The purpose of this dissertation is to present extensions and applications of the modified large-sample approach (MLS) for constructing approximate confidence intervals on functions of variance components.; Manuscript 1 proposes a MLS approach for constructing confidence intervals for intraclass correlation coefficients. Two particular intraclass correlation coefficients are studied from an interrater and intrarater reliability study in which both raters and subjects are random effects in a balanced two-factor design, with and without subject-by-rater interaction term. A simulation study is conducted to investigate the confidence interval coverage proportions. In general, the MLS method provides satisfactory performance.; Manuscript 2 considers the problem of constructing confidence intervals for a particular intraclass correlation coefficient in an interrater reliability study in which both raters and subjects are random effects in a balanced two-factor design, with and without the rater-by-subject interaction term. A simulation study is conducted to compare the coverage of the confidence intervals of existing MLS methods. The newest MLS approach (GiTCH) is compared with (1) the Levia and Graybill approach for the balanced two-factor design with interaction term and (2) the Arteaga, Jeyaratnam, and Graybill approach for the balanced two-factor design without the interaction term. Overall, coverage of confidence intervals for the GiTCH approaches are either correct or conservative, with narrower interval widths, than the other MLS approaches.; Finally, the U.S. Food and Drug Administration (FDA) requires pharmaceutical companies to demonstrate bioequivalence between different formulations of drug products before approval. In Manuscript 3, an improved MLS approach is proposed for constructing confidence intervals on population bioequivalence (PBE) in a four-period, two-sequence, two-formulation crossover design where variance component estimators are dependent. A computer simulation is conducted to compare the proposed method's upper bound to test for PBE with the current FDA and an existing MLS method. The proposed MLS method's ability to maintain the power of testing the hypothesis for PBE was comparable, but slightly less, than both the FDA and existing MLS methods. Regarding upper bound coverage, the proposed MLS method provided marginally accurate coverage with confidence coefficients that were either correct or slightly liberal.; All three manuscripts contain an example using data.
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