# Friedman test

Command: | Statistics ANOVA Friedman test |

## Description

The **Friedman test** is a non-parametric test for testing the difference between several related samples. The Friedman test is an alternative for Repeated measures analysis of variances which is used when the same parameter has been measured under different conditions on the same subjects.

## How to enter data

The columns contain the data of the different measurements (example adapted from Conover, 1999).

## Required input

- Variables: the variables that contain the related observations.
- Select: an optional filter to include only a selected subgroup of cases.
**Options****Significance level**: the desired significance level for the post-hoc test. If the Friedman test results in a P-value less than this significance level, MedCalc performs a test for pairwise comparison of variables according to Conover, 1999.

## Results

### Descriptive statistics

This table gives the descriptive statistics for the different variables: number of cases (n), minimum, 25^{th} percentile, median, 75^{th} percentile and maximum. Since the Friedman test is for related samples, cases with missing observations for one or more of the variables are excluded from the analysis, and the sample size is the same for each variable.

### Friedman test

The null hypothesis for the Friedman test is that there are no differences between the variables. If the calculated probability is low (P less than the selected significance level) the null-hypothesis is rejected and it can be concluded that at least 2 of the variables are significantly different from each other.

### Multiple comparisons

When the Friedman test is positive (P less than the selected significance level) then a table is displayed showing which of the variables is significantly different from which other variables.

In the example variable (1), which is TREATMENT1, is significantly different from the variables (2) and (3), which correspond to TREATMENT2 and TREATMENT3.

## Literature

- Conover WJ (1999) Practical nonparametric statistics, 3
^{rd}edition. New York: John Wiley & Sons.