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In this article, we discuss ideas about two by two contingency tables in terms of the geometry of the three dimensional simplex. In particular, we derive the loci of points corresponding to certain classes of two by two tables. We relate the geometry to a discussion of the mean square contingency, which is also associated with rejection regions for the chi-square goodness of fit test for independence.
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Fienberg et al. (1970) studied this question.
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