Permutation ANOVA

Permutation ANOVA tests differences among k groups by recomputing the F (or Welch F) statistic over random or complete reassignments of the group labels to obtain its null distribution.

순열 분산분석은 집단 라벨을 무작위로(또는 모두) 다시 배정하며 F 또는 Welch F 를 다시 계산해 영분포를 만들고 k 집단의 차이를 검정하는 방법입니다.

My groups are small and the residuals are clearly not normal; can I get an ANOVA p-value without relying on the F distribution?

집단이 작고 잔차가 정규분포가 아닌데, F 분포에 기대지 않고 분산분석 p 값을 얻을 수 있나요?

Shuffle the group labels many times, recompute F for each shuffle and take the proportion of shuffled F values at least as large as the observed one as the p-value. Pairwise comparisons can be adjusted with the max-T method from the same permutations.

When to use Permutation ANOVA

• Normality is doubtful and samples are small.
• You want an exact p-value when the number of distinct label assignments is small.
• You want pairwise comparisons with familywise error control from the same resampling.

When to use something else

• Group variances differ markedly and you only care about means; use Welch's ANOVA or the Welch F option, since label permutation assumes exchangeability.
• Observations are repeated on the same subjects; use a within-subject permutation or repeated-measures ANOVA instead.

Assumptions and requirements

• Exchangeability of observations across groups under the null hypothesis.
• Independent observations.

What the analysis reports

• Observed F or Welch F with the parametric p for comparison
• Exact or Monte Carlo permutation p (with seed)
• Pairwise mean differences, |t| and max-T adjusted p

How to report it

A permutation ANOVA ([value] permutations) indicated differences among the [value] groups, F = [value], permutation p = [value].

Related methods

• One-Way ANOVA
• Permutation Test for Two Groups
• Kruskal-Wallis Test

Run Permutation ANOVA on Quorant