Het gebruik van een‐ en tweezijdige overschrijdingskansen voor het toetsen van hypothesen*

J. Hernelrilk and H. R. van der Voor

Statistica Neerlandica, 1950, vol. 4, issue 1‐2, 54-66

Abstract: The use of unilateral and bilateral critical regions in the testing of hypotheses. This paper endeavours to explain in simple terms the principles of the Neyman‐Pearson theory. Let H0 be the hypothesis to be tested. Then the observations availuble for testing H0 are first condensed into a single statistic, x, the distribution of which can be evaluated when H0 is true. Out of the possible range of values of this statistic a critical region is selected, and H0 is rejected when x falls in this region, and not rejected when x falls outside. This critical region is chosen so that (A). the probability of rejecting H0 when true has a prescribed upper limit a (or preferably is equal to a); (B). the probability of rejecting H0 is higher when an alternative hypothesis H1, is true than when H0 itself is true; and (C). if possible, the probability of rejecting H0 is a maximum when any hypothesis h out of a set of alternative hypotheses is true. When the set of alternative hypotheses is specified by a single parameter θ, H0 corresponding to θ=θ0, these requirements will, under conditions of a general nature, lead to the use of unilateral or of bilateral tail‐errors according to the range of values of θ taken into consideration. If it may be assumed that either θ=θ0 or θ=θθ0, the critical regions must be unilateral, but if θ can be both greater or smaller than θ0, they have to be bilateral. The arguments are illustrated by a few simple examples.

Date: 1950
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