Stein's two sample test of a general linear hypothesis and a noncentral f–type distribution

Abstract

Stein's two–sample procedure for a general linear model is studied and derived in terms of matrices in which the error tems are distributed as multivatriate student t–error terms. Tests and confidence regions are constructed in a similar way to classical linear models which involves percentage points of student t and F distributions. The advantages of taking two samples are: the variance of the error terms is known, and the power of tests are size of confidence regions are controllable. A new distribution called noncentral F–type distribution different from the nencentral F is found when considerinf the power of the test of general linear hypothesis.

Keywords:

• General linear models
• multivariate student t distribution
• F distribution
• controllable variance