A Double Sampling Scheme for Estimating from Binomial Data with Misclassifications: Sample size Determination

Abstract

Tenenbein [1970] presented a double sampling scheme for estimating from binomial data with misclassifications. At the first stage a sample of n units was classified by both an expensive true measuring device which made no errors and a relatively inexpensive fallible device which was subject to misclassification errors. The estimation of p was discussed, and the optimum sample sizes were derived which minimize the variance of estimation, subject to fixed measurement costs, and the cost, subject to a fixed variance of estimation. The optimum sample sizes depend upon the unknown probabilities of misclassification. In this paper we present practical methods of determining n and N by taking a preliminary sample of m true-fallible data pairs order to estimate the unknown parameters, and thus to estimate n and N. The resulting 3-stage scheme is discussed and recommendations for determining the value of m are made.