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