Confidence Interval Estimation for the Difference Between Correlated Proportions: An Empirical Investigation of the Accuracy and Precision of Three Methods

• Activity Number: 552
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Social Statistics Section
• Author(s): Jeanine Romano*+ and Eun Sook Kim and Patricia Rodriguez de Gil and Thanh Pham and Pei-Chen Wu and Diep Nguyen and Jeffrey D. Kromrey
• Companies: University of South Florida and University of South Florida and University of South Florida and University of South Florida and University of South Florida and University of South Florida and University of South Florida
• Keywords: Interval estimates ; Correlate Proportions ; Dichotomous Outcomes

Abstract

Three methods for computing confidence intervals (CI) around differences in correlated proportions (Wald CI, adjusted Wald CI, and a likelihood-based CI method proposed by Tango, 1998) were investigated to determine which of these methods produces the most accurate and precise CI estimates. Two dichotomous outcomes measured from dependent samples were simulated. The factors manipulated in the simulation study included overall sample size (10, 50, 100, 500, 1000), direction and strength of the relationship between the two proportions (±.40, ±.30, ±.20, ±10, 0), and the population difference in marginal proportions (±.3, ±.25, ±.10, ±.05, 0). For each sample generated (i.e., 100,000 replications), each of the three proposed CI methods was calculated. The adjusted Wald CI provided the best coverage across the conditions investigated and is easier to calculate than the Tango intervals. In addition, both the original Wald CI and the Tango CI produced substantial undercoverage in some small sample conditions.