On heterogeneity tests based on efficient scores

Abstract

For cases in which a parameter may be estimated from several independent data sets, Mather (1935) proposed a heterogeneity test based on the efficient scores for the individual data sets evaluated at the overall maximum likelihood estimator. Following Fisher (1946), a modification of the heterogeneity score test is presented wherein a consistent but inefficient estimator of the parameter of interest is substituted for the overall maximum likelihood estimator. The modified test is also derived using the C (α) theory of Neyman (1959). Using the modified procedure, we derive a test for a common odds ratio in several 2×2 tables based on the Mantel-Haenszel estimator.