On methods in the analysis of profile data
Tóm tắt
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.
Tài liệu tham khảo
Anderson, T. W.Introduction to multivariate statistical analysis. New York: Wiley, 1958.
Block, J., Levine, L., and McNemar, Q. Testing for the existence of psychometric patterns.J. abnorm. soc. Psychol., 1951,46, 356–359.
Box, G. E. P. A general distribution theory for a class of likelihood criteria.Biometrika, 1949,36, 317–346.
Box, G. E. P. Problems in the analysis of growth and wear curves.Biometrics, 1950,6, 362–389.
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.
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.
Eisenhart, C. The assumptions underlying the analysis of variance.Biometrics, 1947,3, 1–21.
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.
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.
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.
Kullback, S. An application of information theory to multivariate analysis, II.Ann. math. Statist., 1956,27, 122–146.
Rao, C. R.Advanced statistical methods in biometric research. New York: Wiley, 1952.
Roy, S. N. On a heuristic method of test construction and its use in multivariate analysis.Ann. math. Statist., 1953,24, 220–238.
Scheffé, H. A “mixed model” for the analysis of variance.Ann. math. Statist., 1956,27, 23–36.
Welch, B. L. Note on Mrs. Aspin's Tables and on certain approximations to the tabled functions.Biometrika, 1949,36, 293–296.
Wilk, M. B. and Kempthorne, O. Fixed, mixed, and random models.J. Amer. statist. Ass., 1955,50, 1144–1167.
Wilks, S. S. Certain generalizations in the analysis of variance.Biometrika, 1932,24, 471–494.