New measures of effect size in moderation analysis

Area of Science:

• Psychometrics
• Statistical Modeling
• Quantitative Psychology

Background:

• Traditional effect size measures like delta-R2 and f-squared have limitations in evaluating moderation effects.
• These limitations include conflating moderation with interaction and potential violations of homoscedasticity.

Purpose of the Study:

• To develop new, more accurate measures for the size of moderation effects.
• To differentiate the roles of predictor and moderator variables more effectively.

Main Methods:

• Proposed new conceptualization of moderation effects based on the variance of the outcome variable Y via the predictor variable X (X→Y).
• Developed two new effect size measures using sequential regression models and variance decomposition of the outcome variable.
• Utilized R code for computation and provided empirical examples for comparison.

Main Results:

• The new effect size measures accurately characterize moderation effects by focusing on relevant variance components.
• These measures effectively distinguish the predictor's influence from the moderator's influence.
• Empirical examples demonstrated the advantages of the new measures over traditional ΔR2 and f2.

Conclusions:

• The proposed effect size measures offer a more precise and theoretically sound approach to evaluating moderation.
• Researchers can utilize the provided R code to implement these new measures in their analyses.
• These advancements contribute to more accurate statistical inference in moderation analysis.