Disantostefano Rachael L, Muller Keith E
Family Health International, P.O. Box 13950, Research Triangle Park, North Carolina 27709.
Commun Stat Simul Comput. 1995;24(3):583-593. doi: 10.1080/03610919508813260.
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.
在检验来自两个独立正态总体的均值是否相等时，许多统计学家更喜欢使用容忍异质性的检验方法。莫泽、史蒂文斯和瓦茨描述了非中心密度以及用于计算功效的数值积分算法。我们给出了萨特思韦特检验统计量功效的简单且准确的近似值。这带来了两个优点。首先，这些近似值大大减轻了诸如绘制功效曲线等任务的计算负担。其次，这些近似值极大地简化了编程，从而使功效计算更广泛地可用。针对检验规模为0.001、0.01、0.05和0.10，样本量为6和51，方差比为1和10，以及非中心参数从0到50（步长为1）的情况，对四种功效近似方法进行了评估。由于其准确性和简单性，推荐一种基于期望值比率的方法。
