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To check multivariate normality, which is the best plot - a chi square qq plot for the entire set of variables or as many qqplots as the number of variables?

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  • $\begingroup$ Which method do you think gives the most information? (Neither is "best", though, because they give information only about marginal distributions and therefore their diagnostic capabilities are incomplete.) $\endgroup$
    – whuber
    Jul 26 '14 at 18:59
  • $\begingroup$ Of the two which is better? $\endgroup$
    – user52672
    Jul 26 '14 at 19:00
  • $\begingroup$ I don't know what you mean by a "chi square qq plot for the entire set of variables." When I first read the question I thought it meant a QQ plot comparing the sum of squares of the values to a relevant $\chi^2$ distribution, but it now occurs to me you might have had something else in mind--I just don't know exactly what. $\endgroup$
    – whuber
    Jul 26 '14 at 23:49
  • $\begingroup$ chi square qq plot = squared Mahalanobis distance against the Chi square quantile. I obtained it by giving qq plot = true when Mardia's MVN test was used in R. $\endgroup$
    – user52672
    Jul 27 '14 at 6:09
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There are some test like the Mardia’s Multivariate Normality Test, Royston’s Multivariate Normality Test but i think chi q-q plot is ideal for showing multivariate normality . Here is vignette in R which you might be interested in http://cran.r-project.org/web/packages/MVN/vignettes/MVN.pdf

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