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Simple Tests of Normality in Small Samples

Summary: 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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  • Topics:
  • Keywords: Moment estimation,Type I error,Shapiro-Wilk statistic,Power
  • Author: Ramsey, Patricia; Ramsey, Philip
  • Journal: Journal of Quality Technology