Estimating the Variance of Empirical Logits and Contrasts in Empirical Log Probabilities

The estimation of contrasts in logits of binomial variates or in log probabilities of multinomial variates is often an integral part of an analysis of cross-classified or assay data. Several estimators of the logit have been proposed. The biases of four such estimators were computed by Gart and Zweifel (1967) and Cook (1977). Their numerical work supports the use of the Haldane-Anscombe empirical logit estimator for smalland moderate-sized samples. We propose a new general class of estimators of the variance of the HaldaneAnscombe empirical logit estimator; this includes the estimator due to Gart (1966) as a special case. Numerical comparisons indicate that certain members of this class are typically less biased than Gart's estimator. The proposed estimators are generalized to allow estimation of the variance of contrasts of empirical log probabilities with constant coefficients.