Asymptotic standard errors of intraclass correlation coefficients for two-way model

Intraclass correlation coefficients are estimated using appropriate analysis of variance models that are commonly used in behavioral measurement, biometric, and psychometric. The ICCs estimation accuracy is quantified by the degree of their sampling variability using the asymptotic standard errors or confidence intervals, which facilitates conducting hypothesis testing on ICCs. The article derived the asymptotic standard errors of absolute agreement ICC and relative consistency ICC for the two-way model. Monte Carlo simulations were performed for both normal data and nonnormal data under different conditions. Results supported that the proposed asymptotic standard errors for all ICCs were converging to the simulated true standard errors under different test conditions.