A Brief Review of Existing Approaches of Statistical Hypotheses Testing

What is it about?

A short consideration of the existing approaches of statistical hypotheses testing is given below. Among classical methods, comparatively new Constrained Bayesian Method and its peculiarities are introduced. A brief description of the essences of these methods is given. Recommendation for choosing a concrete method for statistical hypotheses testing is given finally.

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Why is it important?

As a conclusion we have to note that despite the categorical support of some authors for one of the above approaches (see, for example, Christensen, 2005; Good, 1992; Marden, 2000), we believe that all of them have pros and cons and each of them should be used for solving the existing problem, taking into account its specificity as well as the purpose stated and the information available. In particular, the p-value method requires minimum information (only a distribution law at the validity of basic hypothesis) among the considered methods, then the Neyman-Pearson’s method (two distribution laws at the validity of basic and alternative hypotheses), after the Bayes method (a priori probabilities are added to the information necessary for Neyman-Pearson’s method). CBM, Wald’s and Berger’s methods require information similar to the Bayes method.