Book description
Describes statistical intervals to quantify sampling uncertainty,focusing on key application needs and recently developed methodology in an easytoapply 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 easytoapply format. In addition to extensive updating of the original chapters, the second edition includes new chapters on:
• Likelihoodbased statistical intervals
• Nonparametric bootstrap intervals
• Parametric bootstrap and other simulationbased 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 uptodate working guide and reference for all who analyze data, allowing them to quantify the uncertainty in their results using statistical intervals.
William Q. Meeker is Professor of Statistics and Distinguished Professor of Liberal Arts and Sciences at Iowa State University. He is coauthor of Statistical Methods for Reliability Data (Wiley, 1998) and of numerous publications in the engineering and statistical literature and has won many awards for his research.
Gerald J. Hahn served for 46 years as applied statistician and manager of an 18person statistics group supporting General Electric and has coauthored four books. His accomplishments have been recognized by GE’s prestigious Coolidge Fellowship and 19 professional society awards.
Luis A. Escobar is Professor of Statistics at Louisiana State University. He is coauthor of Statistical Methods for Reliability Data (Wiley, 1998) and several book chapters. His publications have appeared in the engineering and statistical literature and he has won several research and teaching awards.
Table of contents
 Preface to Second Edition
 Preface to First Edition
 Acknowledgments
 About the Companion Website

Chapter 1: Introduction, Basic Concepts, and Assumptions
 Objectives and Overview
 1.1 Statistical Inference
 1.2 Different Types of Statistical Intervals: An Overview
 1.3 The Assumption of Sample Data
 1.4 The Central Role of Practical Assumptions Concerning Representative Data
 1.5 Enumerative Versus Analytic Studies
 1.6 Basic Assumptions for Inferences from Enumerative Studies
 1.7 Considerations in the Conduct of Analytic Studies
 1.8 Convenience and Judgment Samples
 1.9 Sampling People
 1.10 Infinite Population Assumption
 1.11 Practical Assumptions: Overview
 1.12 Practical Assumptions: Further Example
 1.13 Planning the Study
 1.14 The Role of Statistical Distributions
 1.15 The Interpretation of Statistical Intervals
 1.16 Statistical Intervals and Big Data
 1.17 Comment Concerning Subsequent Discussion
 Bibliographic Notes

Chapter 2: Overview of Different Types of Statistical Intervals
 Objectives and Overview
 2.1 Choice of a Statistical Interval
 2.2 Confidence Intervals
 2.3 Prediction Intervals
 2.4 Statistical Tolerance Intervals
 2.5 Which Statistical Interval do I Use?
 2.6 Choosing a Confidence Level
 2.7 TwoSided Statistical Intervals Versus OneSided Statistical Bounds
 2.8 The Advantage of Using Confidence Intervals Instead of Significance Tests
 2.9 Simultaneous Statistical Intervals
 Bibliographic Notes
 Chapter 3: Constructing Statistical Intervals Assuming a Normal Distribution Using Simple Tabulations

Chapter 4: Methods for Calculating Statistical Intervals for a Normal Distribution
 Objectives and Overview
 4.1 Notation
 4.2 Confidence Interval for the Mean of A Normal Distribution
 4.3 Confidence Interval for The Standard Deviation of a Normal Distribution
 4.4 Confidence Interval for a Normal Distribution Quantile
 4.5 Confidence Interval for the Distribution Proportion Less (Greater) than a Specified Value
 4.6 Statistical Tolerance Intervals
 4.7 Prediction Interval to Contain a Single Future Observation or the Mean of m Future Observations
 4.8 Prediction Interval to Contain at Least k of m Future Observations
 4.9 Prediction Interval to Contain the Standard Deviation of m Future Observations
 4.10 The Assumption of a Normal Distribution
 4.11 Assessing Distribution Normality and Dealing with Nonnormality
 4.12 Data Transformations and Inferences from Transformed Data
 4.13 Statistical Intervals for Linear Regression Analysis
 4.14 Statistical Intervals for Comparing Populations and Processes
 Bibliographic Notes

