Approximate Power for Repeated-Measures ANOVA Lacking Sphericity
针对重复测量方差分析中协方差矩阵违反球形性假设时无法计算检验力的问题，提出一种近似方法，适用于校正或未校正的检验统计量，并通过模拟验证其有效性。
Abstract Violation of sphericity of covariance across repeated measures inflates Type I error rates in univariate repeated-measures analysis of variance. Hence the use of Geisser—Greenhouse or Huynh—Feldt is now common (to provide improved Type I error rate). With nonsphericity, no method has been available to compute power. A convenient method is suggested for approximating power and test size under nonsphericity. New approximations are suggested for (a) a weighted sum of independent noncentral χ2,s, (b) the trace of a noncentral Wishart (or pseudo-Wishart) matrix, (c) the expected values of and , and (d) the noncentral test statistic, whether corrected or uncorrected. The new approximations are extensions of the work of Box (1954a,b) and Satterthwaite (1941). The method performed well when evaluated against published and new simulations.