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

Summary 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 H 0 be the hypothesis to be tested. Then the observations availuble for testing H 0 are first condensed into a single statistic, x, the distribution of which can be evaluated when H 0 is true. Out of the possible range of values of this statistic a critical region is selected, and H 0 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 H 0 when true has a prescribed upper limit a (or preferably is equal to a); (B).  the probability of rejecting H 0 is higher when an alternative hypothesis H 1 , is true than when H 0 itself is true; and (C).  if possible, the probability of rejecting H 0 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, H 0 corresponding to θ=θ 0 , 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=θ 0 or θ=θθ 0 , the critical regions must be unilateral, but if θ can be both greater or smaller than θ 0 , they have to be bilateral. The arguments are illustrated by a few simple examples.