# Kruskal-Wallis test

## Description

The Kruskal-Wallis test (H-test) is an extension of the Wilcoxon test and can be used to analyse the effect of a classification factor on ordinal data. It tests the hypothesis that a number of unpaired samples originate from the same population.

## Required input

- Variable: select a continuous variable.
- Factor codes: select a categorical or qualitative variable. This variable may either contain character or numeric codes. These codes are used to break-up the data into several subgroups.
- Optionally select a filter to include a subset of cases.

### Options

**Post-hoc test significance level**: the desired significance level for the post-hoc test. If the Kruskal-Wallis test results in a P-value less than this significance level, SciStat.com performs a post-hoc test.**Jonckheere-Terpstra trend test**: when the qualitative factor is ordered the Jonckheere-Terpstra trend test can be used to test the hypothesis that the medians are ordered (increase or decrease) according to the order of the qualitative factor (Bewick et al., 2004; Sheskin 2011).

## Results

If the null-hypothesis, being the hypothesis that the samples originate from the same population, is rejected (P<0.05), then the conclusion is that there is a statistically significant difference between at least two of the subgroups.

### Post-hoc analysis

If the Kruskal-Wallis test is positive (P less than the selected significance level) then SciStat.com performs a test for pairwise comparison of subgroups.

## Literature

- Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall.
- Bewick V, Cheek L, Ball J (2004) Statistics review 10: further nonparametric methods. Critical Care 8:196-199.
- Conover WJ (1999) Practical nonparametric statistics, 3
^{rd}edition. New York: John Wiley & Sons. - Dunn OJ (1964) Multiple comparisons using rank sums. Technometrics 6:241-252.
- Rosner B (2006) Fundamentals of Biostatistics. 6
^{th}ed. Pacific Grove: Duxbury. - Sheskin DJ (2011) Handbook of parametric and nonparametric statistical procedures. 5
^{th}ed. Boca Raton: Chapman & Hall /CRC.

## See also

## Link

Go to Kruskal-Wallis test.