# What's the best function to test multivariate normality when sample size more than 3000?

Before MANOVA, I need to test multivariate normality.
Then I tried MVN::mvn() function in R, output as below:
Error in FUN(newX[, i], ...) : sample size must be between 3 and 5000

Based on the qq-plot, I don't think data fit multivariate normality.

As my sample size always more than 3000, among Mardia’s test, Henze-Zirkler’s test, Royston’s test, Doornik-Hansen’s test, E-statistic, which one is best to test multivariate normality?

• You don't need a "best" test. Just test a random subsample of 3K observations. If you're right--and it looks that way--the test will reject normality. This is of little interest, though, because what you do afterward is the key. The departures from normality are curious, because they indicate clustering of values around $3$ and $6$ in the squared Mahalanobis distance. You need to investigate that and decide to what extent this clustering might affect whatever analyses you are interested in.
– whuber
Commented May 13, 2020 at 18:14
• @whuber,based the above plot,is data multivariate normality? Commented May 13, 2020 at 18:48