Approximations to the Power of Some Order Restricted Tests with Slippage Alternatives
研究在单因素方差分析中，当均值顺序已知时，对有序约束检验的功效进行近似，提出了基于非中心F变量混合的近似方法，并用于样本量选择。
In the one-way analysis of variance, a researcher may believe that the ordering of the means is known and would like to incorporate this information into the test of hypotheses. Bartholomew developed likelihood ratio tests for such situations and proposed a two-moment chi-squared approximation for the minimum power of the test for the case of known variances. The accuracy of a closely related approximation is studied and an approximation based on mixtures of noncentral F variables is developed for the case of unknown variances. The simple ordering, the simple tree ordering and a class of slippage alternatives are considered, and an example concerning the choice of sample size needed to provide a specified power at a particular alternative is treated. For powers in the range typically of interest the two-moment approximation seems adequate.