Should the Interquartile Range Divided by the Standard Deviation be Used to Assess Normality?

Richard L. Warr and Roger A. Erich

The American Statistician, 2013, vol. 67, issue 4, 242-244

Abstract: We discourage the use of a diagnostic for normality: the interquartile range divided by the standard deviation. This statistic has been suggested in several introductory statistics books as a method to assess normality. Through simulation, we explore the rate at which this statistic converges to its asymptotic normal distribution, and the actual size of tests based on the asymptotic distribution at several sample sizes. We show that there are nonnormal distributions from which this method cannot detect a difference. Additionally, we show the power of this test for normality is quite poor when compared with the Shapiro--Wilk test.

Date: 2013
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DOI: 10.1080/00031305.2013.847385

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