Friedman test

Information

• The Friedman test is a non-parametric statistical test that compares three or more related samples to test if their underlying population distributions are different.
• The Friedman test is used when the data are not normally distributed or the assumptions of the parametric tests, such as the repeated measures ANOVA, are violated.
• The Friedman test ranks the observations in each sample and calculates the sum of ranks for each sample, and then calculates a test statistic, called the Friedman chi-square, which measures the degree of difference between the samples.
• The null hypothesis of the Friedman test is that there is no difference between the population distributions of the three or more samples, while the alternative hypothesis is that the population distributions are different.
• The p-value of the Friedman test indicates the probability of observing the Friedman chi-square, or a more extreme value, if the null hypothesis is true.
• A small p-value (<0.05) indicates strong evidence against the null hypothesis and in favor of the alternative hypothesis, while a large p-value (>0.05) indicates weak evidence against the null hypothesis and failure to reject it.
• The Friedman test has some assumptions and limitations, such as requiring related samples, ordinal or interval data, and no ties in the ranks, and being less powerful than the parametric tests when the assumptions are met.
• If the null hypothesis of the Friedman test is rejected, post-hoc tests, such as the Wilcoxon signed-rank test with Bonferroni correction, can be used to identify the pairwise differences between the samples.
• The Friedman test can be used in a variety of applications, such as comparing the performance of three or more algorithms or methods on a dataset, testing for differences in medians or location, and examining the effects of categorical or nominal variables on a continuous outcome.