Exact Binomial Confidence Intervals for Randomized Response

Jesse Frey and Andrés Pérez

The American Statistician, 2012, vol. 66, issue 1, 8-15

Abstract: We consider the problem of finding an exact confidence interval for a proportion that is estimated using randomized response. For many randomized response schemes, this is equivalent to finding an exact confidence interval for a bounded binomial proportion. Such intervals can be obtained by truncating standard exact binomial confidence intervals, but the truncated intervals may be empty or misleadingly short. We address this problem by using exact confidence intervals obtained by inverting a likelihood ratio test that takes into account that the proportion is bounded. A simple adjustment is made to keep the intervals from being excessively conservative. An R function for computing the intervals is available as online supplementary material.

Date: 2012
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DOI: 10.1080/00031305.2012.663680

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