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Different methods of obtaining confidence intervals for the intraclass correlation coefficient rho in the unbalanced one-way random-effects model are investigated, focusing on applications to family studies. Methods based on simple modifications of formulas for the case of equal group sizes are found to provide adequate coverage at small to moderate values of rho. A method based on the large-sample standard error of the sample intraclass correlation, as derived by Smith (1956, Annals of Human Genetics 21, 363-373), is shown to provide consistently good coverage at all values of rho. A method proposed by Thomas and Hultquist (1978, Annals of Statistics 6, 582-587) also provides consistently good coverage, but generates mean interval widths substantially greater than those generated by Smith's method at values of rho likely to arise in practice.
Donner et al. (Sun,) studied this question.