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On tests of homogeneity of factorially-structured populations: An additive approach
析因结构总体的同质性检验:加性方法
Lancaster's additive approach to absence of interaction in contingency tables has been used quite frequently in agriculture in recent years, sometimes incorrectly. In this paper, we wish to compare the frequency distributions of response for a number of treatment groups which are factorially structured. An additive model is proposed which enables us to examine the role of the individual factors in explaining any differences among responses. Test statistics are developed, and…
The Distribution of Higher-Order Interactions in Contingency Tables
列联表中高阶交互作用的分布
Summary Lancaster's definition of the absence of second-order interactions in contingency tables produces test statistics which have asymptotic ***x 2 distributions under complete independence, but not (in general) otherwise. This paper obtains the asymptotic distributions of all interaction components in the partitioning of Pearson's x 2, and indicates a test procedure for higher-order interactions when lower-order interactions are found to be significant.
Distributional Expansions for Canonical Correlations from Contingency Tables
列联表典型相关的分布展开
Summary The asymptotic distribution of the canonical correlations from contingency tables was investigated by the author (1978) for a general theoretical correlation structure. In this paper, the structure examined is one in which all theoretical, non-zero correlations are different. For the observed canonical correlations corresponding to non-zeros, an analytic expansion is obtained enabling not only the asymptotic distributions to be obtained, but also a correction for…