Analysis of variance (ANOVA) models have become widely used tools and play a fundamental role in much of the application of statistics today. In particular, ANOVA models involving random effects have found widespread application to experimental design in a variety of fields requiring measurements of variance, including agriculture, biology, animal breeding, applied genetics, econometrics, quality control, medicine, engineering, and social sciences. This two-volume work is a comprehensive presentation of different methods and techniques for point estimation, interval estimation, and tests of hypotheses for linear models involving random effects. Both Bayesian and repeated sampling procedures are considered. Volume I examines models with balanced data (orthogonal models); Volume II studies models with unbalanced data (nonorthogonal models). Features and Topics: * Systematic treatment of the commonly employed crossed and nested classification models used in analysis of variance designs* Detailed and thorough discussion of certain random effects models not commonly found in texts at the introductory or intermediate level* Numerical examples to analyze data from a wide variety of disciplines* Many worked examples containing computer outputs from standard software packages such as SAS, SPSS, and BMDP for each numerical example* Extensive exercise sets at the end of each chapter* Numerous appendices with background reference concepts, terms, and results* Balanced coverage of theory, methods, and practical applications* Complete citations of important and related works at the end of each chapter, as well as an extensive general bibliographyAccessible to readers with only a modest mathematical and statistical background, the work will appeal to a broad audience of students, researchers, and practitioners in the mathematical, life, social, and engineering sciences. It may be used as a textbook in upper-level undergraduate and graduate courses, or as a reference for readers interested in the use of random effects models for data analysis.