friedman repeated measures analysis of variance on ranks

Friedman repeated measures analysis of variance (ANOVA) on ranks, also known as the Friedman test, is a non-parametric statistical test used to determine whether there are statistically significant differences between the means of three or more related groups. It is the non-parametric equivalent of repeated measures ANOVA.

This test is particularly useful when the data do not meet the assumptions of parametric tests, such as normal distribution or homogeneity of variances. Instead of using raw data, the Friedman test ranks the observations within each group and then compares the average ranks between groups.

The null hypothesis of the Friedman test is that there are no differences between the groups. If the p-value obtained from the test is below a predetermined significance level (usually 0.05), the null hypothesis is rejected, indicating that there are statistically significant differences between the groups.

The Friedman test is commonly used in various fields, including medicine, psychology, and environmental science, where researchers want to compare the effects of different treatments or conditions over time.