Comparing Equal-Tail Probability and Unbiased Confidence Intervals for the Intraclass Correlation Coefficient

Abstract

The conventional confidence interval for the intraclass correlation coefficient assumes equal-tail probabilities. In general, the equal-tail probability interval is biased and other interval procedures should be considered. Unbiased confidence intervals for the intraclass correlation coefficient are readily available. The equal-tail probability and unbiased intervals have exact coverage as they are constructed using the pivotal quantity method. In this article, confidence intervals for the intraclass correlation coefficient are built using balanced and unbalanced one-way random effects models. The expected length of confidence intervals serves as a tool to compare the two procedures. The unbiased confidence interval outperforms the equal-tail probability interval if the intraclass correlation coefficient is small and the equal-tail probability interval outperforms the unbiased interval if the intraclass correlation coefficient is large.

Keywords:

• Expected length
• Ghosh–Pratt identity
• One-way random effects model
• Variance components

Mathematics Subject Classification:

• Primary 62F25
• Secondary 62E15

Acknowledgments

The author is very grateful to Dr. Ian Harris for helpful conversations. The author would also like to acknowledge the comments from the referee that improved the presentation of the article.