Abstract:
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.
