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Permutational tests for correlation matrices

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Abstract

Permutational tests are proposed for the hypotheses that two population correlation matrices have common eigenvectors, and that two population correlation matrices are equal. The only assumption made in these tests is that the distributional form is the same in the two populations; they should be useful as a prelude either to tests of mean differences in grouped standardised data or to principal component investigation of such data.

The performance of the permutational tests is subjected to Monte Carlo investigation, and a comparison is made with the performance of the likelihood-ratio test for equality of covariance matrices applied to standardised data. Bootstrapping is considered as an alternative to permutation, but no particular advantages are found for it. The various tests are applied to several data sets.

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References

  • Andrews, D. F. and Herzberg, A. M. (1985) Data, Springer-Verlag, New York.

    Google Scholar 

  • Ashikaga, T. and Chang, P. C. (1981) Robustness of Fisher's linear discriminant function under two-component mixed normal models. Journal of the American Statistical Association, 76, 676–680.

    Google Scholar 

  • Costanza, M. C. and Afifi, A. A. (1979) Comparison of stopping rules in forward stepwise discriminant analysis. Journal of the American Statistical Association, 74, 777–785.

    Google Scholar 

  • Flury, B. N. (1988) Common Principal Components and Related Multivariate Models. Wiley, New York.

    Google Scholar 

  • Heiberger, R. M. (1978) Generation of random orthogonal matrices. Algorithm AS127, Applied Statistics, 27, 199–206.

    Google Scholar 

  • Krzanowski, W. J. (1979) Between-groups comparison of principal components. Journal of the American Statistical Association, 74, 703–707, with correction in volume 76, (1981), 1022.

    Google Scholar 

  • Krzanowski, W. J. (1982) Between-group comparison of principal components -some sampling results. Journal of Statistical Computation and Simulation, 15, 141–154.

    Google Scholar 

  • Krzanowski, W. J. (1988) Principles of Multivariate Analysis: A User's Perspective. Clarendon Press, Oxford.

    Google Scholar 

  • Manly, B. F. J. (1986) Multivariate Statistical Methods, A Primer. Chapman and Hall, London.

    Google Scholar 

  • Manly, B. F. J. and Rayner, J. C. W. (1987) The comparison of sample covariance matrices using likelihood ratio tests. Biometrika, 74, 841–847.

    Google Scholar 

  • Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979) Multivariate Analysis. Academic Press, London.

    Google Scholar 

  • Rayner, J. C. W., Manly, B. F. J. and Liddell, G. F. (1990) Hierarchic likelihood ratio tests for equality of covariance matrices. Journal of Statistical Computation and Simulation, 35, 91–99.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical Statistics and Operational Research, University of Exeter, North Park Road, EX4 4QE, Exeter, UK

    W. J. Krzanowski

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  1. W. J. Krzanowski
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Krzanowski, W.J. Permutational tests for correlation matrices. Stat Comput 3, 37–44 (1993). https://doi.org/10.1007/BF00146952

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