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检验简单有序备择的单侧学生化极差检验AI 解读

Consider the usual balanced one-way fixed effects analysis of variance (ANOVA) model X ij = μ i + ε ij (1 ≤ j ≤ n; 1 ≤ i ≤ k), where the ε ij are independent N(0, [sgrave]2) random variables and μ i is the mean of the ith treatment (1 ≤ i ≤ k). The μ i and [sgrave] 2 are unknown parameters. Let X i be the sample mean of the ith treatment based on n observations (1 ≤ i ≤ k), and let S 2 be an unbiased estimate of [sgrave]2, which is distributed independently of the X i as a…

学生化极差检验的功效函数AI 解读

In this paper we investigate the power function of the Studentised range test for comparing the means of normal populations in the one-way fixed effects analysis of variance model. The main results provide rigorous proofs of certain least favourable configurations of population means. These results are important in the calculation of the sample sizes required to guarantee power levels under certain restrictions on the ranges of the population means.

一般相关均值下的成对比较AI 解读

A commonly occurring statistical inference problem in practice is that of making simultaneous comparisons among three or more treatment means μi (1 ≤ i ≤ k) for certain experimental designs. One way to do this, the T method proposed by Tukey (1953), constructs simultaneous confidence intervals for all pairwise differences of the treatment means μi – μj (1 ≤ i, j ≤ k, i ≈ j). The joint confidence level of these confidence intervals, however, depends in a very complicated…