Conover Post Hoc Test

The Conover post hoc test compares every pair of groups on mean ranks using a t distribution with the pooled rank variance from a Kruskal-Wallis or Friedman omnibus test.

Conover 사후검정은 Kruskal-Wallis 또는 Friedman 전체 검정의 합동 순위 분산을 써서 모든 집단 쌍의 평균 순위 차이를 t 분포로 비교하는 비모수 사후검정입니다.

My Kruskal-Wallis test was significant; which groups actually differ from each other?

Kruskal-Wallis 검정이 유의하게 나왔는데, 어느 집단끼리 차이가 나는지 어떻게 확인하나요?

After a significant Kruskal-Wallis test, the Conover test compares each pair of groups by the difference in mean ranks, scaled by the rank variance left over after the omnibus test, and refers it to a t distribution with N - k degrees of freedom. The p values are then adjusted for multiple comparisons, usually with the Holm method.

When to use Conover Post Hoc Test

• A Kruskal-Wallis test across three or more independent groups was significant and you need pairwise follow-up.
• A Friedman test on repeated measures or blocks was significant and you want to know which conditions differ.
• You want a rank-based post hoc test with more power than Dunn's test.

When to use something else

• The omnibus rank test was not significant; report the omnibus result instead of pairwise tests.
• The data meet ANOVA assumptions; use Tukey HSD or Games-Howell on the means.

Assumptions and requirements

• Observations are independent within and between groups (or blocks are independent in the Friedman design).
• The outcome is at least ordinal.
• Group distributions have a similar shape, so rank differences reflect location differences.

What the analysis reports

• Mean ranks (or rank sums for blocks) for each pair and their difference
• Conover t statistic with its degrees of freedom
• Raw and adjusted p values (Holm by default; Bonferroni, BH, Sidak or none available)
• Omnibus Kruskal-Wallis H or Friedman chi-square with p value

How to report it

Following a significant Kruskal-Wallis test, H([df]) = [value], p = [value], Conover post hoc comparisons with Holm adjustment showed that [group 2] differed from [group 1], t([df]) = [value], adjusted p = [value].

Related methods

• Dunn's Post Hoc Test
• Kruskal-Wallis Test
• Friedman Test

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