A comparison of power approximations for satterthwaite's test

When testing equality of means from two independent normal populations, many statisticians prefer heterogeneity tolerant tests. Moser, Stevens, and Watts described the noncentral density and a numerical integration algorithm for computing power. We present simple and accurate approximations for the power of the Satterthwaite test statistic. Two advantages accrue. First, the approximations substantially reduce the computational burden for tasks such as plotting power curves. Second, the approximations substantially simplify the programming and thereby make power calculations more widely available. Four methods of power approximation are evaluated for test sizes of .001, .01, .05, and .10, sample sizes of 6 and 51, variance ratios of 1 and 10, and noncentrality parameters from 0 to 50 by 1. A method based on a ratio of expected values is recommended due to its accuracy and simplicity