statsmodels.stats.multivariate.test_cov_spherical¶

statsmodels.stats.multivariate.test_cov_spherical(cov, nobs)[source]¶

One sample hypothesis test that covariance matrix is spherical

The Null and alternative hypotheses are

\[\begin{split}H0 &: \Sigma = \sigma I \\ H1 &: \Sigma \neq \sigma I\end{split}\]

where \(\sigma_i\) is the common variance with unspecified value.

Parameters

covarray_like: Covariance matrix of the data, estimated with denominator (N - 1), i.e. ddof=1.
nobsint: number of observations used in the estimation of the covariance

Returns

resinstance of HolderTuple: results with statistic, pvalue and other attributes like df

References

Bartlett, M. S. 1954. “A Note on the Multiplying Factors for Various Χ2 Approximations.” Journal of the Royal Statistical Society. Series B (Methodological) 16 (2): 296–98.

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.