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Abstract Several different statistics have been proposed for testing the independence between successive observations from a normal population. In order to choose between the various tests a theory of testing this hypothesis in certain populations is needed. In this paper the problem is studied within the framework of the Neyman-Pearson theory. Certain theorems concerning more general problems of quadratic forms are developed and later applied to the question of testing serial correlation.
T. W. Anderson (Thu,) studied this question.