Friedman Test Calculator

The Friedman test is a non-parametric statistical test used to detect differences across multiple related groups or repeated measurements. It is the non-parametric equivalent of the one-way repeated-measures ANOVA and is appropriate when the data does not meet normality assumptions, is ordinal, or contains outliers.

Use the Friedman test when your data violates the normality assumption required by repeated-measures ANOVA, when you have ordinal data, or when your sample size is small. It is also suitable if you have significant outliers that could distort the ANOVA results.

Enter your data matrix in the text area with one subject per row and one treatment per column, separating values with commas or spaces. Set the number of treatments and your desired significance level (α), then click Calculate. The tool outputs the Q statistic, p-value, degrees of freedom, critical value, and the hypothesis decision.

The null hypothesis (H₀) states that all treatment conditions have the same distribution — in other words, there is no significant difference between the groups. If the p-value is less than your chosen α, you reject H₀ and conclude that at least one treatment differs significantly from the others.

The Friedman test works by ranking the values within each subject (row) across all treatments. It then sums the ranks for each treatment across all subjects. The Q statistic is derived from these rank sums using the formula: Q = [12 / (n·k·(k+1))] · Σ(Rⱼ²) − 3n(k+1), where n is the number of subjects, k is the number of treatments, and Rⱼ is the rank sum for treatment j.

The p-value represents the probability of observing a Q statistic as extreme as the calculated one, assuming the null hypothesis is true. A p-value below your significance level (e.g. 0.05) indicates statistically significant differences between at least two of the treatment conditions.

If the Friedman test is significant, you should perform post-hoc pairwise comparisons to determine which specific groups differ. Common post-hoc tests include the Nemenyi test and the Dunn-Bonferroni test, both of which control for multiple comparisons while preserving the overall Type I error rate.

You need at least 3 treatment conditions (columns) and ideally at least 5 subjects (rows) for reliable results. The test requires that the same subjects are measured under each condition — this is the repeated-measures or within-subjects design requirement.