# Multivariate normality

Multivariate normal distribution is assumed by a number of multivariate tests. PAST computes Mardia's multivariate skewness and kurtosis, with tests based on chi-squared (skewness) and normal (kurtosis) distributions. A powerful omnibus (overall) test due to Doornik & Hansen (1994) is also given. If at least one of these tests show departure from normality (small *p* value), the distribution is significantly non-normal. Sample size should be reasonably large (>50), although a small-sample correction is also attempted for the skewness test.

Missing data supported by column average substitution.

#### References

Doornik, J.A. & H. Hansen. 1994. An omnibus test for univariate and multivariate normality. W4&91 in Nuffield Economics Working Papers.

Mardia, K.V. 1970. Measures of multivariate skewness and kurtosis with applications. *Biometrika* 36:519-530.