AN ANALYSIS OF CORRELATION-MATRICES - EQUAL CORRELATIONS
成果类型：
Article
署名作者：
BRIEN, CJ; VENABLES, WN; JAMES, AT; MAYO, O
署名单位：
University of Adelaide; University of Adelaide
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
发表日期：
1984
页码：
545554
关键词：
摘要：
The large-sample joint distribution of Z, the 1/2p(p-1) Fisher z-transforms of the elements in a p variable correlation matrix was studied. Under the null hypothesis of equal population correlations the variance matrix of Z has just 3 projector matrices in its spectral decomposition. These define 3 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 sample vector onto each of these subspaces, when divided by the stratum variance, provide a natural partition for the large-sample chisquared test for equality of correlations. A linear model is given which provides a statistical interpretation for the error strata, and hence the components in the partition. As well as providing a simple test for equality of correlations, the procedure indicates how familiar techniques in the spirit of analysis of variance can be used to investigate correlation matrices.