Mathematical Geology

, Volume 18, Issue 6, pp 563–575 | Cite as

Power and robustness of Aitchison's test for complete subcompositional independence in closed arrays

  • Alex Woronow


This paper examines some aspects of the power and robustness of the test for complete subcompositional independence proposed by Aitchison (1982). Although the computed test statistics commonly do not approach being χ2 distributed throughout their range, the upper tail of their distribution does mimic the χ2 distribution sufficiently to yield a quite robust test when variates are drawn from identical distributions with different distribution parameters or even when variates are drawn from different distributions. But the magnitude of correlations among the variables and the proportion of correlated to independent variables that compose the closed data vectors affect the power of the test.

Key words

closed number systems closure log ratio compositional data logistic-normal distribution correlations among proportions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aitchison, J., 1981, A new approach to null correlations of proportions: Math. Geol. v. 13, p. 175–189.Google Scholar
  2. Aitchison, J., 1982, The statistical analysis of compositional data: J. R. Stat. Soc. B, v. 44, p. 139–177.Google Scholar
  3. Aitchison, J., 1984, The statistical analysis of geochemical compositions: Math. Geol., v. 16, p. 531–564.Google Scholar
  4. Butler, J. C., 1979, Trends in ternary petrologic variation diagrams—Fact or fantasy? Am. Min., v. 64, p. 1115–1121.Google Scholar
  5. Butler, J. C. and Woronow, A., 1985, Modal analyses: A new perspective (or, yet another procedure for the extraction of information from ternary variables): Proceedings of Houston Geotech '85, in press.Google Scholar
  6. Chayes, F., 1960, On correlation between variables of constant sum: J. Geophys. Res., v. 65, p. 4185–4193.Google Scholar
  7. Chayes, F., 1971, Ratio correlation: A manual for students of petrology and geochemistry, University of Chicago Press, Chicago, Ill., 99 p.Google Scholar
  8. Halmos, P. R., 1944, Random Alms: Ann. Math. Stat., v. 15, p. 182–189.Google Scholar
  9. Mukherjee, B. N., 1970, Likelihood ratio tests of statistical hypotheses associated with patterned covariance matrices in psychology: Brit. J. Math. Stat. Psych., v. 23, p. 89–120.Google Scholar
  10. Nelder, J. A. and Mead, R., 1965, A simplex method for function minimization: Comput. J., v. 7, p. 308–313.Google Scholar
  11. Woronow, A. and Butler, J., 1985, Complete subcomposition independence testing of closed arrays: Comput. Geosci., in press.Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • Alex Woronow
    • 1
  1. 1.Geosciences DepartmentUniversity of Houston, UPHouston

Personalised recommendations