Statistical Intervals

A Guide for Practitioners and Researchers

William Q. Meeker, Gerald J. Hahn, Luis A. Escobar

• Publisher: Wiley
• Year: 2017
• Print ISBN: 9780471687177
• eBook ISBN: 9781118594957
• Edition: 2
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Describes statistical intervals to quantify sampling uncertainty, focusing on key application needs and recently developed methodology in an easy-to-apply format

Statistical intervals provide invaluable tools for quantifying sampling uncertainty. The widely hailed first edition, published in 1991, described the use and construction of the most important statistical intervals. Particular emphasis was given to intervals—such as prediction intervals, tolerance intervals and confidence intervals on distribution quantiles—frequently needed in practice, but often neglected in introductory courses.

Vastly improved computer capabilities over the past 25 years have resulted in an explosion of the tools readily available to analysts. This second edition—more than double the size of the first—adds these new methods in an easy-to-apply format. In addition to extensive updating of the original chapters, the second edition includes new chapters on:

• Likelihood-based statistical intervals
• Nonparametric bootstrap intervals
• Parametric bootstrap and other simulation-based intervals
• An introduction to Bayesian intervals
• Bayesian intervals for the popular binomial, Poisson and normal distributions
• Statistical intervals for Bayesian hierarchical models
• Advanced case studies, further illustrating the use of the newly described methods

New technical appendices provide justification of the methods and pathways to extensions and further applications. A webpage directs readers to current readily accessible computer software and other useful information.

Statistical Intervals: A Guide for Practitioners and Researchers, Second Edition is an up-to-date working guide and reference for all who analyze data, allowing them to quantify the uncertainty in their results using statistical intervals.

Table of contents

• Statistical Intervals
• Contents
• Preface to Second Edition
• Preface to First Edition
• Acknowledgments
• About the Companion Website
• Chapter 1 Introduction, Basic Concepts, and Assumptions
• Chapter 2 Overview of Different Types of Statistical Intervals
• Chapter 3 Constructing Statistical Intervals Assuming a Normal Distribution Using Simple Tabulations
• Chapter 4 Methods for Calculating Statistical Intervals for a Normal Distribution
• Chapter 5 Distribution-Free Statistical Intervals
• Chapter 6 Statistical Intervals for a Binomial Distribution
• Chapter 7 Statistical Intervals for a Poisson Distribution
• Chapter 8 Sample Size Requirements for Confidence Intervals on Distribution Parameters
• Chapter 9 Sample Size Requirements for Tolerance Intervals, Tolerance Bounds, and Related Demonstration Tests
• Chapter 10 Sample Size Requirements for Prediction Intervals
• Chapter 11 Basic Case Studies
• Chapter 12 Likelihood-Based Statistical Intervals
• Chapter 13 Nonparametric Bootstrap Statistical Intervals
• Chapter 14 Parametric Bootstrap and Other Simulation-Based Statistical Intervals
• Chapter 15 Introduction to Bayesian Statistical Intervals
• Chapter 16 Bayesian Statistical Intervals for the Binomial, Poisson, and Normal Distributions
• Chapter 17 Statistical Intervals for Bayesian Hierarchical Models
• Chapter 18 Advanced Case Studies
• Epilogue
• Appendix A Notation and Acronyms
• Appendix B Generic Definition of Statistical Intervals and Formulas for Computing Coverage Probabilities
• Appendix C Useful Probability Distributions
• Appendix D General Results from Statistical Theory and Some Methods Used to Construct Statistical Intervals
• Appendix E Pivotal Methods for Constructing Parametric Statistical Intervals
• Appendix F Generalized Pivotal Quantities
• Appendix G Distribution-Free Intervals Based on Order Statistics
• Appendix H Basic Results from Bayesian Inference Models
• Appendix I Probability of Successful Demonstration
• Appendix J Tables
• References
• Index
• WILEY SERIES IN PROBABILITY AND STATISTICS
• EULA