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

Abstract

The problem of pooling two mean squares to use as error in analysis of variance is studied. The effects of varying standards of preliminary tests, to determine whether to pool or not to pool, are investigated. Numerical illustrations with curves and a table give comparisons of the power of tests with varying conditions, and mathematical derivations with two lemmas are included. The standard recommended for preliminary tests, is to avoid pooling unless the ratio of the two mean squares is less than twice the 50% point for "F".