Constructing Confidence Intervals for Effect Size Measures of an Indirect Effect

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• Confidence intervals (CIs) are crucial for interpreting effect size magnitude and precision.
• Assessing indirect effects in statistical models often involves ratio measures, posing unique challenges for CI construction.

Purpose of the Study:

• To compare the performance of five distinct methods for constructing confidence intervals for ratio effect size measures of indirect effects.
• Evaluate methods based on power, coverage rates, Type I error rates, and CI widths.

Main Methods:

• Percentile bootstrap method
• Bias-corrected and accelerated (BCa) bootstrap method
• Delta method
• Fieller method
• Monte Carlo method

Main Results:

• All five CI methods yielded similar results for sample sizes exceeding 500.
• For samples smaller than 500, CIs were only sufficiently narrow to inform about population effect sizes when the underlying regression coefficients were large.

Conclusions:

• Method choice for indirect effect CIs may depend on sample size and effect size magnitude.
• The nature of ratio quantities and distributional assumptions impact CI performance, particularly in smaller samples.