Wilcoxon/Mann-Whitney test and Kruskal-Wallis test

In this blog, i'm going to talk about Mann-Whitney test and Kruskal-Wallis test

 

1. Wilcoxon/Mann-Whitney test : To evaluate whether two samples could originate from the same distribution, a T-test is often used to evaluate whether just the means of the two samples are different. To test the same basic hypotheses, you could also look at other statistics, the mean rank. The test using this statistic is called the Wilcoxon test for two samples.

 1-1) hypotheses : The null hypothesis for this test would be that there is no difference between two samples. The test statistic in this test is the sum of the ranks for the smallest group.

 ** If group sizes are bigger than 10, the rank-sums become normally distributed, so then a z-test can be used.

 ** The Wilcoxon test for two independent samples is often the most suitable test to compare measures of central tendency. It can be applied to data with ordinal as well as numerical measurement levels. The Wilcoxon test is sometimes said to test for a difference in medians among two samples.

 ** It assumes independent random samples from two groups and requires that the data have at least an ordinal measurement level.

 

2. Kruskal-Wallis test : Just as the comparison of means among two groups can be extended to comparisons of means across many groups, the non-parametric approach to compare mean ranks between two groups, can also be extended to multiple groups. And the test that does this is called the Kruskal-Wallis test. It's a nonparametric counterpart to the one-way analysis of variance.

 2-1) The Kruskal-Wallis test : It compares the mean ranks for several groups within a total sample to help decide whether these groups might be coming from different populations.

 ** The kruskal-Wallis test statistics follows a chi square distribution.

 ** The Kruskal-Wallis test does not show which groups differ among each other.