Friedman Test Calculator
Run the Friedman test on repeated measures or blocked data — tie-corrected chi-square statistic, degrees of freedom, p-value, Kendall’s W and the mean rank of every condition.
How it works
Rank each row 1…k; Rⱼ = rank sum of condition j; χ²F = [12 ÷ (n·k·(k+1))]·ΣRⱼ² − 3n(k+1), divided by 1 − Σ(t³−t) ÷ [n·k·(k²−1)] for ties; df = k − 1; Kendall’s W = χ²F ÷ [n(k−1)]
The Friedman test is the non-parametric alternative to one-way repeated-measures ANOVA: the same subjects (or matched blocks) are measured under three or more conditions, the values are ranked within each subject, and the test asks whether some conditions get consistently higher ranks. The statistic follows a chi-square distribution with k − 1 degrees of freedom; the tie correction matches SciPy’s friedmanchisquare and R’s friedman.test. Kendall’s W rescales it to 0–1 as an effect size.
Worked example
Eight subjects rate three products: rank sums 23.5, 15.5 and 9, so χ²F = 14.552 with 2 df (tie-corrected), p = 0.0007 and Kendall’s W = 0.909 — the products are rated differently.
Sources: SciPy — scipy.stats.friedmanchisquare · NIST Dataplot — Friedman test
Frequently asked questions
When should I use the Friedman test?
When the same subjects are measured under three or more conditions and the data are ordinal, skewed or have outliers, so repeated-measures ANOVA is not appropriate.
What does Kendall’s W mean?
It is the coefficient of concordance: 0 means no consistent ordering of the conditions across subjects, 1 means every subject ranks them identically. Roughly 0.1 small, 0.3 moderate, 0.5 large.
The test is significant — what next?
Run pairwise Wilcoxon signed-rank tests (or the Nemenyi/Conover post-hoc test) with a multiple-comparison correction such as Bonferroni or Holm.
Is the chi-square p-value accurate for small samples?
It is a good approximation once you have about 10 subjects or more than 4 conditions; with very few subjects exact tables are slightly more conservative.
Related calculators
Educational tool: check the test’s assumptions (sample size, independence, distribution) before relying on a result for a real decision.