Determining Sample Size With a Given Range of Mean Effects in One-Way Heteroscedastic Analysis of Variance

Abstract

The authors examined 2 approaches for determining the required sample size of Welch's test for detecting equality of means when the greatest difference between any 2 group means is given. It is shown that the actual power obtained with the sample size of the suggested approach is consistently at least as great as the nominal power. However, the sample size given by the method of Guo and Luh (2008) does not always guarantee the minimum power performance. Furthermore, the computed sample size and associated power of their formula tend to be larger than those provided with the proposed procedure. A supplementary computer program is provided to aid the implementation of the proposed technique in planning analysis of variance designs.

Keywords:

• equality of means
• heteroscedasticity
• noncentrality parameter
• power
• Welch test