On Pooling Means when Variance is Unknown

Abstract

Abstract Given two random samples from normal populations, the experimenter wishes to estimate the mean of the first population. Whether to pool the two samples or not is made to depend on the result of a preliminary test. The bias and mean square error of the sometimes-pool estimator are given. The relative efficiency of the sometimes-pool estimator to the never-pool estimator is tabulated and the tables can be used to determine a proper choice of the significance level of the preliminary test. A pooling procedure for means, based on prior information, is discussed when the prior distribution is normal.