Abstract
Summary We investigate a statistic introduced by de Wet and Venter to test for normality and a Cramér–von Mises statistic asymptotically equivalent to this statistic. It is shown that the Cramér–von Mises statistic can be written as a sum of components which are polynomial functions of the original standardized observations, the most important of which are Pearson's moment ratio statistics, √b 1 and b 2. Approximate small sample percentage points are given for the de Wet and Venter statistic. The asymptotic power of this statistic is investigated and the results of a small sample power study reported, confirming these results.
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