statsmodels.stats.multivariate.test_cov_oneway(cov_list, nobs_list)[source]

Multiple sample hypothesis test that covariance matrices are equal.

This is commonly known as Box-M test.

The Null and alternative hypotheses are

\[\begin{split}H0 &: \Sigma_i = \Sigma_j \text{ for all i and j} \\ H1 &: \Sigma_i \neq \Sigma_j \text{ for at least one i and j}\end{split}\]

where \(\Sigma_i\) is the covariance of sample i.

cov_listlist of array_like

Covariance matrices of the sample, estimated with denominator (N - 1), i.e. ddof=1.


List of the number of observations used in the estimation of the covariance for each sample.

resinstance of HolderTuple

Results contains test statistic and pvalues for both chisquare and F distribution based tests, identified by the name ending “_chi2” and “_f”. Attributes statistic, pvalue refer to the F-test version.


approximations to distribution of test statistic is by Box


Rencher, Alvin C., and William F. Christensen. 2012. Methods of Multivariate Analysis: Rencher/Methods. Wiley Series in Probability and Statistics. Hoboken, NJ, USA: John Wiley & Sons, Inc.

StataCorp, L. P. Stata Multivariate Statistics: Reference Manual. Stata Press Publication.