On sample size calculation for 2x2 fixed-effect ANOVA when variances are unknown and possibly unequal

Area of Science:

• Statistics
• Experimental Design

Background:

• The 2x2 factorial ANOVA is common for comparing group means.
• Violating the homogeneity of variance assumption can invalidate ANOVA results.
• Unequal variances necessitate robust sample size calculations for reliable power analysis.

Purpose of the Study:

• To develop a sample size formula for 2x2 fixed-effect ANOVA with heterogeneous variances.
• To provide a method for researchers to plan studies with unknown or unequal variances.
• To ensure adequate statistical power when the homogeneity assumption is violated.

Main Methods:

• Derivation of a sample size formula using the approximate Welch t-test.
• Inclusion of the variance ratio to account for unequal variances.
• Development of a two-step iterative process for sample size determination.

Main Results:

• A simple formula is proposed for sample size calculation in 2x2 ANOVA with heterogeneous variances.
• Approximate sample sizes for main and interaction effects can be determined independently.
• The method facilitates power analysis for studies with unequal variances.

Conclusions:

• The proposed formula offers a practical solution for sample size planning in 2x2 ANOVA under heterogeneity of variance.
• Researchers can use this method to ensure adequate power and valid inferences.
• An accompanying SAS program aids in the practical application of the formula.