# Kruskal-Wallis test

Command: | Statistics ANOVA Kruskal-Wallis test |

## Description

The **Kruskal-Wallis test** (*H*-test) is an extension of the Wilcoxon test and can be used to test the hypothesis that a number of unpaired samples originate from the same population. In MedCalc, *Factor codes* are used to break-up the (ordinal) *data* in one variable into different sample subgroups. 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.

## Required input

The following need to be entered in the dialog box: for *Data* select the variable containing the data, and for *Factor codes* the qualitative factor. The qualitative factor may either be character or numeric codes. These are the codes that will be used to break-up the data into several subgroups.

### Options

**Post-hoc test**: this is the test used for pairwise comparison of subgroups, when the Kruskal-Wallis test is positive (i.e. P is less than the selected significance level, see below). MedCalc offers 2 post-hoc tests: the test according to Dunn (1964) (see also Rosner, 2006) and Conover (1999).**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, MedCalc performs the selected 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

In this example, it is tested whether different treatment regimens coded A, B and C in the variable *Treatment*, have an influence on the data in the variable *Pain_relief*. Pain relief was recorded on an ordinal scale from 0 to 9. Since the null-hypothesis is not rejected (P=0.1995), the conclusion is that there is no statistical significant difference between the different treatments.

For a graphical representation of this test, refer to Multiple comparison graphs.

### Post-hoc analysis

If the Kruskal-Wallis test is positive (P less than the selected significance level) then MedCalc 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 non-parametric methods. Critical Care 8:196-199.
- Conover WJ (1999) Practical non-parametric 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 non-parametric statistical procedures. 5
^{th}ed. Boca Raton: Chapman & Hall /CRC.