Stata 15 help for mvtest_normality

[MV] mvtest normality -- Multivariate normality tests


mvtest normality varlist [if] [in] [weight] [, options]

options Description ------------------------------------------------------------------------- Options univariate display tests for univariate normality (sktest) bivariate display tests for bivariate normality (Doornik-Hansen) stats(stats) statistics to be computed -------------------------------------------------------------------------

stats Description ------------------------------------------------------------------------- dhansen Doornik-Hansen omnibus test; the default hzirkler Henze-Zirkler's consistent test kurtosis Mardia's multivariate kurtosis test skewness Mardia's multivariate skewness test all all tests listed here -------------------------------------------------------------------------

bootstrap, by, jackknife, rolling, and statsby are allowed; see prefix. Weights are not allowed with the bootstrap prefix. aweights are not allowed with the jackknife prefix. fweights are allowed; see weight.


Statistics > Multivariate analysis > MANOVA, multivariate regression, and related > Multivariate test of means, covariances, and normality


mvtest normality performs tests for univariate, bivariate, and multivariate normality.

See [MV] mvtest for more multivariate tests.


+---------+ ----+ Options +----------------------------------------------------------

univariate specifies that tests for univariate normality be displayed, as obtained from sktest.

bivariate specifies that the Doornik-Hansen (2008) test for bivariate normality be displayed for each pair of variables.

stats(stats) specifies one or more test statistics for multivariate normality. Multiple stats are separated by white space. The following stats are available:

dhansen produces the Doornik-Hansen (2008) omnibus test.

hzirkler produces Henze-Zirkler's (1990) consistent test.

kurtosis produces the test based on Mardia's (1970) measure of multivariate kurtosis.

skewness produces the test based on Mardia's (1970) measure of multivariate skewness.

all is a convenient shorthand for stats(dhansen hzirkler kurtosis skewness).


The Doornik-Hansen (2008) test and Mardia's (1970) test for multivariate kurtosis take computing time roughly proportional to the number of observations. In contrast, the computing time of the test by Henze-Zirkler (1990) and Mardia's (1970) test for multivariate skewness are roughly proportional to the square of the number of observations.


Setup . webuse iris . keep if iris==1

Display Doornik-Hansen omnibus test . mvtest normality pet* sep*

Same as above, but also display test for univariate normality . mvtest normality pet* sep*, univariate

Display univariate, bivariate, and multivariate tests for normality . mvtest normality pet* sep*, univariate bivariate stats(all)

Stored results

mvtest normality stores the following in r():

Scalars r(p_dh) p-value for Doornik-Hansen test (stats(dhansen)) r(df_dh) degrees of freedom of chi2_dh (stats(dhansen)) r(chi2_dh) Doornik-Hansen statistic (stats(dhansen)) r(rank_hz) rank of covariance matrix (stats(hzirkler)) r(p_hz) p-value for two-sided Hanze-Zirkler's test (stats(hzirkler)) r(z_hz) normal variate associated with hz (stats(hzirkler)) r(V_hz) expected variance of log(hz) (stats(hzirkler)) r(E_hz) expected value of log(hz) (stats(hzirkler)) r(hz) Henze-Zirkler discrepancy statistic (stats(hzirkler)) r(rank_mkurt) rank of covariance matrix (stats(kurtosis)) r(p_mkurt) p-value for Mardia's multivariate kurtosis test (stats(kurtosis)) r(z_mkurt) normal variate associated with Mardia mKurtosis (stats(kurtosis)) r(chi2_mkurt) chi-squared of Mardia mKurtosis (stats(kurtosis)) r(mkurt) Mardia mKurtosis test statistic (stats(kurtosis)) r(rank_mskew) rank for Mardia mSkewness test (stats(skewness)) r(p_mskew) p-value for Mardia's multivariate skewness test (stats(skewness)) r(df_mskew) degrees of freedom of Mardia mSkewness test (stats(skewness)) r(chi2_mskew) chi-squared of Mardia mSkewness test (stats(skewness)) r(mskew) Mardia mSkewness test statistic (stats(skewness))

Matrices r(U_dh) matrix with the skewness and kurtosis of orthonormalized variables (used in the Doornik-Hansen test): b1, b2, z(b1), and z(b2) (stats(dhansen)) r(Btest) bivariate test statistics (bivariate) r(Utest) univariate test statistics (univariate)


Doornik, J. A., and H. Hansen. 2008. An omnibus test for univariate and multivariate normality. Oxford Bulletin of Economics and Statistics 70: 927-939.

Henze, N., and B. Zirkler. 1990. A class of invariant consistent tests for multivariate normality. Communications in Statistics, Theory and Methods 19: 3595-3617.

Mardia, K. V. 1970. Measures of multivariate skewness and kurtosis with applications. Biometrika 57: 519-530.

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