Distribution Theory of Group

SUMMARY We derive the joint distribution of the sequence of estimates of the parameter vector in a normal general linear model when data accumulate over a series of analyses. This sequence of estimates has a remarkably simple covariance structure, even when observations are correlated, allowing standard group sequential tests to be applied in very general settings. If variances and covariances of the observations depend on an unknown scale factor 2 , the joint distribution of the sequence of estimates of and 2 is required in order to construct sequential t-tests. We show that this joint distribution has a simple form, again even in the case of correlated observations, and a general treatment of group sequential t-tests can be obtained. Our results also provide a basis for group sequential 2 and F-tests appropriate to the cases of known and unknown variance, respectively.