フリードマン検定計算ツール

What is the Friedman Test?

The Friedman test is a non-parametric statistical test used to detect differences across three or more related groups (repeated measures). It is the non-parametric alternative to repeated measures ANOVA. Developed by Milton Friedman in 1937, the test ranks observations within each subject across conditions and tests whether the mean ranks differ significantly among conditions. It is widely used in medicine, psychology, and education for pre-post-follow-up designs and within- subject experiments.

When to Use the Friedman Test

Use the Friedman test when you have a repeated measures or matched design with three or more conditions and one or more of the following apply: your data are measured on an ordinal scale, the assumption of normality is violated, your sample sizes are small, or your data contain outliers. Common applications include comparing treatment effects over time, evaluating product preferences from the same judges, and analyzing questionnaire responses measured at multiple time points.

Friedman Test vs. Repeated Measures ANOVA

Assumptions of the Friedman Test

While the Friedman test is less restrictive than repeated measures ANOVA, it still has assumptions:

Understanding Kendall's W

Kendall's W (coefficient of concordance) is the effect size for the Friedman test. It ranges from 0 to 1, where 0 indicates no agreement in rankings and 1 indicates complete agreement.

How to Report Friedman Test Results in APA Format

According to APA 7th edition guidelines, report the chi-square statistic, degrees of freedom, p-value, and Kendall's W:

Note: Report χ² to two decimal places, degrees of freedom as an integer, and p to three decimal places. Use p < .001 when the value is below .001. Always include Kendall's W as the effect size measure.

Common Mistakes to Avoid

• Using repeated measures ANOVA on non-normal data: If your repeated measures data are ordinal or clearly non-normal with small samples, use the Friedman test instead.
• Using Kruskal-Wallis for related groups: The Kruskal-Wallis test is for independent groups. For repeated measures or matched designs, always use the Friedman test.
• Unequal observations per condition: The Friedman test requires the same number of subjects in each condition. Missing data must be handled before analysis (e.g., listwise deletion or imputation).
• Skipping post-hoc tests: A significant Friedman result only tells you that at least one condition differs. Always follow up with pairwise comparisons to identify specific differences.
• Ignoring effect size: A significant p-value alone does not indicate practical importance. Always report Kendall's W alongside the test result.