Chapter 5: DistributionFree Statistical Intervals
 Objectives and Overview
 5.1 Introduction
 5.2 DistributionFree Confidence Intervals and OneSided Confidence Bounds for a Quantile
 5.3 DistributionFree Tolerance Intervals and Bounds to Contain a Specified Proportion of a Distribution
 5.4 Prediction Intervals and Bounds to Contain a Specified Ordered Observation in a Future Sample
 5.5 DistributionFree Prediction Intervals and Bounds to Contain at Least k of m Future Observations
 Bibliographic Notes

Chapter 6: Statistical Intervals for a Binomial Distribution
 Objectives and Overview
 6.1 Introduction
 6.2 Confidence Intervals for the Actual Proportion Nonconforming in the Sampled Distribution
 6.3 Confidence Interval for the Proportion of Nonconforming Units in a Finite Population
 6.4 Confidence Intervals for the Probability that The Number of Nonconforming Units in a Sample is Less than or Equal to (or Greater Than) a Specified Number
 6.5 Confidence Intervals for the Quantile of the Distribution of the Number of Nonconforming Units
 6.6 Tolerance Intervals and OneSided Tolerance Bounds for the Distribution of the Number of Nonconforming Units
 6.7 Prediction Intervals for the Number Nonconforming in a Future Sample
 Bibliographic Notes

Chapter 7: Statistical Intervals for a Poisson Distribution
 Objectives and Overview
 7.1 Introduction
 7.2 Confidence Intervals for the EventOccurrence Rate of a Poisson Distribution
 7.3 Confidence Intervals for the Probability that the Number of Events in a Specified Amount of Exposure is Less than or Equal to (or Greater Than) A Specified Number
 7.4 Confidence Intervals for the Quantile of the Distribution of the Number of Events in a Specified Amount of Exposure
 7.5 Tolerance Intervals and OneSided Tolerance Bounds for the Distribution of the Number of Events in a Specified Amount of Exposure
 7.6 Prediction Intervals for the Number of Events in a Future Amount of Exposure
 Bibliographic Notes

Chapter 8: Sample Size Requirements for Confidence Intervals on Distribution Parameters
 Objectives and Overview
 8.1 Basic Requirements for Sample Size Determination
 8.2 Sample Size for a Confidence Interval for a Normal Distribution Mean
 8.3 Sample Size to Estimate a Normal Distribution Standard Deviation
 8.4 Sample Size to Estimate a Normal Distribution Quantile
 8.5 Sample Size to Estimate a Binomial Proportion
 8.6 Sample Size to Estimate a Poisson Occurrence Rate
 Bibliographic Notes

Chapter 9: Sample Size Requirements for Tolerance Intervals, Tolerance Bounds, and Related Demonstration Tests
 Objectives and Overview
 9.1 Sample Size for Normal Distribution Tolerance Intervals and OneSided Tolerance Bounds
 9.2 Sample Size to Pass a OneSided Demonstration Test Based on Normally Distributed Measurements
 9.3 Minimum Sample Size for DistributionFree TwoSided Tolerance Intervals and OneSided Tolerance Bounds
 9.4 Sample Size for Controlling The Precision of TwoSided DistributionFree Tolerance Intervals and OneSided DistributionFree Tolerance Bounds
 9.5 Sample Size to Demonstrate that a Binomial Proportion Exceeds (Is Exceeded By) a Specified Value
 Bibliographic Notes
 Chapter 10: Sample Size Requirements for Prediction Intervals

