Mood's Median Test Calculator

Mood's Median Test is a non-parametric statistical method used to test whether two or more independent groups share the same population median. It works by classifying each data point as above or below the overall combined median, then applying a Chi-square test on the resulting contingency table. It makes no assumptions about the underlying distribution of the data.

Use Mood's Median Test when your data does not meet the normality assumption required by one-way ANOVA. It is especially appropriate for ordinal data, heavily skewed distributions, or small samples where distribution assumptions are uncertain. However, it is less powerful than the Kruskal-Wallis test when data are continuous.

The null hypothesis (H₀) states that all groups have equal population medians. The alternative hypothesis (H₁) states that at least one group has a median different from the others. Rejecting H₀ means there is statistically significant evidence that at least one group median differs.

The test combines all group data to compute the overall median, then counts how many values in each group fall above and below that median. These counts form a 2×k contingency table (k = number of groups). A standard Chi-square test for independence is applied to this table, yielding the test statistic with k−1 degrees of freedom.

If the p-value is less than or equal to your chosen significance level α (e.g. 0.05), you reject the null hypothesis and conclude that at least one group median differs significantly. If the p-value exceeds α, you fail to reject H₀ and conclude there is insufficient evidence of a difference in medians.

Mood's Median Test has lower statistical power compared to the Kruskal-Wallis test, particularly with continuous data. It can also be unreliable with small sample sizes or when many values equal the overall median. Additionally, it does not tell you which specific groups differ — post-hoc analysis is needed for that.

The Chi-square test underlying Mood's Median Test is inherently two-tailed. Selecting one-tailed halves the p-value, appropriate only when you have a strong prior directional hypothesis (e.g. group A's median is specifically higher than group B's). Two-tailed is the standard and recommended choice for most analyses.

Common alternatives include the Kruskal-Wallis test (more powerful for continuous data across k groups), the Mann-Whitney U test (for comparing exactly two groups), and the sign test (for one-sample or paired comparisons). If your data are normally distributed, one-way ANOVA is preferred for its greater statistical power.