Abstract:
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Confidence intervals for the intraclass correlation coefficient are used to determine the optimal allocation of experimental material in one-way random effects models. The authors investigate the number of classes and the number of observations per class required to minimize the expected length of confidence intervals. We obtain results using asymptotic calculations, which are confirmed using exact small-sample calculations. We find that for fixed sample size and fixed number of groups, one should select a balanced design, or the design which is closest to balanced. If one is allowed to choose the number of groups, we find that the best design depends on the unknown coefficient; choose a few large groups if the coefficient is small, but choose many small groups if the coefficient is large. A good overall recommendation, which works well when averaged over possible values of the coefficient, is to choose group sizes of four.
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