Sample size determinations for Welch's test in one-way heteroscedastic ANOVA.

Area of Science:

• Statistics
• Biostatistics
• Experimental Design

Background:

• The conventional F test in one-way ANOVA is sensitive to unequal variances (heteroscedasticity).
• Welch's procedure is a robust alternative for comparing means under variance heterogeneity.
• Accurate sample size calculation is crucial for the practical application of Welch's test.

Purpose of the Study:

• To evaluate the accuracy of two approximate power functions for Welch's test in sample size calculations.
• To identify the most reliable method for determining sample size for one-way ANOVA with heteroscedasticity.

Main Methods:

• Conducted simulation studies to compare the performance of two power functions: Levy (1978a) and Luh and Guo (2011).
• Assessed Type I error control and power performance across diverse model configurations and heteroscedastic structures.
• Developed computer programs to implement the recommended power calculation and sample size determination technique.

Main Results:

• Levy's (1978a) power function demonstrated superior accuracy compared to Luh and Guo's (2011) formula.
• The findings held true across a wide range of model specifications and heteroscedastic conditions.
• Welch's procedure, with Levy's method, offers reliable statistical power for unequal variance ANOVA.

Conclusions:

• Levy's (1978a) method is recommended for accurate sample size determination in one-way ANOVA with unequal variances.
• The provided computer programs facilitate the practical implementation of this accurate sample size calculation technique.
• Enhances the utility of Welch's test for researchers dealing with heteroscedastic data.