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Sociological Methods & Research, Vol. 35, No. 3, 429-446 (2007)
DOI: 10.1177/0049124106292358

Statistical Inference for Generalized Yule Coefficients in 2 x 2 Contingency Tables

Douglas G. Bonett

Iowa State University, Ames

Robert M. Price

East Tennessee State University, Johnson City

The odds ratio is one of the most widely used measures of association for 2 x 2 tables. A generalized Yule coefficient transforms the odds ratio into a correlation-like scale with a range from -1 to 1. Yule’s Y, Yule’s Q, Digby’s H, and a new coefficient are special cases of a generalized Yule coefficient. The new coefficient is shown to be similar in value to the phi coefficient. A confidence interval and sample size formula for a generalized Yule coefficient are proposed. The proposed confidence interval is shown to perform much better than the Wald intervals that are implemented in statistical packages.

Key Words: interval estimation • phi coefficient • sample size requirement • tetrachoric correlation


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