However, when all individual variables are normally distributed, the set of variables may not be distributed as multivariate normal. Hence, testing each variable only for univariate normality is not sufficient. If the p-value of any of the tests is small, then multivariate normality can be rejected. However, it is important to note that the univariate Shapiro-Wilk W test is a very powerful test and is capable of detecting small departures from univariate normality with relatively small sample sizes. This may cause you to reject univariate, and therefore multivariate, normality unnecessarily if the tests are being done to validate the use of methods that are robust to small departures from normality.
Covariance matrix is singular.
If it is not found, a message is printed, nonsinularity is assumed and the macro attempts to perform the tests. For p variables and a large sample size, the squared Mahalanobis distances of the observations to the mean vector are distributed as chi-square with p degrees of freedom. However, the sample size must be quite large for the chi-square distribution to obtain unless p is very small. Also, this plot is sensitive to the presence of outliers. So, this plot should be cautiously used as a rough indicator of multivariate normality.