Games-Howell Post Hoc Test

The Games-Howell post hoc test is a pairwise comparison procedure that compares all pairs of group means without assuming equal variances or equal group sizes.

Games-Howell 사후검정은 등분산이나 동일한 집단 크기를 가정하지 않고 모든 집단 쌍의 평균을 비교하는 사후 다중비교 방법이다.

Which post hoc test should I use when group variances are unequal?

집단 간 분산이 같지 않을 때 어떤 사후검정을 써야 하나요?

The Games-Howell test is the standard post hoc choice after a significant Welch ANOVA when group variances or sample sizes differ. It uses Welch-type standard errors and degrees of freedom with the studentized range distribution to control the familywise error rate across all pairwise comparisons.

When to use Games-Howell Post Hoc Test

• Levene's test indicates unequal variances across three or more groups
• Group sizes are unequal and variances differ
• Following up a significant Welch's ANOVA with all pairwise comparisons

When to use something else

• Variances are equal and group sizes similar: use the Tukey HSD test
• Only comparisons against one control group are needed: use Dunnett's test

Assumptions and requirements

• Independent observations
• Approximately normal outcome within each group
• Adequate sample size per group (it can be liberal with very small groups)

What the analysis reports

• Mean difference for each pair of groups
• Standard error and Welch-adjusted degrees of freedom
• Adjusted p-value per pair
• Confidence interval for each mean difference

How to report it

Games-Howell post hoc comparisons indicated that [group 1] scored higher than [group 2], mean difference = [value], 95% CI [[value], [value]], p = [value].

Related methods

• Welch's ANOVA
• Tukey HSD Post Hoc Test
• Dunnett's T3 Test

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