Asymptotic two-tailed confidence intervals for the difference of proportions

Abstract

In order to obtain a two-tailed confidence interval for the difference between two proportions (independent samples), the current literature on the subject has proposed a great number of asymptotic methods. This paper assesses 80 classical asymptotic methods (including the best proposals made in the literature) and concludes that (1) the best solution consists of adding 0.5 to all of the data and inverting the test based on the arcsine transformation; (2) a solution which is a little worse than the previous one (but much easier and even better when both samples are balanced) is a modification of the adjusted Wald method proposed by Agresti and Caffo (usually adding to all of the data and then applying the classical Wald CI); (3) surprisingly, the classical score method is among the worst solutions, since it provides excessively liberal results.

Keywords:

• arcsine transformation
• asymptotic confidence interval
• difference between proportions
• Score method
• Wald methods and adjusted Wald methods

Acknowledgements

This research was supported by the Spanish Ministry of Education and Science, grant number MTM2009-08886 (co-financed by the European Regional Development Fund).