Estimation of means from proportions with extraneous variance

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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 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 for a single sample, one- and two-way classifications with moderate and small sample sizes 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. (Author).