Written by Dackohn; last reviewed November 2026.
The Friedman test compares three or more related conditions without assuming normal data, such as the same people rating three products. It ranks each subject’s values and checks whether some conditions consistently rank higher. It is the nonparametric alternative to repeated-measures ANOVA.
When to use it
- The same subjects appear in every condition, or subjects are matched into blocks.
- There are three or more conditions. For two, use the Wilcoxon signed-rank test.
- The outcome is ordinal, such as ratings, or clearly non-normal.
Worked example
Eight tasters rate three recipes:
| Taster | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Recipe A | 7 | 5 | 8 | 6 | 9 | 7 | 6 | 8 |
| Recipe B | 9 | 7 | 8 | 8 | 10 | 9 | 7 | 9 |
| Recipe C | 12 | 9 | 11 | 10 | 13 | 11 | 10 | 12 |
- Rank within each taster. Taster 1 rated 7, 9, 12, which become ranks 1, 2, 3. Taster 3 gave A and B the same score, so they share rank 1.5.
- Sum the ranks for each recipe: A = 8.5, B = 15.5, C = 24. The mean ranks are 1.06, 1.94 and 3.00.
- Compute the statistic: χ² = 12 / (nk(k + 1)) × ΣR² − 3n(k + 1). Here that is 15.06, and the correction for the tie raises it to 15.55.
- Find the p-value: with df = k − 1 = 2, p < .001.
Effect size
Kendall’s W = χ² / (n(k − 1)) = 15.55 / 16 = .97. It runs from 0 to 1, and here the tasters agree almost perfectly on the order.
Which recipes differ?
A significant result only says that not all conditions are the same. Follow up with pairwise Wilcoxon tests and a multiple-comparison correction. Here, all three Holm-adjusted p-values are .023. With only 8 subjects, adjusted p-values cannot get much smaller, so report effects as well.
Friedman or Kruskal–Wallis?
| Friedman | Kruskal–Wallis | |
|---|---|---|
| Design | Same subjects in every condition | Different subjects in each group |
| Ranks | Within each subject | Across all data |
| Parametric equivalent | Repeated-measures ANOVA | One-way ANOVA |
Writing it up
“A Friedman test showed a significant difference between the recipes, χ²(2, N = 8) = 15.55, p < .001, Kendall’s W = .97.”
Limits
- It uses only order within subjects, which can lose power compared with repeated-measures ANOVA on normal data.
- Its chi-square approximation is rough with few subjects.
Try it yourself
Friedman Test Calculator →With Kendall’s W and post-hoc tests. Wilcoxon Signed-Rank Test →For two related conditions.Frequently asked questions
What is the Friedman test used for?
Comparing three or more related conditions when the data are ordinal or non-normal.
What is the post-hoc test after Friedman?
Pairwise Wilcoxon signed-rank tests with a correction such as Holm are a common choice.
Is the Friedman test the same as repeated-measures ANOVA?
It answers a similar question using ranks, so it does not require normality.
Related reading: Parametric vs nonparametric tests · Paired vs independent samples · Sign test vs Wilcoxon
Sources & further reading: NIST/SEMATECH e-Handbook of Statistical Methods · OpenStax Introductory Statistics. How we compute & validate: methodology. Written & reviewed by Dackohn; last reviewed August 2026.