Exact distributions associated with an i×j×k contingency table |
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Authors: | RH Stumpf HS Steyn |
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Institution: | 1. Institute for Statistical Research, Human Sciences Research Council , Private BAg X41, Pretoria, 0001, REPUBLIC OF SOUTH AFRICA;2. Department of Statistics , University of South Africa , P.O. Box 392, Pretoria, 0001, REPUBLIC OF SOUTH AFRICA |
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Abstract: | In this paper an exact distributional framework is developed for analysing an IxJxK contingency table. It is shown that for the case of hypotheses H0:Pijk=Pi..P.j./K and H0:Pijk =Pi..P.j.P..k the exact distributional results do not follow as simple extensions of the corresponding results obtained for an I×J table under the hypothesis of independence. From the factorial moment generating functions, expressions for the covariance matrices in terms of the Kronecker products of matrices, are presented. These expressions give indications whether or not Pearson's chi-square statistic should be corrected by the factor (n?1)/n or not. Marginal and conditional distributions are considered briefly and important differences with regard to the resuits for marginal and conditional distributions for an IxJ table are mentioned. |
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Keywords: | contingency table exact distribution Appell's F -hypergeometric function probability generating function |
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