A Two-Sample Test for Independence in 2×2 Contingency Tables with Both Margins Subject to Misclassification

A double sampling scheme is considered for estimation and testing under misclassification in both margins of a 2×2 contingency table; the matrix of misclassification probabilities is assumed to be unknown and nonsingular. Maximum likelihood estimators are given for the error-free and misclassification probabilities. Numerical methods are utilized to obtain maximum likelihood estimates under the independence hypothesis and the regularity conditions are affirmed for the asymptotic properties of the estimates to hold. The log-likelihood ratio statistic is shown to be asymptotically distributed as a chi-square. Computer simulations indicated important considerations for testing under double margin misclassification.