Sample size determination for confidence intervals of interaction effects in moderated multiple regression with...

Area of Science:

• Social Sciences
• Behavioral Sciences
• Psychology
• Sociology

Background:

• Moderated multiple regression (MMR) is crucial for analyzing interaction effects in social and behavioral sciences.
• Existing literature primarily focuses on sample size for hypothesis testing, neglecting interval estimation precision.

Purpose of the Study:

• To present novel approaches for sample size determination in MMR.
• To enable precise interval estimation of interaction effects for continuous moderator and predictor variables.

Main Methods:

• Developed two distinct sample size determination methods for confidence interval precision in MMR.
• Method 1: Ensures specified coverage probability for the interval of moderating effects.
• Method 2: Guarantees a desired confidence interval width within a tolerance probability.

Main Results:

• The proposed methods provide practical guidelines for sample size calculations.
• Numerical examples and simulations demonstrate the effectiveness and advantages of the new approaches.
• The methods account for the inherent randomness and distributional properties of variables in MMR.

Conclusions:

• The presented methods facilitate accurate confidence interval reporting in MMR analyses.
• These approaches enhance the informativeness of interaction effect estimation beyond traditional significance testing.
• The study offers valuable tools for researchers seeking precise estimates of moderating effects.