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按两个因素交叉分类的变量之相关矩阵分析AI 解读

A procedure similar to an analysis of variance is presented for examining the structure in correlation matrices whose variables are cross-classified by two factors, such as multitrait-multimethod matrices. The method tests an equal correlation hypothesis against natural alternative hypotheses suggested by group representations. When there is significant departure from the hypothesized pattern, alternative models to be pursued are indicated. The method is illustrated using an…

按两个因素交叉分类的变量相关矩阵分析AI 解读

A procedure similar to an analysis of variance is presented for examining the structure in correlation matrices whose variables are cross-classified by two factors, such as multitrait-multimethod matrices. The method tests an equal correlation hypothesis against natural alternative hypotheses suggested by group representations. When there is significant departure from the hypothesized pattern, alternative models to be pursued are indicated. The method is illustrated using an…

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相关矩阵分析：总体相关系数相等的情形AI 解读

We study the large-sample joint distribution of Z, the ½p(p - 1) Fisher z-transforms of the elements in a p variable correlation matrix. Under the null hypothesis of equal population correlations the variance matrix of Z has just three projector matrices in its spectral decomposition. These define three mutually orthogonal invariant subspaces of sample space, or ‘error strata’ as they would be called in the analysis of variance. The squared lengths of the projections of the…