Games-Howell multiple comparison test — Games_Howell

Performs the Games-Howell multiple comparison procedure for all pairwise comparisons of group means. The Games-Howell test does not assume equal variances or equal sample sizes and is commonly used following a one-way analysis of variance when the homogeneity of variance assumption is violated.

Usage

Games_Howell_test(
  data,
  formula = NULL,
  alpha = 0.05,
  rounding = 4,
  verbose = TRUE
)

Arguments

data: A data frame, or an object returned by oneway_anova(), from which the response and grouping variables are obtained.
formula: A two-sided formula specifying the response and grouping variables in the form response ~ group. Ignored if data is a "oneway_aov" object.
alpha: A numeric value between 0 and 1 specifying the significance level. The default is 0.05.
rounding: An integer specifying the number of decimal places to display in the output. The default is 4.
verbose: Logical (default: TRUE). Show warnings and messages.

Value

A list containing the following components:

method: The name of the statistical procedure.
data: The input data used in the analysis.
pre_hoc: The one-way analysis of variance results.
post_hoc: Results of all pairwise Games-Howell comparisons, including mean differences, confidence intervals, test statistics, adjusted p-values, and effect sizes.
summary: Descriptive statistics for each group, including compact letter displays (CLD).

Details

The Games-Howell test is based on the studentized range distribution and uses Welch-Satterthwaite degrees of freedom for each pairwise comparison. Unlike Tukey's HSD test, it does not require equal variances or balanced sample sizes.

References

Howell, D. C. (2013). Statistical Methods for Psychology (8th ed.). Cengage Learning. Chapter 12: Multiple comparisons among treatment means, Section 12.7: Tukey's test, pg. 395.

Zar, J. H. (2014). Biostatistical analysis (5th ed.). Pearson. Chapter 11: Multiple comparisons, pg. 246.

Examples

out <- Games_Howell_test(O_X_X, val ~ grp)
#> 
#> -------------------------------------------
#> Games-Howell multiple comparison procedure
#> -------------------------------------------
#> Data: O_X_X ; Formula: val ~ grp
#> 
#>   GROUP CLD  N     AVG     SD     MED
#> 1    G1   a 27 15.8754 1.9604 15.5641
#> 2    G2  cd 24 10.4570 2.5398 10.1372
#> 3    G3  cd 16  9.0211 1.6341  9.0953
#> 4    G4   e 30  5.2209 0.9513  5.2100
#> 5    G5  bc 11 10.4630 3.3207 10.6098
#> 6    G6   b 20 13.8619 0.7809 13.8442
#>