Friedman Test

The Friedman test is a nonparametric test that compares three or more related measurements of the same subjects by ranking values within each subject, serving as a rank-based alternative to repeated-measures ANOVA.

Friedman 검정은 각 대상 내에서 값을 순위화하여 같은 대상의 세 번 이상 반복 측정값을 비교하는 비모수 검정으로, 반복측정 분산분석의 순위 기반 대안이다.

How do I compare three or more repeated measurements when the data are not normally distributed?

자료가 정규분포를 따르지 않을 때 세 번 이상의 반복 측정값을 어떻게 비교하나요?

The Friedman test compares three or more conditions or time points measured on the same subjects using within-subject ranks. It fits ordinal outcomes or skewed continuous outcomes where the normality assumption of repeated-measures ANOVA is doubtful.

When to use Friedman Test

• The same participants rated under three or more conditions
• Ordinal outcomes such as Likert ratings measured repeatedly
• Skewed repeated measurements with small samples

When to use something else

• Only two related measurements: use the Wilcoxon signed-rank test
• Normally distributed differences and interest in means: use repeated-measures ANOVA

Assumptions and requirements

• Each subject is measured under every condition (complete blocks)
• Subjects are independent of one another
• Outcome is at least ordinal

What the analysis reports

• Friedman chi-square statistic
• Degrees of freedom (k − 1)
• p-value
• Mean ranks per condition
• Kendall's W effect size

How to report it

A Friedman test indicated a significant difference across the [k] conditions, χ²([df], N = [n]) = [value], p = [value], Kendall's W = [value].

Related methods

• Wilcoxon Signed-Rank Test
• Repeated Measures ANOVA
• Kruskal-Wallis Test

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