Standard Article

Bartlett Test

Statistical Theory and Methods

  1. Marc Hallin1,2

Published Online: 15 JAN 2013

DOI: 10.1002/9780470057339.vnn076

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Hallin, M. 2013. Bartlett Test. Encyclopedia of Environmetrics. 1.

Author Information

  1. 1

    ECARES, Université Libre de Bruxelles, Bruxelles, Belgium

  2. 2

    ORFE, Princeton University, Princeton, NJ, USA

Publication History

  1. Published Online: 15 JAN 2013


The standard test for homogeneity of covariance matrices, known as the Bartlett test, is notoriously sensitive to violations of Gaussian assumptions. Its asymptotic behavior under non-Gaussian densities and its robustification (validity-robustness and efficiency-robustness) have been the subject of an abundant literature, which we briefly review.


  • multivariate analysis of variance (MANOVA);
  • multivariate analysis of covariance (MANOCOVA);
  • multivariate linear discriminant analysis;
  • homogeneity of covariance matrices;
  • homogeneity of scatter matrices;
  • likelihood ratio test;
  • Wald test;
  • elliptical symmetry;
  • kurtosis;
  • robustness;
  • ranks