Kruskal Wallis Test

Statistics MOC #fleeting Statistics

Application

1. The problem objective is to compare 2 or more populations
2. The data are either ordinal or interval, but nonnormal
3. The samples are independent

The application of Kruskal Wallis Test and Friedman Test are all for non-parameters test, but they differ in their application scenarios and test statistics. The Key difference is that the experimental design is independent samples and randomized blocks

Hypothesis

$H_0$: The locations of all $k$ populations are the same. $H_1$: At least two population locations differ.

Test Statistic

The test statistic of KW, is denoted by $H$, and the equation is If the rank sum is similar, the test statistic will be small. The smaller the H, the

Sampling distribution

The distribution of the test statistic can be derived in the same way in Wilcoxon Signed Rank Sum Test When the sample size small (smaller than 5), we could just easily list all the content. But when the sample size is larger than 5, the test statistic $H$ is approximately like the one in Chi-squared Distribution The rejection region

What is the difference between Wilcoxon Signed Rank Sum Test?

The KW method could produce the same result to the Wilcoxon Signed Rank Sum Test as the two-tail case, but it could only determine whether the difference exist ($H_0$), to determine whether it is at right or left, we still need to use Wilcoxon Signed Rank Sum Test