Rank multiple groups without strict normality assumptions. Get H statistic, p-value, effect size, and summaries. Review tables, charts, formulas, exports, and practical guidance easily.
This sample helps you test the calculator instantly. Replace the values with your own observations when you are ready.
| Observation | Group A | Group B | Group C |
|---|---|---|---|
| 1 | 12 | 18 | 9 |
| 2 | 15 | 19 | 8 |
| 3 | 14 | 17 | 11 |
| 4 | 10 | 16 | 10 |
| 5 | 13 | 20 | 7 |
This calculator uses the Kruskal-Wallis test, a rank-based alternative to one-way ANOVA. It is suitable when data are ordinal, skewed, or when normality assumptions are not reasonable.
Main statistic:
H = [12 / (N(N + 1))] × Σ(Ri2 / ni) - 3(N + 1)
Here, N is the total observation count, Ri is the sum of ranks for group
i, and ni is that group size.
Tie correction:
C = 1 - Σ(t3 - t) / (N3 - N)
Hcorrected = H / C
The p-value is estimated from the chi-square distribution with k - 1 degrees of freedom,
where k is the number of analyzed groups.
Effect size:
ε² = (H - k + 1) / (N - k)
When the p-value is below alpha, the ranked distributions are considered different enough to reject the null hypothesis. When it is above alpha, the observed ranking differences may reflect ordinary variation rather than a systematic group effect.
A nonparametric ANOVA calculator helps compare three or more independent groups when classic one-way ANOVA assumptions do not fit the data well. Many real datasets contain skewness, outliers, unequal spreads, or ordinal responses. In such cases, rank-based analysis provides a practical alternative.
This page uses the Kruskal-Wallis framework to transform raw values into ranks across all submitted observations. It then evaluates whether the groups share a similar distribution pattern. The method is especially useful in biology, education, operations research, quality analysis, survey scoring, and applied social science work.
Beyond the main H statistic, the calculator also reports degrees of freedom, p-value, effect size, group medians, means, minimums, maximums, rank totals, and mean ranks. Those outputs make interpretation easier when you need both an inferential result and a readable summary for reporting.
The included pairwise comparisons add another practical layer. While the overall test tells you whether at least one group differs, the pairwise rank checks help identify where the strongest differences may exist. Because multiple comparisons can inflate error, the calculator also shows Bonferroni-adjusted p-values for cautious follow-up review.
The export buttons are useful when sharing results with colleagues, students, or clients. The CSV file supports spreadsheet analysis, while the PDF option creates a portable summary for documentation. The chart provides a quick visual view of spread, clustering, and unusual points across groups.
For the best interpretation, use this calculator with independent samples, numeric or ordinal observations, and a reasonable sample size in each group. Always combine the statistical output with domain knowledge, study design, and data quality checks before making final conclusions.
It tests whether independent groups differ in their ranked outcomes using the Kruskal-Wallis method, which is commonly treated as nonparametric ANOVA.
Use it when data are not normally distributed, include outliers, are ordinal, or when sample conditions make standard one-way ANOVA less reliable.
Yes. The calculator still works with two groups, although the procedure becomes closely related to rank-based two-sample testing.
The p-value estimates how likely the observed rank differences would appear if all groups truly came from similar distributions.
Ranks reduce sensitivity to distribution shape and extreme observations, making the method more robust for non-normal or ordinal data.
Epsilon squared is an effect size estimate. It helps show how much of the group variation is associated with ranked group differences.
They are useful follow-up indicators. You should still interpret them carefully, especially with small samples or many simultaneous comparisons.
Yes. It applies a tie correction so the H statistic remains more accurate when repeated values occur across the combined dataset.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.