On a Preliminary Test for Pooling Mean Squares in the Analysis of Variance

Abstract

The paper describes the consequences of performing a preliminary $F$-test in the analysis of variance. The use of the 5% or 25% significance level for the preliminary test results in disturbances that are frequently large enough to lead to incorrect inferences in the final test. A more stable procedure is recommended for performing the preliminary test in which the two mean squares are pooled only if their ratio is less than twice the 50% point.