MedCalc

# Kruskal-Wallis test

 Command: StatisticsANOVAKruskal-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 nonparametric methods. Critical Care 8:196-199.
• Conover WJ (1999) Practical nonparametric statistics, 3rd edition. New York: John Wiley & Sons.
• Dunn OJ (1964) Multiple comparisons using rank sums. Technometrics 6:241-252.
• Rosner B (2006) Fundamentals of Biostatistics. 6th ed. Pacific Grove: Duxbury.
• Sheskin DJ (2011) Handbook of parametric and nonparametric statistical procedures. 5th ed. Boca Raton: Chapman & Hall /CRC.