# Kruskal Wallis Test - Explained

What is the Kruskal Wallis Test?

# What is the Kruskal Wallis Test?

The KruskalWallis test refers to a rank-based nonparametric test that is used in statistical research or calculations to determine existing differences in the statistical differences between groups of independent variables on dependent variables. Also known as one-way ANOVA on ranks or KruskalWallis H test, the test is an extended alternative of the Mann-Whitney U test which is used to statistically compare more than 2 independent variable groups. When using KruskalWallis test, no assumptions are needed, unlike ANOVA where it is assumed that there is a normal distribution of dependent variable as well as an equal variance among group scores. Thus, we can apply KruskalWallis test in both ordinal- and continuous-level dependent variables. It is, however, noted that ANOVA is more powerful than KruskalWallis test.

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## How is the Kruskal Wallis Test Used?

AKruskalWallis test generally indicates that within a group of dependent variables, one sample dominates over another sample stochastically. However, the test fails to identify how the dominance occurs or even how many groups can result in the stochastic dominance. In order to analyze a specific sample pair for the stochastic dominance, the recommended methods to use include Dunns test, Conover, or Mann-Whitney tests.Unlike the analogous one-way variance analysis, the KruskalWallis test does not assume a normal residual distribution. In the case that a researcher is able to assume that all groups have identically scaled and shaped distributions, then the null hypothesis is that all the groups have equal medians. In this case, the alternative hypothesis would hold that at least one population median of a single group is different from the median of the population of at least another group.

## Examples of questions to be answered using the KruskalWallis test

•  Do the scores of job satisfaction differ by race/ethnicity?
•  What is the test scores difference between two variable grade levels in an elementary school?

In order to answer the above questions, it is important to note that KruskalWallis test approximates a chi-square distribution if the number of observations in every group is at least 5. In case the calculated value of the KruskalWallis test is less than the critical value of chi-square, then the null hypothesis would not be rejected. On the other hand, if the calculated value of the test is greater than the value of chi-square, then the researcher is able to reject the null hypothesis.

## Exact probability tables

In order to compute the exact probabilities for KruskalWallis test, research would need several computing resources. Software can only provide exact probabilities for studies with less sample size of 30 participants. Such programs require asymptotic approximation for samples with larger sizes.Studies have revealed in the past that the exact probability of larger sample sizes exists. For instance, in 2003, Spurrier published probability tables for a sample size of 45 participants. Later in 2006, Meyer and Seaman produced similar probability distribution using a larger sample size of 105 participants.