statsmodels.stats.multivariate.test_cov_oneway¶
- 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.
- Parameters:
- cov_list
list
of
array_like Covariance matrices of the sample, estimated with denominator
(N - 1)
, i.e. ddof=1.- nobs_list
list
List of the number of observations used in the estimation of the covariance for each sample.
- cov_list
- Returns:
- res
instance
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.
- res
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.