Components of Variance

Components of Variance

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Description

Identifying the sources and measuring the impact of haphazard variations are important in any number of research applications, from clinical trials and genetics to industrial design and psychometric testing. Only in very simple situations can such variations be represented effectively by independent, identically distributed random variables or by random sampling from a hypothetical infinite population. Components of Variance illuminates the complexities of the subject, setting forth its principles with focus on both the development of models for detailed analyses and the statistical techniques themselves. The authors first consider balanced and unbalanced situations, then move to the treatment of non-normal data, beginning with the Poisson and binomial models and followed by extensions to survival data and more general situations. In the final chapter, they discuss ways of extending and assessing various models, including the study of exceedances, the use of nonlinear representations, the study of transformations of the response variable, and the detailed examination of the distributional form of the underlying random variables. Careful signposting and numerous examples from genetic data analysis, clinical trial design, longitudinal data analysis, industrial design, and meta-analysis make this book accessible - and valuable - not only to statisticians but to all applied research scientists who use statistical methods.show more

Product details

  • Hardback | 184 pages
  • 151.9 x 240.3 x 16mm | 385.56g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • United States
  • English
  • 9 black & white illustrations, 16 black & white tables
  • 1584883545
  • 9781584883548

Review quote

This is a superb book on a topic of central importance in a wide variety of areas of research. A particular strength is attention given to first principles as a prelude to the treatment of many of the technical topics. .... What distinguishes this book from other material is the depth of the discussion combined with the use of only essential technical details.show more

Table of contents

KEY MODELS AND CONCEPTS Preliminaries Some Simple Special Models A Distributional Specification Two Key Concepts Objectives Bibliographic Notes Further Results and Exercises ONE-WAY BALANCED CASE Analysis of Variance Some More Assumptions Synthesis of Variance Finite Population Aspects Formulation Some More Theory Bibliographic Notes Computational/Software Notes Further Results and Exercises MORE GENERAL BALANCED ARRANGEMENTS Preliminaries Components of Covariance and Regression Time as a Factor Bayesian Considerations Measurement Error in Regression Heterogeneous Variability Design Issues Bibliographic Notes Computational/Software Notes Further Results and Exercises UNBALANCED SITUATIONS Introduction One-Way Classification A More General Formulation A Special Case Synthesis of Studies Maximum Likelihood and REML A Different Approach Bibliographic Notes Computational/Software Notes Further Results and Exercises NON-NORMAL PROBLEMS Preliminaries Poisson Distribution Binomial Distribution Survival Data Some Extensions A More General Formulation Generalized Linear Mixed Model Development of Analysis An Outline Example Bibliographic Notes Computational/Software Notes Further Results and Exercises MODEL EXTENSIONS AND CRITICISM Introduction Modifications of Structure Outliers Robust Estimation of an Internal Variance Model Assessment: Predicting Exceedances Analysis of Variability Within Small Groups Analysis by Model Elaboration: A Nonlinear Form Analysis by Model Elaboration: Transformation Nonparametric Estimation of Distributional Form Bibliographic Notes Further Results and Exercises APPENDIX: Fitting Separate Logistic Regressions to the ANZICS Data REFERENCES AUTHOR INDEX SUBJECT INDEXshow more