A comparison of two indices for the intraclass correlation coefficient

Abstract

In the present study, we examined the behavior of two indices for measuring the intraclass correlation in the one-way random effects model: the prevailing ICC(1) (Fisher, 1938) and the corrected eta-squared (Bliese & Halverson, 1998). These two procedures differ both in their methods of estimating the variance components that define the intraclass correlation coefficient and in their performance of bias and mean squared error in the estimation of the intraclass correlation coefficient. In contrast with the natural unbiased principle used to construct ICC(1), in the present study it was analytically shown that the corrected eta-squared estimator is identical to the maximum likelihood estimator and the pairwise estimator under equal group sizes. Moreover, the empirical results obtained from the present Monte Carlo simulation study across various group structures revealed the mutual dominance relationship between their truncated versions for negative values. The corrected eta-squared estimator performs better than the ICC(1) estimator when the underlying population intraclass correlation coefficient is small. Conversely, ICC(1) has a clear advantage over the corrected eta-squared for medium and large magnitudes of population intraclass correlation coefficient. The conceptual description and numerical investigation provide guidelines to help researchers choose between the two indices for more accurate reliability analysis in multilevel research.