Abstract
The problem of whether to pool two samples in variance estimation is often decided via a preliminary F-test. Since our ultimate objective is to estimate an unknown parameter, the theory of testing in this problem should be discussed as a part of the theory of estimation. If we consider the procedure of preliminary test estimation as an estimation procedure, the choice of the level of significance will not be arbitrary. The procedure of minimizing Akaike's information criterion uniquely determines the necessary significance levels of one-sided and two-sided preliminary tests.
