games_howell_test: Games Howell Post-hoc Tests

In rstatix: Pipe-Friendly Framework for Basic Statistical Tests

Games Howell Post-hoc Tests

Description

Performs Games-Howell test, which is used to compare all possible combinations of group differences when the assumption of homogeneity of variances is violated. This post hoc test provides confidence intervals for the differences between group means and shows whether the differences are statistically significant.

The test is based on Welch’s degrees of freedom correction and uses Tukey’s studentized range distribution for computing the p-values. The test compares the difference between each pair of means with appropriate adjustment for the multiple testing. So there is no need to apply additional p-value corrections.

See the Datanovia tutorial One-Way ANOVA in R for a worked walkthrough.

Usage

games_howell_test(
  data,
  formula,
  conf.level = 0.95,
  detailed = FALSE,
  effect.size = FALSE
)

Arguments

data	a data.frame containing the variables in the formula.
formula	a formula of the form x ~ group where x is a numeric variable giving the data values and group is a factor with one or multiple levels giving the corresponding groups. For example, formula = TP53 ~ cancer_group.
conf.level	confidence level of the interval.
detailed	logical value. Default is FALSE. If TRUE, a detailed result is shown.
effect.size	logical. Default is FALSE. If TRUE, a cohens.d column and its magnitude are added. Because Games-Howell assumes unequal variances, this is the Welch (averaged-variance) Cohen's d, estimate / sqrt((s1^2 + s2^2) / 2), oriented like the reported mean difference so the two never disagree in sign.

Details

The Games-Howell method is an improved version of the Tukey-Kramer method and is applicable in cases where the equivalence of variance assumption is violated. It is a t-test using Welch’s degree of freedom. This method uses a strategy for controlling the type I error for the entire comparison and is known to maintain the preset significance level even when the size of the sample is different. However, the smaller the number of samples in each group, the it is more tolerant the type I error control. Thus, this method can be applied when the number of samples is six or more.

Because the test relies on Welch's variance correction, comparisons involving a group with zero variance (constant values) or undefined variance (a single observation) can be undefined; such pairs are returned as NA (with a warning) while all other comparisons are computed as usual.

Value

return a data frame with some of the following columns:

• .y.: the y (outcome) variable used in the test.

• group1,group2: the compared groups in the pairwise tests.

• n1,n2: Sample counts.

• estimate, conf.low, conf.high: mean difference and its confidence intervals.

• statistic: Test statistic (t-value) used to compute the p-value.

• df: degrees of freedom calculated using Welch’s correction.

• p.adj: adjusted p-value using Tukey's method.

• method: the statistical test used to compare groups.

• p.adj.signif: the significance level of p-values.

The returned object has an attribute called args, which is a list holding the test arguments.

References

• Aaron Schlege, https://rpubs.com/aaronsc32/games-howell-test.

• Sangseok Lee, Dong Kyu Lee. What is the proper way to apply the multiple comparison test?. Korean J Anesthesiol. 2018;71(5):353-360.

See Also

The Datanovia tutorial: One-Way ANOVA in R.

Examples

# Simple test
ToothGrowth %>% games_howell_test(len ~ dose)

# Grouped data
ToothGrowth %>%
  group_by(supp) %>%
  games_howell_test(len ~ dose)

rstatix documentation built on July 24, 2026, 1:06 a.m.