Games-Howell Post-Hoc Test
Also known as: Games-Howell post-hoc, Games-Howell procedure, Games-Howell Post-Hoc Testi
The Games-Howell test is a parametric post-hoc multiple comparison procedure that identifies which pairs of group means differ significantly after an omnibus ANOVA reveals a significant overall effect. Proposed by Games and Howell in 1976, it is specifically designed for situations where group variances and/or sample sizes are unequal, making it the recommended alternative to Tukey HSD whenever Levene's test signals heteroscedasticity.
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When to use it
Use the Games-Howell test as a follow-up to a significant one-way ANOVA or Welch ANOVA when comparing three or more independent groups on a continuous outcome and when group variances are unequal (flagged by a significant Levene's test) or group sizes differ substantially. Three conditions should be satisfied: the dependent variable is continuous, groups are independent, and within-group distributions are approximately normal. When normality is seriously violated, the nonparametric Kruskal-Wallis test followed by Dunn's post-hoc procedure is more appropriate.
Strengths & limitations
- Does not assume equal variances, making it robust when Levene's test is significant.
- Handles unequal group sizes without inflating the Type I error rate.
- Controls the family-wise error rate across all pairwise comparisons.
- Validated by Monte Carlo simulation in the original 1976 paper, providing strong empirical support.
- Still requires approximate normality within each group; severely skewed distributions require nonparametric alternatives.
- Less powerful than Tukey HSD when variances are actually equal and group sizes are balanced — use Tukey HSD in that scenario.
- The Welch-Satterthwaite degrees-of-freedom approximation introduces a small conservatism for very small samples.
Frequently asked
When should I choose Games-Howell over Tukey HSD?
Prefer Games-Howell whenever Levene's test for homogeneity of variance is significant, or whenever your group sizes are noticeably unequal. If variance and group sizes are balanced, Tukey HSD is slightly more powerful and is the conventional choice.
Can I use Games-Howell after a non-significant ANOVA?
No. Post-hoc tests, including Games-Howell, are performed only after the omnibus ANOVA (or Welch ANOVA) returns a significant result. Running pairwise comparisons without a significant overall test inflates the family-wise Type I error rate.
What if my data are not normally distributed?
Games-Howell assumes approximate normality within each group. If this assumption is clearly violated — particularly with small samples — the Kruskal-Wallis test followed by Dunn's test (with Bonferroni or Holm correction) is the recommended nonparametric path.
Does Games-Howell control the family-wise error rate?
Yes. By using the studentized range distribution as the reference rather than individual t-tests, the procedure controls the probability of at least one false rejection across all pairwise comparisons. Monte Carlo evidence from the original paper shows good Type I error control under heteroscedastic conditions.
Sources
- Games, P. A. & Howell, J. F. (1976). Pairwise multiple comparison procedures with unequal N's and/or variances: A Monte Carlo study. Journal of Educational Statistics, 1(2), 113–125. DOI: 10.3102/10769986001002113 ↗
How to cite this page
ScholarGate. (2026, June 1). Games-Howell Post-Hoc Test. ScholarGate. https://scholargate.app/en/statistics/games-howell-test
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Bonferroni CorrectionStatistics↔ compare
- Kruskal-Wallis testStatistics↔ compare
- One-way ANOVAStatistics↔ compare
- Welch ANOVAStatistics↔ compare