A note on Wilson coverage intervals for proportions estimated from complex samples
Section 1. Introduction

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Brown, Cai and Dasgupta (2001) show that a method proposed by Wilson (1927) can produce reasonably well-behaved two-sided coverage intervals for a proportion under simple random sampling with replacement. Section 2 of this note discusses the theoretical foundations for extending this interval-construction method to estimated proportions computed from a complex survey. Section 3 shows that such a Wilson-type interval can be asymptotically equivalent to an interval derived from a logistic transformation. Section 4 offers some concluding remarks.

The term “coverage interval” is used here in place of the more common “confidence interval” because a 95% Wilson coverage interval does not attempt to cover the true proportion at least 95% of the time no matter what that proportion is. Instead, it merely tries to cover the true proportion 95% of the time for reasonable values of the true proportion. For some values it overcovers, for others it undercovers as shown in Brown et al. (2001). By limiting its applicability to two-sided coverage intervals, the Wilson methodology is (mostly) able to ignore the asymmetry of the distribution of an estimated proportion.

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Table of contents

Abstract - Article main page
Section 1. Introduction
Section 2. The extension
Section 3. The logistic transformation
Section 4. Some concluding remarks
Acknowledgements
References

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