Each row is a subject (block). Each column is a treatment or condition being compared.
📋 Paste data from spreadsheet / CSV
Supports comma, tab, semicolon, or space separators. One subject per line.
Mean Ranks per Treatment
Use the +/− buttons to set the number of subjects (rows) and treatments/conditions (columns). Minimum: 2 treatments, 3 subjects.
Type values directly into the table. Each row is one subject measured under all treatments. Or use the paste area to load data from Excel/CSV.
Click "Run Friedman Test". Results include the χ² statistic, degrees of freedom, p-value, and mean ranks for each treatment.
If p < 0.05, at least one treatment differs significantly. Inspect the mean ranks to see which conditions rank higher or lower on average.
The Friedman test is a nonparametric statistical test developed by the economist Milton Friedman in 1937. It detects differences across multiple repeated measurements of the same subjects (or matched blocks) — the nonparametric equivalent of one-way repeated-measures ANOVA.
When to Use the Friedman Test
- The data is ordinal or continuous but not normally distributed
- Assumptions of repeated-measures ANOVA are violated
- Sample sizes are small and normality cannot be established
Assumptions
- Related samples / complete blocks: Each subject is measured under all conditions.
- Ordinal or continuous scale: The dependent variable must be at least ordinal.
- No specific distribution required: Unlike ANOVA, normality is not assumed.
Frequently Asked Questions
Q1: How is the Friedman statistic calculated?
Within each row the values are ranked 1 to k. The column rank sums Rj are then used in:
\[\chi^2_F = \frac{12}{nk(k+1)} \sum_{j=1}^{k} R_j^2 \;-\; 3n(k+1)\]For large samples, χ²F follows a chi-squared distribution with k−1 degrees of freedom.
Q2: How are ties handled?
Tied values within the same row receive the average of the ranks they would occupy. A tie-correction factor is applied automatically.
Q3: What should I do after a significant result?
Follow up with pairwise post-hoc comparisons using the Wilcoxon signed-rank test with Bonferroni or Holm correction, or Dunn's test.
Q4: How does the Friedman test differ from Kruskal-Wallis?
Kruskal-Wallis is for independent groups; Friedman is for related/repeated groups and accounts for within-subject correlation.