Confidence Interval Estimation for Intraclass Correlation Coefficient Under Unequal Family Sizes

Abstract

Confidence intervals (based on the χ² -distribution and (Z) standard normal distribution) for the intraclass correlation coefficient under unequal family sizes based on a single multinormal sample have been proposed. It has been found that the confidence interval based on the χ² -distribution consistently and reliably produces better results in terms of shorter average interval length than the confidence interval based on the standard normal distribution: especially for larger sample sizes for various intraclass correlation coefficient values. The coverage probability of the interval based on the χ² -distribution is competitive with the coverage probability of the interval based on the standard normal distribution. An example with real data is presented.