Abstract
Assessing the assumption of multivariate normality is required by many parametric mul- tivariate statistical methods, such as MANOVA, linear discriminant analysis, principal component analysis, canonical correlation, etc. It is important to assess multivariate normality in order to proceed with such statistical methods. There are many analytical methods proposed for checking multivariate normality. However, deciding which method to use is a challenging process, since each method may give different results under certain conditions. Hence, we may say that there is no best method, which is valid under any condition, for normality checking. In addition to numerical results, it is very useful to use graphical methods to decide on multivariate normality. Combining the numerical results from several methods with graphical approaches can be useful and provide more reliable decisions. Here, we present an R package, MVN, to assess multivariate normality. It contains the three most widely used multivariate normality tests, including Mardia's, Henze-Zirkler's and Royston's, and graphical approaches, including chi-square Q-Q, perspective and contour plots. It also includes two multivariate outlier detection methods, which are based on robust Mahalanobis distances. Moreover, this package offers functions to check the univariate normality of marginal distributions through both tests and plots. Furthermore, especially for non-R users, we provide a user-friendly web application of the package. This application is available at http://www.biosoft.hacettepe.edu.tr/MVN/.
Highlights
Many multivariate statistical analysis methods, such as MANOVA and linear discriminant analysis (MASS, Venables and Ripley (2002)), principal component analysis (FactoMineR, Husson et al (2014), psych, Revelle (2014)), and canonical correlation (CCA, González and Déjean (2012)), require multivariate normality (MVN) assumption
According to the review by Mecklin and Mundfrom (2005), more than fifty statistical methods are available for testing MVN
Deciding which test to use can be a daunting task for researchers and it is very useful to perform several tests and examine the graphical methods simultaneously
Summary
Many multivariate statistical analysis methods, such as MANOVA and linear discriminant analysis (MASS, Venables and Ripley (2002)), principal component analysis (FactoMineR, Husson et al (2014), psych, Revelle (2014)), and canonical correlation (CCA, González and Déjean (2012)), require multivariate normality (MVN) assumption. In addition to statistical tests, the MVN provides some graphical approaches such as chi-square Q-Q, perspective, and contour plots This package includes two multivariate outlier detection methods, which are based on Mahalanobis distance. If data are multivariate normal, the test statistic (HZ) is approximately log-normally distributed with mean μ and variance σ2 as given below: a−. Example I: For simplicity, we will work with a subset of these data which contain only 50 samples of setosa flowers, and check MVN assumption using Mardia’s, Royston’s and Henze-Zirkler’s tests. The mardiaTest function is used to calculate the Mardia’s test multivariate skewness and kurtosis coefficients as well as their corresponding statistical significance This function can calculate the corrected version of the skewness coefficient for small sample size (n < 20). : 26.53766 : 1.294992 : 0.1953229 chi.small.skew : 27.85973 p.value.small : 0.1127617
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