Rank analyses Kruskal-Wallis test

Having calculated the level of significance can be obtained from appropriate tables. The Wilcoxon signed rank test is the non-parametric equivalent of the paired t-test. The Kruskal-Wallis test is another rank sums test that is used to test the null hypothesis that k independent samples come from identical populations against the alternative that the means of the populations are unequal. It provides a non-parametric alternative to the one-way analysis of variance. 

In the Kruskal-Wallis test the original scores are first ranked and an ANOVA analysis is then carried out on the ranks. As with Wilcoxon s rank sum test, ranking of the observations must deal with ties. The sums of squares are based on... 

The post-intervention data were not distributed in a way that allowed transformation to normality. No information was collected on subjects that had been sampled multiple times, so it was not possible to account for this in analysis. Medians were reported and nonparametric Wilcoxon and Kruskal—Wallis tests were used to examine group differences, and the Spearman rank procedure for the analysis of correlations. 

The tests performed were the same used for the analysis of individual motivational values. The Kruskal-Wallis test and the Dunn s post-test are used for the first comparison, and the Wilcoxon signed-ranked test is used for the second comparison. 

The analysis of rank data, what is generally called nonparametric statistical analysis, is an exact parallel of the more traditional (and familiar) parametric methods. There are methods for the single comparison case (just as Student s t-test is used) and for the multiple comparison case (just as analysis of variance is used) with appropriate post hoc tests for exact identification of the significance with a set of groups. Four tests are presented for evaluating statistical significance in rank data the Wilcoxon Rank Sum Test, distribution-free multiple comparisons, Mann-Whitney U Test, and the Kruskall-Wallis nonparametric analysis of variance. For each of these tests, tables of distribution values for the evaluations of results can be found in any of a number of reference volumes (Gad, 1998). 

We used t-tests with a Bonferroni adjustment for multiple comparisons when appropriate. When assumptions for parametric analysis were not met, we used Kruskal-Wallis (H) analysis of variance on rank, followed by planned pairwise comparisons of interest using Dunn s (Q) method. 

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