Bartlett's, Cochran's, and Hartley's Tests on Variances are Liberal When the Underlying Distribution is Long-Tailed
研究发现，对于等样本量情况，基于正态假设的巴特利特、科克伦和哈特利方差齐性检验的p值会低估真实p值，当总体分布是正态或卡方1尺度混合分布或存在样本内依赖时。
Abstract Abstract For samples of equal size, the p values of Bartlett's, Cochran's, and Hartley's tests for the equality of several variances, obtained under the normality assumption, are shown to underestimate the true p values when the parent distribution is a normal or a X 2 1 scale mixture or when there is within-sample dependence. The proof uses elements of majorization theory. When the sample sizes are not equal, a partial extension is obtained for the two-sample case. Key Words: MajorizationNormal mixtureSchur convexityStar-shaped ordering X 2 distribution