Friedman Test Calculator
Enter data for n subjects measured under k conditions to perform the Friedman test, the non-parametric alternative to repeated measures ANOVA. No normality assumption required.
What is the Friedman Test?
The Friedman test is a non-parametric test for comparing three or more related groups. It is the repeated-measures extension of the Kruskal-Wallis test and the non-parametric alternative to one-way repeated measures ANOVA.
How it works:
- Rank the scores within each subject (block) from 1 to k
- Sum the ranks for each condition across all subjects
- Compute the Q statistic from the rank sums
- Compare Q to a chi-square distribution with k-1 degrees of freedom
Formula:
Q = (12 / (nk(k+1))) x ΣRj^2 - 3n(k+1)
Where n = number of subjects, k = number of conditions, and Rj = sum of ranks for condition j.
When to use the Friedman test:
- Repeated measures on the same subjects (pre/mid/post)
- Randomized complete block designs
- Ordinal data or data that is not normally distributed
- You want to compare more than two related conditions without assuming normality
Post-hoc testing:
If the Friedman test is significant, follow up with pairwise Wilcoxon signed-rank tests (with Bonferroni correction) or Nemenyi's test to identify which conditions differ.
Example applications:
- Comparing three or more treatments applied to the same patients
- Rating different products by the same panel of judges
- Testing three teaching methods on the same group of students