2011
DOI: 10.1080/00949655.2010.520163
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Comparisons of various types of normality tests

Abstract: Normality tests can be classified into tests based on chi-squared, moments, empirical distribution, spacings, regression and correlation and other special tests. This paper studies and compares the power of eight selected normality tests: the Shapiro-Wilk test, the Kolmogorov-Smirnov test, the Lilliefors test, the Cramer-von Mises test, the Anderson-Darling test, the D'Agostino-Pearson test, the Jarque-Bera test and chi-squared test. Power comparisons of these eight tests were obtained via the Monte Carlo simu… Show more

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Cited by 637 publications
(396 citation statements)
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“…Social, environmental and global sustainability CIs passed the test showing high significances (Sig > 0.05), and therefore can be considered normally distributed variables. The significance of the economic CI (Sig = 0.032) was slightly below 0.05; however, this value is acceptable using some authors' criteria (Eckel and Grossman, 1998;Óztuna et al, 2006;Lorenz, 2009;Yap and Sim, 2011), who argue that the K-S and S-W test is the most powerful and the strictest. We also contrasted these results with alternative graphical and numerical tests, following the recommendations of Hair et al (2010).…”
Section: Correlation Analysismentioning
confidence: 96%
“…Social, environmental and global sustainability CIs passed the test showing high significances (Sig > 0.05), and therefore can be considered normally distributed variables. The significance of the economic CI (Sig = 0.032) was slightly below 0.05; however, this value is acceptable using some authors' criteria (Eckel and Grossman, 1998;Óztuna et al, 2006;Lorenz, 2009;Yap and Sim, 2011), who argue that the K-S and S-W test is the most powerful and the strictest. We also contrasted these results with alternative graphical and numerical tests, following the recommendations of Hair et al (2010).…”
Section: Correlation Analysismentioning
confidence: 96%
“…The Shapiro-Francia test was chosen because of its known performance and the Shapiro-Wilk test was chosen because it is one of the best-known tests for normality [12]. An a priori alpha level for the goodness-of-fit tests was specified to be .10 [14]. Data were not normally distributed and thus the Wilcoxon rank sum (Mann-Whitney U) tests were used for significance testing.…”
Section: Discussionmentioning
confidence: 99%
“…the power of the test is low. [17] Therefore, the further developed variant, the Kolmogorow-Smirnow-Lilliefors test, [18] which is specially optimised for the comparison to normal distributions, was used to analyse whether the populations were normal distributed.…”
Section: Normal Distributed Populationmentioning
confidence: 99%