pingouin.multivariate_normality#

pingouin.multivariate_normality(X, alpha=0.05)[source]#

Henze-Zirkler multivariate normality test.

Parameters:

Xnp.array: Data matrix of shape (n_samples, n_features).
alphafloat: Significance level.

Returns:

hzfloat: The Henze-Zirkler test statistic.
pvalfloat: P-value.
normalboolean: True if X comes from a multivariate normal distribution.

See also

normality: Test the univariate normality of one or more variables.
homoscedasticity: Test equality of variance.
sphericity: Mauchly’s test for sphericity.

Notes

The Henze-Zirkler test [1] has a good overall power against alternatives to normality and works for any dimension and sample size.

Adapted to Python from a Matlab code [2] by Antonio Trujillo-Ortiz and tested against the MVN R package.

Rows with missing values are automatically removed.

References

[1]

Henze, N., & Zirkler, B. (1990). A class of invariant consistent tests for multivariate normality. Communications in Statistics-Theory and Methods, 19(10), 3595-3617.

[2]

Trujillo-Ortiz, A., R. Hernandez-Walls, K. Barba-Rojo and L. Cupul-Magana. (2007). HZmvntest: Henze-Zirkler’s Multivariate Normality Test. A MATLAB file.

Examples

>>> import pingouin as pg
>>> data = pg.read_dataset('multivariate')
>>> X = data[['Fever', 'Pressure', 'Aches']]
>>> pg.multivariate_normality(X, alpha=.05)
HZResults(hz=0.540086101851555, pval=0.7173686509622386, normal=True)