Two-way ANOVA: Inferences about interactions based on robust measures of effect size

Area of Science:

• Statistics
• Biostatistics
• Psychometrics

Background:

• Two-way ANOVA designs are common in various scientific fields.
• Interactions in ANOVA are typically assessed using measures of effect size based on differences in location, most frequently means.
• Existing methods may lack robustness, especially with heteroscedastic data.

Purpose of the Study:

• To extend existing results on effect size measures in two-way ANOVA.
• To introduce two robust and heteroscedastic measures of effect size.
• To provide a more nuanced understanding of group comparisons in complex experimental designs.

Main Methods:

• Development of a robust, heteroscedastic analogue of Cohen's d.
• Characterization of effect size using quantiles of the null distribution.
• Application of a percentile bootstrap method for confidence interval estimation.

Main Results:

• The proposed robust effect size measures are suitable for heteroscedastic conditions.
• Simulation results demonstrate that the percentile bootstrap method yields accurate confidence intervals.
• The novel effect size measures offer valuable insights when comparing groups in real-world studies.

Conclusions:

• The study successfully extends robust effect size measures for two-way ANOVA.
• These new measures enhance the analysis of group differences, particularly in the presence of unequal variances.
• The findings support the use of these robust measures for more reliable statistical comparisons.