Watch my youtube tutorial on Multivariate normality Test in R - Mardia's Test, Henze-Zirkler, Royston

https://youtu.be/pBJNXhl4cxQ

for univariate normality see https://youtu.be/l6eG_YQdXFo

https://en.wikipedia.org/wiki/Multivariate_normal_distribution#Multivariate_normality_tests

HTH,

Peter.

http://CRAN.R-project.org/package=mvtnorm

Thanks for the references. The listed tests concentrate on the moments of the multivariate normal distribution, not on other aspects of multivariate normality. But those will do - I was not keen to reject multivariate normality anyway, so if I can state that I did those tests and the null hypothesis could not be rejected, I have answered their question.

Royston's Multivariate Normality Test, which can be considered as an extension, in the multivariate space, of the Shapiro-Wilk test. This test has been found to fit also in small samples size and in relatively uncorrelated variables [Mecklin and Mundfrom, 2005. A Monte Carlo comparison of the Type I and Type II error rates of tests of multivariate normality. Journal of Statistical Computation and Simulation, 75:93-107.].

Thanks Pietro. That is a useful reference.

The energy package for R, mvnorm.etest for arbitrary dimension. this is a powerful omnibus test of multivariate that is particularly good against heavy tailed alternatives and in one dimension is similar to Anderson-Darling normality test. This test is based on a characterization of MVN. Also see the references from JMVA 2005 and JSPI 2013 given in the energy manual. http://cran.us.r-project.org/web/packages/energy/index.html

Thank you very much. This is a useful reference.

@Maria L Rizzo

Hi Maria, I tried to use mvnorm.etest to test the bivariate normality in R, but I got an error message:

'Error in eigen(var(x), symmetric = TRUE) :

infinite or missing values in 'x'

I checked the reference of the package, the author says that if there are missing values, NA will be returned. How to deal with missing values seem not to be specified.

I don't know what to do now.

Watch my youtube tutorial on Multivariate normality Test in R - Mardia's Test, Henze-Zirkler, Royston

https://youtu.be/pBJNXhl4cxQ

for univariate normality see https://youtu.be/l6eG_YQdXFo

You can find the multivariate normality by using mahalanobis distance in spss as well.

you can test multivariate normality by assessing the multivariate skewness and kurtosis through the software in the following link

https://webpower.psychstat.org/models/kurtosis/

(Univariate and multivariate skewness and kurtosis calculation)

for more information about multivariate normality please refer to the attached papers

• Cain, M. K., Zhang, Z., & Yuan, K. H. (2017). Univariate and multivariate skewness and kurtosis for measuring nonnormality: Prevalence, influence and estimation. Behavior research methods, 49(5), 1716-1735.
• Ramayah, T., Yeap, J. A., Ahmad, N. H., Halim, H. A., & Rahman, S. A. (2017). Testing a confirmatory model of facebook usage in smartpls using consistent PLS. International Journal of Business and Innovation, 3(2), 1-14.

Does anyone knows a multi normality test that can handle missing values? Thanks!

Can anybody plainly explain (or suggest a related reference) the concept itself of multinormality of data? (rather than HOW to estimate multinormality)

LT

https://en.wikipedia.org/wiki/Multivariate_normal_distribution