populations are identical and the alternative is that they are not all identical. H0: All the k populations are identical Ha: At least one population is different from the others. The test statistic is: 21123( 1)(1)kiiiTHNNN n==−+∑+ where T is the sum of the ranks for the observations in the i2ith sample. Decision rule: For the specified level of α, reject H0 if H is greater than a . The p-value is given by. 2,1kα−Χ{}21PrkH−Χ> Example: Seasonal Diet Patterns in Ravens • T1 = 12+8+6 = 26 • T2 = 5+9+10.5 = 24.5 • T3 = 4+3+1 = 8 • T4 = 2+10.5+7 = 19.5 Month Season Y' RankNOV 1 1.329721 12DEC 1 1.254080 8JAN 1 1.145808 6FEB 2 1.115957 5MAR 2 1.257474 9APR 2 1.280374 10.5MAY 3 1.113428 4JUN 3 1.039152 3JUL 3 0.605545 1AU G 4 0.967390 2SE P 4 1.280374 10.5OCT 4 1.237554 7Chapter 8: Kruskal-Wallis Test 022222.05,4 12: No seasonal difference vs. : Seasonal Differences12 (26) (24.5) (8) (19.5). .: 3(12 1) 44.12 39 5.1212(12 1) 3 3 3 3..( 0.05): 7.815value: ( 5.12) .1632aHHTS HRR HPPHαχχ−⎡⎤=+++−+=−⎢⎥+⎣⎦=≥=−≥===
View Full Document
Unlocking...