Proportions with extraneous variance: two dependent samples

Data which appear to be binomial proportions sometimes exhibit heterogeneity which results in greater variation than would be exhibited under the binomial distribution. Previous work by the author (Kleinman [1973]) in which estimates of the heterogeneity variances are obtained and used in weighting is extended to the case of comparing means in two dependent samples. The resulting empirical weighting estimates are asymptotically equivalent to exact least squares estimates and Monte Carlo studies for sample size 10 indicate high efficiency relative to exact least squares estimates.