Friedman Test Calculator

About this calculator

The Friedman test is a non-parametric alternative to the repeated-measures ANOVA, used to detect whether there are significant differences across three or more related conditions or treatments measured on the same subjects, without assuming the data is normally distributed. Instead of working with raw values, the test ranks each subject’s scores across the treatments (1 through k for each row), sums the ranks for each treatment across all subjects to get rank sums R_j, and combines these into the test statistic χ²_F = [12 / (n·k·(k+1))] × Σ(R_j²) − 3n(k+1), where n is the number of subjects and k is the number of treatments.

Under the null hypothesis of no real difference between treatments, this statistic approximately follows a chi-square distribution with k−1 degrees of freedom, so the computed value is compared against a chi-square critical value or converted to a p-value to decide whether to reject the null. Biostatisticians, psychologists, and researchers in any field with repeated-measures or matched-subjects designs use the Friedman test when data is ordinal, skewed, or has outliers that would violate the normality assumption behind repeated-measures ANOVA — for example, comparing the same panel of judges’ rankings of several products. This calculator computes the Friedman statistic χ²_F and the degrees of freedom (k−1) from entered rank sums and the number of subjects; it does not return a p-value, so compare χ²_F with a chi-square critical value for those degrees of freedom (or look up the p-value in statistical software). You rank each subject's scores and sum the ranks per treatment yourself before entering them, as a comma-separated list.