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多元方差分析中的 Hotelling 广义 T²AI 解读

SUMMARY Hotelling’s generalized T2 is the sum of the roots of the determinantal equation |Z - θY/n| = 0, where Y and Z have central and non-central p-dimensional Wishart distributions with d.f. Q and n. Y and Z are obtained as the sum of products matrices for p-variate normal distributions N(0, σ1) and N(b(q), σ1). The distribution of this statistic is shown to be a monotonic increasing function of each of the population roots. An unbiased estimate of a linear function of…

Tukey 非加性检验的功效AI 解读

SUMMARY The problem of testing for non-additivity in a two-way classification has been considered in this paper where the mean μii can be expressed as μ+αi+βi where αi and βi are the effects of the two ways of classification (i = 1, …,p;j = 1, …,q). Tukey (1949) has suggested a test for non-additivity. The power function of this test has been found in this paper for alternatives of the form μii = μ+αi+βi+cαi βi and numerical calculations made for the case of p = q = 6. For…