On methods in the analysis of profile data


This paper is concerned with methods for analyzing quantitative, non-categorical profile data, e.g., a battery of tests given to individuals in one or more groups. It is assumed that the variables have a multinormal distribution with an arbitrary variance-covariance matrix. Approximate procedures based on classical analysis of variance are presented, including an adjustment to the degrees of freedom resulting in conservativeF tests. These can be applied to the case where the variance-covariance matrices differ from group to group. In addition, exact generalized multivariate analysis methods are discussed. Examples are given illustrating both techniques.

This is a preview of subscription content, access via your institution.


  1. [1]

    Anderson, T. W.Introduction to multivariate statistical analysis. New York: Wiley, 1958.

    Google Scholar 

  2. [2]

    Block, J., Levine, L., and McNemar, Q. Testing for the existence of psychometric patterns.J. abnorm. soc. Psychol., 1951,46, 356–359.

    Google Scholar 

  3. [3]

    Box, G. E. P. A general distribution theory for a class of likelihood criteria.Biometrika, 1949,36, 317–346.

    Google Scholar 

  4. [4]

    Box, G. E. P. Problems in the analysis of growth and wear curves.Biometrics, 1950,6, 362–389.

    Google Scholar 

  5. [5]

    Box, G. E. P. Some theorems on quadratic forms applied in the study of analysis of variance problems: I. Effect of inequality of variance in the one-way classification.Ann. math. Statist., 1954,25, 290–302.

    Google Scholar 

  6. [6]

    Box, G. E. P. Some theorems on quadratic forms applied in the study of analysis of variance problems: II. Effects of inequality of variance and of correlation between errors in the two-way classification.Ann. math. Statist., 1954,25, 484–498.

    Google Scholar 

  7. [7]

    Eisenhart, C. The assumptions underlying the analysis of variance.Biometrics, 1947,3, 1–21.

    Google Scholar 

  8. [8]

    Geisser, S. and Greenhouse, S. W. An extension of Box's results on the use of theF distribution in multivariate analysis.Ann. math. Statist., 1958,29, 885–891.

    Google Scholar 

  9. [9]

    Heck, D. L. Some uses of the distribution of the largest root in multivariate analysis. Inst. Statist. Univ. North Carolina, Mimeo. Ser. No. 194, 1958.

  10. [10]

    Hotelling, H. A generalizedT test and measure of multivariate dispersion.Proceedings of the second Berkeley symposium on mathematical statistics and probability. Berkeley: Univ. Calif. Press, 1951, 23–42.

    Google Scholar 

  11. [11]

    Kullback, S. An application of information theory to multivariate analysis, II.Ann. math. Statist., 1956,27, 122–146.

    Google Scholar 

  12. [12]

    Rao, C. R.Advanced statistical methods in biometric research. New York: Wiley, 1952.

    Google Scholar 

  13. [13]

    Roy, S. N. On a heuristic method of test construction and its use in multivariate analysis.Ann. math. Statist., 1953,24, 220–238.

    Google Scholar 

  14. [14]

    Scheffé, H. A “mixed model” for the analysis of variance.Ann. math. Statist., 1956,27, 23–36.

    Google Scholar 

  15. [15]

    Welch, B. L. Note on Mrs. Aspin's Tables and on certain approximations to the tabled functions.Biometrika, 1949,36, 293–296.

    Google Scholar 

  16. [16]

    Wilk, M. B. and Kempthorne, O. Fixed, mixed, and random models.J. Amer. statist. Ass., 1955,50, 1144–1167.

    Google Scholar 

  17. [17]

    Wilks, S. S. Certain generalizations in the analysis of variance.Biometrika, 1932,24, 471–494.

    Google Scholar 

Download references

Author information



Additional information

We are indebted to Mrs. Norma French for performing all the calculations appearing in this paper.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Greenhouse, S.W., Geisser, S. On methods in the analysis of profile data. Psychometrika 24, 95–112 (1959). https://doi.org/10.1007/BF02289823

Download citation


  • Multivariate Analysis
  • Public Policy
  • Statistical Theory
  • Classical Analysis
  • Profile Data