Developing the noncentrality parameter for calculating group sample sizes in heterogeneous analysis of variance

Sample size determination is an important issue in planning research. In the context of one-way fixed-effect analysis of variance, the conventional sample size formula cannot be applied for the heterogeneous variance cases. This study discusses the sample size requirement for the Welch test in the one-way fixed-effect analysis of variance with unknown and possibly unequal variances. The authors propose a formula of sample size calculation by considering the number of groups, variances, and the noncentrality parameter. Because efficient algorithms for computing noncentral distribution functions have been developed recently, the authors then used the built-in function and made a statistical analysis system program available to calculate the sample size iteratively. The results of Monte Carlo simulation show that the empirical power of the Welch test statistic using the proposed sample size formula can achieve the desired level, indicating that the formula derived for determining sample sizes is appropriate. Last, the authors provide some concluding remarks.