Distribution theory of group sequential t,χ2and F-tests for general linear models

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Abstract
We derive the joint distribution of the sequence of estimates of the parameter vector θ in a normal general linear model when data accumulate over a series of analyses. This seclllerlce 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 observations variaices and covariances depend on an unknown scale factor σ2, the joint distribution of the sequence of estimates of θ σ2 has a simple form. again even in the case of correlated observations. From these results, we establish a general treatment of group sequential t,χ2and F-tests.