Intraclass correlation coefficient (ICC) represents comparative measure between laboratories, raters, instruments etc. ICC is based on three variance components. A common purpose of inter-rater reliability studies is to construct confidence intervals for ICC. Ggeneralized confidence interval (GCI) and modified large sample (MLS) methods provide nominal coverage for ICC. But no methods are available for determining the sample size for the same. Sample size method for ICC with two variance components is developed by an earlier study. However this approach is not suitable in this setting as no asymptotic approximation of the variance is available. Such approximation or not used in MLS and GCI. Other similar method already proposed also does not suit this context due to the two-way layout that may be highly skewed. The proposed sample size method ensures that the mean confidence interval is below a user specified target width. Controlling the expected widths is carried out here over the observed values of the mean squares. The computation of this multiple integrals is complex and a variety of statistical methods are employed to make it tractable. The inverse Rao-Blackwellization method is used to derive the sample size for GCI. For MLS a method called dependent conditioning is used where I the three variance components are rewritten as a function of two dependent F distributions. The applications of ICC are from manufacturing, psychometry, biomarkers etc and the paper also presents some actual areas of application. In gauge repeatability problems the sources of variation are operators, parts, and replicates. The model does not include interactions and the effects are considered as random effects. Similar examples could be cited in other areas also.
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