The Generalized F-test is derived based on the Generalized P-value Method to test the equality of normally distributed group means under unequal variances. There are two approaches to compute the p-value of the GF test, based on beta and chi-squared random numbers. From prior art in the literature, it appears that the two computation approaches of the Generalized tests are equivalent. In this study, the equivalence of these approaches is investigated in an extensive Monte-Carlo simulation study in terms of Type I error probability and penalized power. It is found that the equivalence of the computation approaches is not quite correct and that there is a difference between their conclusion, and researchers should decide which one is powerful than the others according to the structure of data, such as sample size, and the number of groups. Also, real data examples are given to show the opposite decisions of the computation approaches.

广义 F 检验是基于广义 P 值方法导出的，用于检验不等方差下正态分布组均值的相等性。有两种方法可以根据 beta 和卡方随机数计算 GF 检验的 p 值。从文献中的现有技术来看，广义测试的两种计算方法似乎是等价的。在这项研究中，这些方法的等效性在广泛的蒙特卡罗模拟研究中就 I 类错误概率和惩罚功率进行了研究。发现计算方法的等价性并不十分正确，结论也存在差异，应根据数据的结构，如样本量、数量等来判断哪一种更强大。的组。还，