Mood's Median Test
Also known as: median test, Brown-Mood median test, Mood Medyan Testi
Mood's median test is a nonparametric procedure that compares the medians of k independent groups by counting how many observations in each group fall above and below the pooled (grand) median, then applying a chi-square test to the resulting 2×k contingency table. It traces to A. M. Mood's 1954 work on nonparametric two-sample tests.
Key highlights
- Highly resistant to outliers and extreme values, because it only uses each observation's position relative to the median rather than its magnitude.
- Makes very weak assumptions: it needs only independent groups and orderable data, with no normality requirement.
- Simple to compute and interpret as a chi-square test on a 2×k above/below-median table, and it extends naturally from two to k groups.
Intuition
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How it works
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When to use it
Use Mood's median test to compare the central tendency of two or more independent groups when the outcome is continuous or ordinal and you cannot assume normality. It needs only independent groups and data that can be ordered, and it shines as an outlier-resistant alternative to the Kruskal-Wallis test when extreme values are present. Aim for at least about 20 observations overall; with very small samples (n below 10) its statistical power drops and a permutation test is preferable, and below 5 observations a median-based chi-square is not meaningful.
Strengths & limitations
- Highly resistant to outliers and extreme values, because it only uses each observation's position relative to the median rather than its magnitude.
- Makes very weak assumptions: it needs only independent groups and orderable data, with no normality requirement.
- Simple to compute and interpret as a chi-square test on a 2×k above/below-median table, and it extends naturally from two to k groups.
- Discards information by reducing each value to a binary above/below indicator, so it is generally less powerful than the Kruskal-Wallis test when data are reasonably well behaved.
- Low power in very small samples (n below 10); below 5 observations the median-based chi-square is meaningless.
- Tests equality of medians under broadly similar distribution shapes; differing spreads or shapes across groups can complicate interpretation.
Common pitfalls
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Applications
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Frequently asked
How is Mood's median test different from the Kruskal-Wallis test?
Both are nonparametric ways to compare k groups, but Mood's median test only counts how many observations fall above or below the pooled median, while Kruskal-Wallis uses the full ranking of every value. This makes Mood's test more resistant to outliers but usually less powerful when the data are well behaved.
What is the null hypothesis?
The null hypothesis is that all k groups share the same population median, so that within each group an observation is equally likely to fall above or below the grand median. A large chi-square statistic provides evidence against equal medians.
How many observations do I need?
Aim for at least about 20 observations overall. With fewer than 10 the test loses statistical power and a permutation test is preferable; with fewer than 5 a median-based chi-square is not meaningful.
Does it assume the groups have the same distribution shape?
It assumes independent groups and orderable data and does not require normality. It is most cleanly interpreted as a test of equal medians when the group distributions have broadly similar shapes; large differences in spread or shape can blur what a rejection means.
Sources
- 1.Mood, A. M. (1954). On the Asymptotic Efficiency of Certain Nonparametric Two-Sample Tests. Annals of Mathematical Statistics, 25(3), 514-522.
- 2.Hollander, M., Wolfe, D. A., & Chicken, E. (2014). Nonparametric Statistical Methods (3rd ed.). Wiley.ISBN 978-0470387375
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Cite this page
ScholarGate. (2026, June 1). Mood's Median Test. ScholarGate. https://scholargate.app/statistics/mood-median-test