Analysis of Variance, Design, and Regression

Book excerpt: This text presents a comprehensive treatment of basic statistical methods and their applications. It focuses on the analysis of variance and regression, but also addressing basic ideas in experimental design and count data. The book has four connecting themes: similarity of inferential procedures, balanced one-way analysis of variance, comparison of models, and checking assumptions. Most inferential procedures are based on identifying a scalar parameter of interest, estimating that parameter, obtaining the standard error of the estimate, and identifying the appropriate reference distribution. Given these items, the inferential procedures are identical for various parameters. Balanced one-way analysis of variance has a simple, intuitive interpretation in terms of comparing the sample variance of the group means with the mean of the sample variance for each group. All balanced analysis of variance problems are considered in terms of computing sample variances for various group means. Comparing different models provides a structure for examining both balanced and unbalanced analysis of variance problems and regression problems. Checking assumptions is presented as a crucial part of every statistical analysis. Examples using real data from a wide variety of fields are used to motivate theory. Christensen consistently examines residual plots and presents alternative analyses using different transformation and case deletions. Detailed examination of interactions, three factor analysis of variance, and a split-plot design with four factors are included. The numerous exercises emphasize analysis of real data. Senior undergraduate and graduate students in statistics and graduate students in other disciplines using analysis of variance, design of experiments, or regression analysis will find this book useful.