Kruskal-Wallis Test Calculator
Compare medians of multiple groups with this non-parametric test.
Enter Your Data
Enter comma-separated values for each sample set. Add more sets as needed.
Typical values are 0.05, 0.01, or 0.10
Results
Test Statistic (H):
P-value:
Interpretation:The p-value is less than the significance level (α = ). We reject the null hypothesis. There is a statistically significant difference between the medians of at least two of the sample groups.The p-value is greater than or equal to the significance level (α = ). We fail to reject the null hypothesis. There is no statistically significant difference between the medians of the sample groups.
Understanding Kruskal-Wallis Test
The Kruskal-Wallis test is used to determine if there is a statistically significant difference between the medians of two or more independent groups. It is a non-parametric test, which means it does not assume that the data are normally distributed.
- Null Hypothesis (H0): The medians of all groups are equal.
- Alternative Hypothesis (H1): At least one group median is different from the others.
- Test Statistic (H): Measures the variance between groups. A higher H value suggests greater differences between groups.
- P-value: The probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis.
A low p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, suggesting that there is a significant difference in medians among the groups.
About the Kruskal-Wallis Test
The Kruskal-Wallis test is a non-parametric alternative to the one-way ANOVA. It is used to compare the medians of two or more independent samples to determine if there is a statistically significant difference. Unlike ANOVA, the Kruskal-Wallis test does not assume a normal distribution of the data, making it suitable for ordinal data or when the assumption of normality is violated.
To perform the test, data from all groups are ranked together. The test statistic, denoted as H, is calculated based on the sum of ranks for each group. A significant H statistic indicates that there is evidence to reject the null hypothesis that all group medians are equal. The p-value is then used to determine the statistical significance of the result, typically compared against a chosen significance level (alpha), such as 0.05.
This test is widely used in fields like social sciences, medicine, and business to compare groups when data is not normally distributed. For further reading, you can refer to statistical textbooks or online resources like Wikipedia's Kruskal-Wallis test page.