The odds ratio is one of the most widely used measures of association for 2 × 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.

The tetrachoric correlation describes the linear relation between two continuous variables that have each been measured on a dichotomous scale. The treatment of the point estimate, standard error, interval estimate, and sample size requirement for the tetrachoric correlation is cursory and incomplete in modern psychometric and behavioral statistics texts. A new and simple method of accurately approximating the tetrachoric correlation is introduced. The tetrachoric approximation is then used to derive a simple standard error, confidence interval, and sample size planning formula. The new confidence interval is shown to perform far better than the confidence interval computed by SAS. A method to improve the SAS confidence interval is proposed. All of the new results are computationally simple and are ideally suited for textbook and classroom presentations.