Sample size methods for constructing confidence intervals for the intra-class correlation coefficient

• Sample size methods and programs for reliability studies are developed.
• The two-way balanced analysis of variance model without interaction is the focus.
• The sample size guarantees a user-specified mean confidence interval width.
• Modified large sample and generalized confidence interval methods are used.
• Novel computational algorithms are developed, studied, and implemented.

The intraclass correlation coefficient (ICC) in a two-way analysis of variance is a ratio involving three variance components. Two recently developed methods for constructing confidence intervals (CI’s) for the ICC are the Generalized Confidence Interval (GCI) and Modified Large Sample (MLS) methods. The resulting intervals have been shown to maintain nominal coverage. But methods for determining sample size for GCI and MLS intervals are lacking. Sample size methods that guarantee control of the mean width for GCI and MLS intervals are developed. In the process, two variance reduction methods are employed, called dependent conditioning and inverse Rao-Blackwellization. Asymptotic results provide lower bounds for mean CI widths, and show that MLS and GCI widths are asymptotically equivalent. Simulation studies are used to investigate the new methods. A real data example is used and application issues discussed. The new methods are shown to result in adequate sample size estimates, the asymptotic estimates are accurate, and the variance reduction techniques are effective. A sample size program is developed.1 Future extensions of these results are discussed.