Moment tests, combinations of moment tests, and three other simple tests of normality are compared to the Shapiro-Wilk W statistic. Monte Carlo trials indicate that some of the tests give adequate control of Type I error rates for sample sizes as low as 4. Over a variety of distributions the W statistic is generally the most powerful. However, moment tests are sometimes more powerful and, additionally, may help in identifying the actual shape of the nonnormal population distribution.
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Ramsey et al. (1990) studied this question.
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