Calculator
Enter data as a table: one row per subject, columns separated by commas or tabs. First column = Condition/Time 1; second = Condition/Time 2; etc.
Friedman Test Calculator
Non-parametric repeated measures test for 3 or more time points. Use when data is ordinal, non-normally distributed, or samples are small. Includes pairwise post-hoc comparisons with Bonferroni correction.
About the Friedman Test
The Friedman test (1937) is the non-parametric alternative to one-way repeated measures ANOVA. It works by ranking each subject's values across conditions (1 = lowest, k = highest), then testing whether the sum of ranks differs significantly across conditions. It makes no assumption of normality and is appropriate for ordinal outcomes such as pain scales and Likert ratings.
Formula: Q = [12 / (n × k × (k+1))] × ΣR²ⱼ − 3n(k+1), where n = subjects, k = time points, Rⱼ = sum of ranks for column j. Q follows a χ² distribution with df = k−1.
Post-hoc: When the overall Friedman test is significant, run pairwise Wilcoxon signed-rank tests between all column pairs. Apply Bonferroni correction: α* = 0.05 / number of comparisons.
Reporting: χ²F(df, N=n) = value, p = value. Example: χ²F(2, N=10) = 18.05, p < 0.001.
Frequently Asked Questions
When should I use the Friedman test?
Use Friedman when you have repeated measurements on the same subjects at 3 or more time points, and the data violates normality, uses ordinal scales, or has small samples. It is the non-parametric equivalent of one-way repeated measures ANOVA.
What do I do if the Friedman test is significant?
Run pairwise Wilcoxon signed-rank tests between all pairs of time points and apply Bonferroni correction. Divide your α level (0.05) by the number of comparisons. For 3 time points, α* = 0.05/3 = 0.0167.
What is the difference between Friedman and Kruskal-Wallis?
Kruskal-Wallis is the non-parametric alternative to one-way independent-groups ANOVA — each group consists of different subjects. Friedman is the non-parametric alternative to repeated measures ANOVA — the same subjects measured multiple times. Kruskal-Wallis ignores within-subject correlation that Friedman accounts for.
How do I report Friedman test results?
Report: χ²F(df, N=n) = value, p = value. Example: "Pain scores differed significantly across time points (Friedman test: χ²F(2, N=10) = 18.05, p < 0.001). Post-hoc Wilcoxon tests (Bonferroni-corrected) showed significant reduction from Baseline to Week 8 (Z = 2.80, p = 0.005)."
What is the Friedman test statistic Q?
Q (also written as χ²F) is computed by ranking each subject's values across conditions within each row, summing ranks per column, then applying the Friedman formula. Under the null hypothesis that all conditions are equivalent, Q follows a chi-square distribution with df = k−1.