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An analysis of correlation matrices: Equal correlations
相关矩阵分析：总体相关系数相等的情形
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…
Nearest Neighbour (Nn) Analysis of Field Experiments
田间试验的最近邻分析
SUMMARY The paper is in two parts. Part I presents results of a Monte Carlo randomization study of Papadakis's covariance method of NN analysis which show that (i) a non-iterated Papadakis analysis tends to be conservatively biassed; (ii) iteration of the analysis as suggested by Bartlett (1978) leads to substantial positive bias in the treatment F ratio; (iii) the method is very inefficient when there are substantial trend effects in the data. A theoretical explanation of…