Asymptotic Behaviour of Tests for Normal Means Based on a Variance Pre-Test

摘要

In comparing two normal means, possible inequality of the corresponding variances211u001eplays an important role. Attempts to settle this through a preliminary F-test 211u001epresent new complications: numerical work from literature indicates that the 211u001ecorresponding two-step procedure performs much less satisfactorily than seems to 211u001ebe taken for granted by most textbooks. In the present paper we demonstrate how 211u001esecond order asymptotics can be applied to obtain simple and transparent 211u001eapproximations to size and power of the resulting procedure. This provides both 211u001equalitative insight into the behavior of this procedure, as well as information 211u001eon the magnitude of the occurring deviations.