[R] Test Normality

Michael Friendly friendly at yorku.ca
Wed Mar 28 15:03:55 CEST 2012

On 3/27/2012 8:32 PM, Sindy Carolina Lizarazo wrote:
> Good Night
> I made different test to check normality and multinormality in my dataset,
> but I don´t know which test is better.
> To verify univariate normality I checked: shapiro.test, cvm.test, ad.test,
> lillie.test, sf.test or jaque.bera.test and
> To verify multivariate normal distribution  I use mardia, mvShapiro.Test,
> mvsf, mshapiro.test, mvnorm.e.
> I have a dataset with almost 1000 data and 9 variables, in both cases the
> result is non-normality. For this reason, I transformed data with bcPower
> function and I want to check normality again.

Univariate tests of normality are subsumed within the multivariate 
tests, so there is no real need for the former.

That being said, many of the tests are quite sensitive to mild or small
departures from multivariate normality, such that would have little real
impact on the validity of an analysis.

You may find it more useful to carry out a graphical analysis, such as 
with normal QQ plots, or the multivariate generalization with is a plot
of Mahalanobis squared distances of all observations from their centroid
vs. corresponding quantiles of the Chisquare distribution with p=9 df.

[As a courtesy to readers, you might cite the packages from which you've
used these functions.]


Michael Friendly     Email: friendly AT yorku DOT ca
Professor, Psychology Dept.
York University      Voice: 416 736-5115 x66249 Fax: 416 736-5814
4700 Keele Street    Web:   http://www.datavis.ca
Toronto, ONT  M3J 1P3 CANADA

More information about the R-help mailing list