Some sampling characteristics of three estimators of the intraclass correlation were investigated under a variety of conditions within the context of a one-way three treatment level random effects analysis of variance. The results promote caution in the use of all three estimators since they show both a large negative bias under most conditions and a large standard deviation. The three estimators differed very little in their degree of bias or in the magnitude of their standard errors.
Get full access to this article
View all access options for this article.
References
1.
Bhargava, R.P.Test of significance for intraclass correlation when family sizes are not equal. Sankhya, 1946, 7, 435-438.
2.
Carroll, R.M. and Nordholm, L.A.Sampling characteristics of Kelley's ε2 and Hays' ω2. EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT, 1975, 35, 541-554.
3.
Coombs, C.H.The role of correlation in the analysis of variance. Psychometrika , 1948, 13, 233-243.
4.
Fieller, E.C. and Smith, C.A.B.Note on the analysis of variance and the intraclass correlation. Ann. Eugenics, 16, 97-104, 1951- 52.
5.
Fisher, R.A.Statistical methods for research workers. New York : Hafner Publishing Company, 1952 .
6.
Haggard, E.The intraclass correlation and the analysis of variance. New York: The Dryden Press, Inc., 1958.
7.
Harris, J.A.On the calculation of intraclass and interclass coefficients of correlation from class moments when the number of possible combinations is large. Biometrika, 1913, 9, 446-742.
8.
Hays, W.L.Statistics. New York: Holt, Rinehart and Winston, 1963.
9.
Hoel, P.G.Introduction to mathematical statistics. New York : John Wiley and Sons, Inc., 1966 .
10.
Kelley, T.L.An unbiased correlation ratio measure. Proceedings of the National Academy of Sciences, 1935, 21, 554-559.
11.
Pearson, E., et al. Mathematical contributions to the theory of evolution. IX: On the principle of homotyposis and its relation to heredity, to variability of the individual and to that of race. Part I: Homotyposis in the vegetable kingdom. Philos. Trans. Roy. Soc. (London ), Series A, 197, 285-379, 1901.
12.
Peters, C.C.Interactions in analysis of variance interpreted as intercorrelation . Psychol. Bulletin, 1944, 41, 1287-99.
13.
"Student" The probable error of a mean. Biometrika, 1908, 6, 1-25.
14.
Winer, B.J.Statistical principles in experimental design. New York : McGraw-Hill, 1962.