In this lecture the general statistical procedure and the principles underlying the application of the theory to practical problems were considered critically. After a general discussion of the theory of statistical inference and testing of hypotheses, the conditions underlying the application to practical problems were emphasized. The statician always has to find a compromise between his mathematical and his social conscience, because he hardly ever would be allowed to apply the (mathematical) theory to practical problems if he would consult this mathematical conscience only. The correct application of the theory requires for instance that only one statistical test be applied to each set of observations, whereas practice often requires that more than one (dependent) statistical test be applied to the same set of observations. It is however not justified to test hypotheses suggested by a given set of observations, on the basis of these observations themselves.
Finally, the importance of distribution free methods, which are more generally valid thant the so-called parametric methods, was pointed out. It is especially in the development of the theory of distribution-free methods the staff and students of the Department of Statistics of this University hope to participate.
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