Inferences on the intraclass correlation coefficients in the unbalanced two-way random effects model with interaction

In this paper, the hypothesis testing and interval estimation for the intraclass correlation coefficients are considered in a two-way random effects model with interaction. Two particular intraclass correlation coefficients are described in a reliability study. The tests and confidence intervals for the intraclass correlation coefficients are developed when the data are unbalanced. One approach is based on the generalized p-value and generalized confidence interval, the other is based on the modified large-sample idea. These two approaches simplify to the ones in Gilder et al. [2007. Confidence intervals on intraclass correlation coefficients in a balanced two-factor random design. J. Statist. Plann. Inference 137, 1199–1212] when the data are balanced. Furthermore, some statistical properties of the generalized confidence intervals are investigated. Finally, some simulation results to compare the performance of the modified large-sample approach with that of the generalized approach are reported. The simulation results indicate that the modified large-sample approach performs better than the generalized approach in the coverage probability and expected length of the confidence interval.