What the Friedman test does
The Friedman test compares three or more related conditions, such as the same people rating three products. It ranks the values within each subject, then checks whether some conditions consistently rank higher. It is the nonparametric alternative to repeated-measures ANOVA and extends the Wilcoxon signed-rank test. See the Friedman test explained.
Worked example
Eight tasters rate three recipes. Mean ranks are 1.06, 1.94 and 3.00, and the test gives χ²(2, N = 8) = 15.55, p < .001. Kendall’s W = .97 means the tasters agree closely on the order. All three Holm-adjusted pairwise comparisons give p = .023.
Effect size: Kendall’s W
W = χ² / (n(k − 1)) runs from 0 (no agreement) to 1 (every subject orders the conditions identically). Rough guides are .1 small, .3 medium and .5 large.
Computation
χ² and p come from SciPy’s friedmanchisquare, with a correction for ties. Pairwise tests use the Wilcoxon signed-rank test with Holm adjustment. With very few subjects, adjusted p-values cannot get very small. For independent groups, use Kruskal–Wallis.
Frequently asked questions
When do I use the Friedman test instead of Kruskal-Wallis?
Use Friedman when the same subjects appear in every condition. Use Kruskal-Wallis when each group contains different subjects.
What is the post-hoc test for Friedman?
Pairwise Wilcoxon signed-rank tests with a multiple-comparison correction are a common choice, and this calculator uses Holm's method.
What does Kendall's W mean?
It measures agreement among subjects about the order of the conditions, from 0 for none to 1 for complete agreement.
How many subjects do I need?
The chi-square approximation is rough with very few subjects. Treat results with fewer than about 10 subjects with care.