This calculator helps you compare three or more independent groups using a non-parametric approach. Instead of analyzing raw values like traditional ANOVA, the Kruskal-Wallis test examines the ranks of your data, making it ideal when your data violates normality assumptions or has unequal variances.
💡 Pro Tip: If your data meets normality and equal variance assumptions, consider ourOne-Way ANOVA Calculatorinstead for greater statistical power.
Ready to analyze your groups? to see how rank-based analysis works, or upload your own data to discover if your groups have significantly different distributions.
Kruskal-Wallis Test is a non-parametric method for testing whether samples originate from the same distribution. It's used to determine if there are statistically significant differences between two or more groups of an independent variable on a continuous or ordinal dependent variable. It extends the Mann–Whitney U test, which is used for comparing only two groups.
Where:
where is the number of tied observations at rank .
The corrected test statistic is then calculated as:
Test scores from three groups:
| Value | Rank | Rank (Adjusted for ties) | Group |
|---|---|---|---|
| 5 | 1 | 1 | Group 1 |
| 6 | 2 | 2.5 | Group 1 |
| 6 | 3 | 2.5 | Group 2 |
| 7 | 4 | 4 | Group 1 |
| 8 | 5 | 6 | Group 1 |
| 8 | 6 | 6 | Group 2 |
| 8 | 7 | 6 | Group 3 |
| 9 | 8 | 8.5 | Group 2 |
| 9 | 9 | 8.5 | Group 3 |
| 10 | 10 | 10.5 | Group 2 |
| 10 | 11 | 10.5 | Group 3 |
Referring to the Chi-square distribution table, the critical value for with degrees of freedom at a significance level of is .
The p-value can be found using the Chi-square Distribution Calculator with and , which gives .
Since (critical value), we fail to reject . There is insufficient evidence to conclude that the distributions differ significantly across groups.
Eta-squared () measures the proportion of variability in ranks explained by groups:
Where:
Interpretation guidelines:
For our example:
This indicates a large effect size, suggesting substantial practical significance in the differences between groups, even though the result was not statistically significant.
This calculator helps you compare three or more independent groups using a non-parametric approach. Instead of analyzing raw values like traditional ANOVA, the Kruskal-Wallis test examines the ranks of your data, making it ideal when your data violates normality assumptions or has unequal variances.
💡 Pro Tip: If your data meets normality and equal variance assumptions, consider ourOne-Way ANOVA Calculatorinstead for greater statistical power.
Ready to analyze your groups? to see how rank-based analysis works, or upload your own data to discover if your groups have significantly different distributions.
Kruskal-Wallis Test is a non-parametric method for testing whether samples originate from the same distribution. It's used to determine if there are statistically significant differences between two or more groups of an independent variable on a continuous or ordinal dependent variable. It extends the Mann–Whitney U test, which is used for comparing only two groups.
Where:
where is the number of tied observations at rank .
The corrected test statistic is then calculated as:
Test scores from three groups:
| Value | Rank | Rank (Adjusted for ties) | Group |
|---|---|---|---|
| 5 | 1 | 1 | Group 1 |
| 6 | 2 | 2.5 | Group 1 |
| 6 | 3 | 2.5 | Group 2 |
| 7 | 4 | 4 | Group 1 |
| 8 | 5 | 6 | Group 1 |
| 8 | 6 | 6 | Group 2 |
| 8 | 7 | 6 | Group 3 |
| 9 | 8 | 8.5 | Group 2 |
| 9 | 9 | 8.5 | Group 3 |
| 10 | 10 | 10.5 | Group 2 |
| 10 | 11 | 10.5 | Group 3 |
Referring to the Chi-square distribution table, the critical value for with degrees of freedom at a significance level of is .
The p-value can be found using the Chi-square Distribution Calculator with and , which gives .
Since (critical value), we fail to reject . There is insufficient evidence to conclude that the distributions differ significantly across groups.
Eta-squared () measures the proportion of variability in ranks explained by groups:
Where:
Interpretation guidelines:
For our example:
This indicates a large effect size, suggesting substantial practical significance in the differences between groups, even though the result was not statistically significant.
