Performs the Ryan-Einot-Gabriel-Welsch Studentized Range (REGWQ) multiple comparison procedure for all pairwise comparisons of group means following a one-way analysis of variance. REGWQ is a stepwise procedure based on the studentized range distribution that generally provides greater statistical power than Tukey's HSD while maintaining strong control of the family-wise error rate under balanced designs.
Arguments
- data
A data frame, a list, 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 ifdatais a list or an"oneway_aov"object.- alpha
A numeric value between 0 and 1 (default: 0.05) specifying the significance level.
- rounding
An integer (default: 4). The number of decimal places to display in the output.
- 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 REGWQ comparisons, including mean differences, confidence intervals, studentized range statistics, p-values, modified significance levels, and effect sizes.
- summary
Descriptive statistics for each group, including compact letter displays (CLD).
Details
The REGWQ procedure is a stepwise multiple comparison method based on the studentized range distribution. Group means are first ordered, after which pairwise comparisons are performed using significance levels that depend on the number of ordered means spanned by each comparison. This adaptive strategy generally yields greater statistical power than Tukey's HSD while maintaining control of the family-wise error rate.
The procedure assumes that observations are independent, residuals are approximately normally
distributed, and population variances are equal. It is intended primarily for balanced one-way
designs. When sample sizes are unequal but variances remain homogeneous, consider using
Tukey_Kramer_test(). When variances are unequal, consider using Games_Howell_test().
References
Howell, D.C. (2010). Statistical Methods for Psychology (7th ed.). Cengage Learning. Chapter 12: Multiple comparisons among treatment means, Section 12.6: Post hoc comparisons, pg. 393-394.
Examples
out <- REGWQ_test(morphine, tolerance ~ grp)
#>
#> ------------------------------------
#> REGWQ multiple comparison procedure
#> ------------------------------------
#> Data: morphine ; Formula: tolerance ~ grp
#>
#> GROUP CLD N AVG SD MED
#> 1 MM b 8 10 5.1270 10.5
#> 2 MS c 8 4 3.1623 3.5
#> 3 McM a 8 29 6.1644 28.5
#> 4 SM a 8 24 6.3696 23.0
#> 5 SS b 8 11 6.7188 10.5
#>