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Confidence intervals for the difference of two proportions estimated from pooled samples

This article presents confidence intervals for the difference of two binomial proportions estimated from pooled samples with unequal pool sizes. Asymptotic methods are used to derive Wald, profile score, and profile likelihood ratio intervals. Corrections for bias and skewness of the distribution of the Studentized score statistic are used to improve the profile score interval. Further, the easily computed Wilson score-based interval of Newcombe is adapted. Coverage and noncoverage probabilities and expected lengths of the confidence intervals are estimated for a range of parameter values expected in application, for both one- and two-sample cases. The skewness-corrected profile score interval is generally recommended. The methods are applied to a comparison of West Nile virus mosquito infection prevalences by trapping height in field collections from Louisiana in 2003.