Use of multivariate Shapiro Test for large sample size

Question

I want to check for multivariate normality to conduct a MANOVA with two dependent variables. Can I use Shapiro-Wilk test for multivariate normality if I have a rather large sample size (N = 1200)?

Or would you recommend a different procedure?

Answer 1

Yes, you can use shapiro-wilk (SW) to 1200 elements. The initial study of this test was done for samples below 50 data points. However, over time there have been improvements that allow the use of this test up to 5000 elements. It is important to read in the documentation of the software whether it uses the original or improved version of SW test. Generally, current software uses the improved version.

Here are some references:

• https://link.springer.com/referenceworkentry/10.1007/978-3-642-04898-2_421

• https://link.springer.com/article/10.1007/BF01891203

• https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.shapiro.html#scipy.stats.shapiro

• http://lib.stat.cmu.edu/apstat/R94

• http://lib.stat.cmu.edu/apstat/

• https://www.tandfonline.com/doi/full/10.1080/00949655.2010.520163