By Paul Zarembka

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The authors provide critical bounds for the test statistic for various a levels and « = 3(1)50. The critical region is given by small values of W, n a ^ K n — 1) ^ W < 1. The null hypothesis is the same H0 as given above. The alternative hypothesis, H 3, is that the distribution of is nonnormal in so far as nonnormality will affect the regression of sample order statistics on the mean values of order statistics obtained from an AT(0,1) distribution. The test in this form is known as WSET. The small sample behavior of the W statistic was examined by Monte Carlo means in the same work in which the previous two tests were initially examined; see Ramsey and Gilbert (1969).

603-604). The authors provide critical bounds for the test statistic for various a levels and « = 3(1)50. The critical region is given by small values of W, n a ^ K n — 1) ^ W < 1. The null hypothesis is the same H0 as given above. The alternative hypothesis, H 3, is that the distribution of is nonnormal in so far as nonnormality will affect the regression of sample order statistics on the mean values of order statistics obtained from an AT(0,1) distribution. The test in this form is known as WSET.

The objective is, in some sense, to choose the most likely alternative, or the most likely subspace of the maintained hypothesis space. When discriminating between alternatives, the specification of null and alternative hypotheses is irrelevant and there is no reason to assign an arbitrarily low probability of incorrect rejection to one of the hypotheses. The main problem is how to express an order of preference among the alternatives “which may be said to be rationally induced when the observa tions are known” ; see Barnard (1967, p.