Deviations from the null hypothesis to be detected by statistical tests

Abstract

Deviations from the null hypothesis, which can be detected by tests in an univariate model, are derived by means of the expected value of the test criterion. As shown, the boundary of the detectable deviations is represented by an hyperellipsoid. The variations of the hyperellipsoid due to the variance of the test criterion are also derived. If each equation of the hypothesis involves only one parameter, the deviations detectable in a plane can be obtained from ellipses which are found by multiplying the axes of the confidence ellipse for two parameters by a certain factor. This method is applied to compute movements to be detected in an analysis of data for recent crustal movements.