Proportions with Extraneous Variance: Single and Independent Samples

Abstract

Data which appear to be binomial proportions sometimes exhibit heterogeneity which results in greater variation than would be expected under the binomial distribution. Methods for estimating means and associated inference procedures in a single sample and one-way classification have been developed by a least squares approach in which estimates of the heterogeneity variances are obtained by moments and used in weighting. Monte Carlo studies of the performance of this technique in moderate and small samples indicate that (1) these empirical weighting estimates have high efficiency relative to exact least squares estimates; (2) the variance estimators are nearly unbiased; (3) the resulting inference procedures are usually adequate for practical application.