Estjmation of Variance after a Preliminary Test of Homogeneity and Optimal Levels of Significance for the Pre-test” T. Toyoda

Received May 1974, revised version received April 1975 The question of whether to pool two samples in variance estimation is often decided via a preliminary F test. In this paper we show that the optimal pre-test F value is unity for a onesided alternative, where the objective function is to minimize average relative risk. The outcome is independent of numbers of degrees of freedom in each sample. Optimal significance levels vary somewhat but are close to + for most d.f. and equal to : when numerator and denominator d.f. are equal. The results also apply to regression variance estimation across two data regimes.