A Monte Carlo comparison of the Type I and Type II error rates of tests of multivariate normality

Mecklin, Christopher J.; Mundfrom, Daniel J.

doi:10.1080/0094965042000193233

Cited by 92 publications

(83 citation statements)

References 39 publications

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“…Some recent references are Thulin (2014), Hanusz and Tarasińska (2012), Delmail et al (2011), Tenreiro (2011), Cardoso De Oliveira andFerreira (2010), Okamoto and Seo (2010), Villasenor Alva and Estrada (2009). It can also be seen reviews by Liang et al (2009), Koizumi et al (2009), Hanusz and Tarasińska (2008), Doornik and Hansen (2008), Farrell et al (2007), Arcones (2007), Sürücü (2006), Holgersson (2006), Székely and Rizzo (2005), Pudelko (2005), Mecklin and Mundfrom (2005), Dufour et al (2003), Burdenski (2000), Henze and Wagner (1997), Henze (1997), Looney (1995), Romeu and Ozturk (1993), and Henze and Zirkler (1990).…”

Section: Introductionmentioning

confidence: 92%

Comparison of some multivariate normality tests: A simulation study

Alpu¹,

Yuksek

2016

Int. j. adv. appl. sci

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Many classical multivariate statistical methods are mostly based on the assumption of multivariate normality. Departures from normality, called non-normality, render those statistical methods inaccurate, so it is important to know if datasets are normal or non-normal. Especially in medical and life sciences, most statistical tests required the assumption of multivariate normality have been extensively used. In this study, after summarizing the properties of several most widely used multivariate normality tests, we aim to compare the power and type I error rates of these tests, which have been developed in recent years by many researchers. So, the reader will elucidate the differences and the similarities/superiorities and weaknesses of the tests in order to make the appropriate choice in their practical applications. For this purpose we carried a Monte Carlo simulation study with nominal α level, small, medium and large sample size, different dimension and multivariate distributions which includes different skewness and kurtosis. In conclusion, the results obtained from the comparative study are given.

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Section: Introductionmentioning

confidence: 92%

Comparison of some multivariate normality tests: A simulation study

Alpu¹,

Yuksek

2016

Int. j. adv. appl. sci

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“…Data were then tested for multivariate normality using Henze-Zirkler's test and Mardia's test, as recommended by Mecklin and Mundfrom (2005).…”

Section: Data Preparationmentioning

confidence: 99%

Individual differences in common factors of emotional traits and executive functions predict functional connectivity of the amygdala

et al. 2015

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“…These findings are the results of a study by Farrell et al (2007). Mecklin and Mundfrom (2005) highly recommended HZ as the most reliable test based on its relative ease of use (the test statistic has an approximately lognormal asymptotic distribution), good Monte Carlo simulations, and mathematically proven consistency against all alternatives. Since the optimal solutionŴ min is very computationally intensive and performed unsatisfactorily in a preliminary power test, we excluded it here.…”

Section: Simulated Resultsmentioning

confidence: 66%

A new functional statistic for multivariate normality

Wang

Hwang

2010

Stat Comput

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The test statistics of assessing multivariate normality based on Roy's union-intersection principle (Roy, Some Aspects of Multivariate Analysis, Wiley, New York, 1953) are generalizations of univariate normality, and are formed as the optimal value of a nonlinear multivariate function. Due to the difficulty of solving multivariate optimization problems, researchers have proposed various approximations. However, this paper shows that the (nearly) global solution contrarily results in unsatisfactory power performance in Monte Carlo simulations. Thus, instead of searching for a true optimal solution, this study proposes a functional statistic constructed by the q% quantile of the objective function values. A comparative Monte Carlo analysis shows that the proposed method is superior to two highly recommended tests when detecting widely-selected alternatives that characterize the various properties of multivariate normality.

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A Monte Carlo comparison of the Type I and Type II error rates of tests of multivariate normality

Cited by 92 publications

References 39 publications

Comparison of some multivariate normality tests: A simulation study

Comparison of some multivariate normality tests: A simulation study

Individual differences in common factors of emotional traits and executive functions predict functional connectivity of the amygdala

A new functional statistic for multivariate normality

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