A Note on Pooling Variances

Abstract

Abstract The estimation of variance in the normal distribution is studied under statistical inference based on conditional specification. When there are two samples available for estimating the variance and it is not certain whether the two samples are from the same population, the experimenter usually uses a test to resolve the uncertainty. When the test is not significant, the samples are pooled to obtain a pooled estimator; otherwise, the individual sample variance is used. The bias and mean squared error of such a preliminary test estimator are studied. It is shown that the preliminary test estimator has a smaller mean squared error than the usual unbiased estimator when the level of significance for the preliminary test is appropriately chosen.