statsmodels.stats.multivariate.test_cov_oneway

statsmodels.stats.multivariate.test_cov_oneway(cov_list, nobs_list)

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.

Parameters

cov_listlist of array_like

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

nobs_listlist

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

Returns

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.

Notes

approximations to distribution of test statistic is by Box

References

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. https://doi.org/10.1002/9781118391686.

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