Kruskal-Wallis Test Calculator

Kruskal-Wallis Test

The Kruskal-Wallis test is a non-parametric alternative to the one-way ANOVA. Use it when the normality assumption of ANOVA cannot be met, or when working with ordinal data.

When to use it:

• Comparing 3 or more independent groups
• Data is not normally distributed
• Data is ordinal (ranked categories)
• Sample sizes are small

The H statistic:

H = (12 / (N(N+1))) * sum(R_i^2 / n_i) - 3(N+1)

Where:

• N = total number of observations across all groups
• k = number of groups
• n_i = number of observations in group i
• R_i = sum of ranks assigned to group i

Tie correction: When ties exist, H is divided by: C = 1 - (sum(t^3 - t)) / (N^3 - N) Where t = number of observations in each tied group.

Interpretation:

• H follows a chi-squared distribution with df = k - 1 (for large samples)
• A large H means the groups are likely different
• p < 0.05: reject the null hypothesis (groups likely differ)
• p >= 0.05: insufficient evidence groups differ

Null hypothesis: All groups come from the same distribution (equal medians).

Post-hoc testing: A significant Kruskal-Wallis result tells you that some groups differ, but not which ones. Follow up with pairwise Mann-Whitney U tests (with Bonferroni correction) to identify which pairs differ.

Important note: Kruskal-Wallis tests whether the distributions differ, not just the medians. It assumes the distributions have similar shapes (just potentially different locations).