The Friedman test is a non-parametric statistical test used in biostatistics to compare three or more paired or matched groups.
It is the non-parametric alternative to the repeated measures ANOVA, which is used when the data do not meet the assumptions necessary for ANOVA, particularly the assumption of normality.
The Friedman test is particularly useful for analyzing data from within-subjects designs or repeated measures designs where the same subjects are used across all conditions or time points.
Characteristics of the Friedman Test
1. Non-parametric:
The Friedman test does not require the assumption of normal distribution of the residuals, making it suitable for ordinal data or data that is not normally distributed.
2. Multiple Related Groups:
It is used to compare three or more related (dependent) groups.
This is in contrast to the Kruskal-Wallis test, which is used for independent groups.
3. Rank-based:
The test involves ranking the data within each block (subject) across the different conditions or time points.
Steps to Perform the Friedman Test
1. Rank the Data within Each Block:
For each subject (or block), rank the observations across the different conditions from 1 (lowest) to 𝑘 (highest), where 𝑘k is the number of conditions or groups being compared.
If there are ties, assign the average rank to the tied values.
2. Calculate the Sum of Ranks for Each Condition:
Calculate the sum of ranks for each condition across all subjects.
3. Compute the Friedman Test Statistic:
Let 𝑛n be the number of subjects (blocks), and 𝑘k be the number of conditions or groups.
The Friedman statistic is calculated using:
where 𝑅𝑗 is the sum of ranks for the 𝑗-th condition.
4. Determine the Degrees of Freedom and Calculate the P-value:
The degrees of freedom (df) for the Friedman test are 𝑘−1, where 𝑘 is the number of groups.
For large samples, 𝜒2𝐹 follows a chi-square distribution with 𝑘−1 degrees of freedom. Use this distribution to calculate the p-value.
5. Interpret the Results:
Compare the p-value with your chosen significance level (commonly 0.05). If the p-value is less than the significance level, reject the null hypothesis that there is no difference among the groups.