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Departures from statistical independence are conjoined with an assessment of predictive accuracy' in a coefficient of association for nominal-level 2 x 2 contingency tables which is both interpretable as a PRE measure and consistent with research hypotheses of manifold forms. Measurement assumptions and operating characteristics o[ the measure are delineated; definitional and computational formulate are derived from classical probability theory; comparisons with other relevant statistics are made' and The test of significance is shown to be the traditional chi-square test. [ABSTRACT FROM AUTHOR]

This article shows that information partitioning in contingency tables is a very general property of exponential families, One partitioning scheme occurs when the hypotheses of interest are stated as linear expressions in the natural parameters, A second partitioning scheme is possible when the hypotheses are stated as linear in the parameter which is the expectation of the statistic in the exponent. [ABSTRACT FROM AUTHOR]

A step-by-step method is presented herein far partitioning a certain kind of hypothesis H about the m-way contingency table into (a) a series of hypotheses about marginal tables formed from the m-way table by ignoring one or more of table's m dimensions; and (b) a hypothesis about independence, conditional independence, or conditional equiprobability in the m-way table. This step-by-step method facilitates both the testing of H and the calculation of F, the estimated expected frequencies in the m-way table under FI. The method introduced herein for calculating F is easier to apply than the usual iterative-scaling method in many cases. [ABSTRACT FROM AUTHOR]

The article focuses on comments given by the author on topics related to 2 X 2 contingency tables. In the article two ideas are proposed. The first is that the Yates continuity correction should not be used in 2 X 2 contingency tables unless row and column totals are nonrandom. The second idea is that if row totals, or column totals, are not fixed in advance of the experiment, the Yates correction should not be used for two reasons. First, it provides poor estimates of the desired probabilities. Second, it sometimes exchanges points inside the critical region for points outside the critical region, thus providing a different test. Statistician Olli S. Miettinen points out that much of the controversy over use of a continuity correction is due to a lack of distinguishing between two distinct situations. The first situation involves estimating the exceedance probability associated with a known possible value of a discrete random variable. The second situation involves estimating the exceedance probability associated with an arbitrary real number, such as a quantile from the chi-square' distribution.