THE COMPARISON OF PROPORTIONS: A REVIEW OF SIGNIFICANCE TESTS, CONFIDENCE INTERVALS AND ADJUSTMENTS FOR STRATIFICATION'

Probably the most common quantitative problem in biological research involves the question of the presence or absence of a particular attribute. In its simplest form it reduces to a 2 x 2 table analysis or a test for the difference between two proportions; in a more complex form it may involve comparison of several proportions adjusted for an auxiliary variable. This paper reviews the theory and application of statistical analyses appropriate for such data. The theory is set forth in the general framework of logistic models as formulated by Cox [16, 21] (see also Rasch [60]). This analysis uses the notion of conditioning the distribution of the test statistic on the ancillary statistics, which implies, in most cases, the so-called "fixed marginals" analysis of contingency tables. Other theoretical formulations are also considered briefly. The paper is divided into three parts: the first deals with 2 x 2 tables, the second with the combination of 2 x 2 tables, and the last with the combination of 2 x t tables. The latter two subjects are closely related to the analyses of higher order interaction in contingency tables and the fitting of multivariate contingency table data. These subjects are treated only peripherally here: the former subject has been thoroughly reviewed recently by Plackett [58] and the latter subject has been treated by Bishop [7] whose paper contains an extensive bibliography. The excellent papers by Birch [5, 6] deal with many of the questions we discuss here. For additional references, see Cox [21].

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