Abstract
In this paper we address the problem of testing the equality ofk intraclass correlation coefficients based on samples from independentp-variate normal populations, and explore various aspects of optimality through invariance. A UMPIU test is derived fork=2, and LMMPIU test of SenGupta and Vermeire (1986) is indicated fork>2. Several approximately optimum invariant tests are also proposed. The tests are compared with the approximate LR tests and Fisher'sZ-tests derived in Konishi and Gupta (1987, 1989). As expected, the performance of the proposed tests turns out to be quite satisfactory and superior to the LR tests andZ-tests.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cohen, A., Sackrowitz, H. B. and Strawderman, W. (1985). Multivariate locally most powerful unbiased tests,Multivariate Analysis VI (ed. P. R. Krishnaiah), 121–144, North-Holland, Amsterdam.
Donner, A. and Bull, S. (1983). Inferences concerning a common intraclass correlation coefficient,Biometrics,39, 771–775.
Gokhale, D. V. and SenGupta, A. (1986). Optimal tests for the correlation coefficient in a symmetric multivariate normal population,J. Statist. Plann. Inference,14, 263–268.
Isaacson, S. L. (1951). On the theory of unbiased tests of simple statistical hypotheses specifying the values of two or more parameters,Ann. Math. Statist.,22, 217–234.
Kariya, T. and Sinha, B. K. (1989).Robustness of Statistical Tests, Academic Press, Boston.
Kariya, T. and Sinha, B. K. (1991). A note on LBI tests for homogeneity,Gujarat Journal of Statistics: Khatri memorial volume (to appear).
Karlin, S. (1968).Total Positivity, Stanford University Press, California.
Konishi, S. (1985). Normalizing and variance stabilizing transformations for intraclass correlations,Ann. Inst. Statist. Math.,37, 87–94.
Konishi, S. and Gupta, A. K. (1987). Inferences about interclass and intraclass correlations from familial data,Biostatistics (eds. I. B. McNeill and G. J. Umphrey), 225–233, Reidel, Dordrecht.
Konishi, S. and Gupta, A. K. (1989). Testing the equality of several intraclass correlation coefficients,J. Statist. Plann. Inference,21, 93–105.
Lehmann, E. L. (1986).Testing Statistical Hypotheses, 2nd ed., Wiley, New York.
Rao, C. R. (1973).Linear Statistical Inference and Its Applications, Wiley, New York.
Rosner, B., Donner, A. and Hennekens, C. H. (1977). Estimation of interclass correlation from familial data,Appl. Statist.,26, 179–187.
Rosner, B., Donner, A. and Hennekens, C. H. (1979). Significance testing of interclass correlations from familial data,Biometrics,35, 461–471.
Scheffe, H. (1959).The Analysis of Variance, Wiley, New York.
SenGupta, A. (1988). On loss of power under additional information—an example,Scand. J. Statist.,15, 25–31.
SenGupta, A. and Vermeire, L. (1986). Locally optimal tests for multiparameter hypotheses,J. Amer. Statist. Assoc.,81, 819–825.
Srivastava, M. S. (1984). Estimation of interclass correlations in familial data,Biometrika,71, 177–185.
Wijsman, R. A. (1967). Cross-sections of orbits and their application to densities of maximal invariants,Proc. Fifth Berkerley Symp-on Math. Statist. Prob.,1, 389–400.
Author information
Authors and Affiliations
About this article
Cite this article
Huang, WT., Sinha, B.K. On optimum invariant tests of equality of intraclass correlation coefficients. Ann Inst Stat Math 45, 579–597 (1993). https://doi.org/10.1007/BF00773357
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00773357