Sample size determination for examining interaction effects in factorial designs under variance heterogeneity

Area of Science:

• Social Sciences
• Psychology
• Education
• Management

Background:

• Moderation analysis is crucial in social sciences, but variance heterogeneity can reduce statistical power.
• Existing methods for detecting moderating effects are often hindered by methodological artifacts, particularly non-constant variance.

Purpose of the Study:

• To propose feasible solutions for sample size calculations in moderation analysis.
• To address the challenge of variance heterogeneity in detecting interaction effects.

Main Methods:

• The study focuses on sample size calculations for tests of hypothesized interactions between categorical variables.
• It specifically addresses scenarios with heterogeneity of variance.
• Numerical illustrations and simulation studies are used to demonstrate the proposed technique.

Main Results:

• The proposed technique provides feasible solutions for sample size calculations under variance heterogeneity.
• The method is demonstrated for 2- and 3-way factorial designs.
• SAS and R programs are provided for practical implementation.

Conclusions:

• The suggested sample size procedure enhances statistical power for detecting moderating effects in the presence of variance heterogeneity.
• This research offers practical tools for researchers to improve the rigor of their moderation analyses.