Nemenyi Post Hoc Test

The Nemenyi test is a post hoc procedure for repeated-measures rank data that compares the mean within-subject ranks of every pair of conditions against a studentized-range critical difference.

Nemenyi 검정은 같은 대상을 여러 조건에서 측정한 순위 자료에서 조건별 평균 순위 차이를 학생화 범위 분포의 임계차와 비교해 모든 조건 쌍을 검정하는 사후검정이다.

After a significant Friedman test on several conditions measured on the same people, how do I see which conditions differ?

같은 사람들을 여러 조건에서 측정해 Friedman 검정이 유의했는데, 어느 조건끼리 다른지 어떻게 확인하나요?

The Nemenyi test ranks conditions within each subject, averages the ranks per condition, and declares two conditions different when their mean-rank difference exceeds the critical difference q_α √(k(k+1)/6n). It controls the familywise error rate across all pairs and is widely used to compare algorithms across datasets.

When to use Nemenyi Post Hoc Test

• A Friedman test across three or more related conditions was significant.
• Every pair of conditions is to be compared.
• Data are ordinal or non-normal repeated measures, or classifiers ranked across datasets.

When to use something else

• The groups are independent rather than repeated; use Dunn's test instead.
• Only comparisons with one control condition are needed; use a Bonferroni-Dunn or Holm procedure against the control.

Assumptions and requirements

• Subjects (blocks) are independent of each other.
• Within each subject, the conditions can be ranked.
• There are few ties within subjects, since the standard error is not tie-corrected.

What the analysis reports

• Mean rank per condition
• Critical difference (CD)
• Pairwise rank differences with adjusted p-values
• Friedman chi-square test

How to report it

After a Friedman test, χ²([df], N = [value]) = [value], p = [value], Nemenyi post hoc comparisons (CD = [value]) showed that [condition A] differed from [condition B], p = [value].

Related methods

• Friedman Test
• Dunn's Post Hoc Test
• Wilcoxon Signed Rank Test

Run Nemenyi Post Hoc Test on Quorant