Interval Estimation of a Finite Population Proportion Using Randomized Response

• Activity Number: 520
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Survey Research Methods Section
• Author(s): Jesse Frey*+
• Companies: Villanova University
• Keywords: Bayesian inference ; Likelihood ratio ; Simple random sampling ; Unrelated question technique

Abstract

We consider the problem of constructing confidence intervals for a finite population proportion that is estimated using the unrelated question randomized response technique. If we apply one of the standard methods for creating confidence intervals, we get intervals that may be empty or misleadingly short. If we obtain intervals using the likelihood ratio method, our intervals are never empty or misleadingly short, but tend to be longer than necessary. We develop a hybrid method and demonstrate that it performs well in terms of length, in terms of the likelihood ratio, and even by Bayesian criteria. We apply the method to a dataset from the randomized response literature.