Chapter 11: Basic Case Studies
 Objectives and Overview
 11.1 Demonstration That the Operating Temperature of Most Manufactured Devices will not Exceed a Specified Value
 11.2 Forecasting Future Demand for Spare Parts
 11.3 Estimating the Probability of Passing an Environmental Emissions Test
 11.4 Planning A Demonstration Test to Verify that a Radar System has a Satisfactory Probability of Detection
 11.5 Estimating the Probability of Exceeding a Regulatory Limit
 11.6 Estimating the Reliability of a Circuit Board
 11.7 Using Sample Results to Estimate the Probability that a Demonstration Test will be Successful
 11.8 Estimating the Proportion within Specifications for a TwoVariable Problem
 11.9 Determining the Minimum Sample Size for a Demonstration Test

Chapter 12: LikelihoodBased Statistical Intervals
 Objectives and Overview
 12.1 Introduction to LikelihoodBased Inference
 12.2 Likelihood Function and Maximum Likelihood Estimation
 12.3 LikelihoodBased Confidence Intervals for SingleParameter Distributions
 12.4 LikelihoodBased Estimation Methods for LocationScale and LogLocationScale Distributions
 12.5 LikelihoodBased Confidence Intervals for Parameters and Scalar Functions of Parameters
 12.6 WaldApproximation Confidence Intervals
 12.7 Some Other LikelihoodBased Statistical Intervals
 Bibliographic Notes
 Chapter 13: Nonparametric Bootstrap Statistical Intervals

Chapter 14: Parametric Bootstrap and Other SimulationBased Statistical Intervals
 Objectives and Overview
 14.1 Introduction
 14.2 Parametric Bootstrap Samples and Bootstrap Estimates
 14.3 Bootstrap Confidence Intervals Based on Pivotal Quantities
 14.4 Generalized Pivotal Quantities
 14.5 SimulationBased Tolerance Intervals for LocationScale or LogLocationScale Distributions
 14.6 SimulationBased Prediction Intervals and OneSided Prediction Bounds for at least k of m Future Observations from LocationScale or LogLocationScale Distributions
 14.7 Other Simulation and Bootstrap Methods and Application to Other Distributions and Models
 Bibliographic Notes

Chapter 15: Introduction to Bayesian Statistical Intervals
 Objectives and Overview
 15.1 Bayesian Inference: Overview
 15.2 Bayesian Inference: An Illustrative Example
 15.3 More About Specification of A Prior Distribution
 15.4 Implementing Bayesian Analyses using Markov Chain Monte Carlo Simulation
 15.5 Bayesian Tolerance and Prediction Intervals
 Bibliographic Notes
 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
 Objectives and Overview
 18.1 Confidence Interval for the Proportion of Defective Integrated Circuits
 18.2 Confidence Intervals for Components of Variance in a Measurement Process
 18.3 Tolerance Interval to Characterize the Distribution of Process Output in the Presence of Measurement Error
 18.4 Confidence Interval for the Proportion of Product Conforming to a TwoSided Specification
 18.5 Confidence Interval for the Treatment Effect in a Marketing Campaign
 18.6 Confidence Interval for the Probability of Detection with Limited Hit/Miss Data
 18.7 Using Prior Information to Estimate the ServiceLife Distribution of a Rocket Motor
 Bibliographic Notes
 Epilogue
 Appendix A: Notation and Acronyms

Appendix B: Generic Definition of Statistical Intervals and Formulas for Computing Coverage Probabilities
 B.1 Introduction
 B.2 TwoSided Confidence Intervals and OneSided Confidence Bounds for Distribution Parameters or a Function of Parameters
 B.3 TwoSided ControltheCenter Tolerance Intervals to Contain at Least a Specified Proportion of a Distribution
 B.4 TwoSided Tolerance Intervals to Control Both Tails of a Distribution
 B.5 OneSided Tolerance Bounds
 B.6 TwoSided Prediction Intervals and OneSided Prediction Bounds for Future Observations
 B.7 TwoSided Simultaneous Prediction Intervals and OneSided Simultaneous Prediction Bounds
 B.8 Calibration of Statistical Intervals
 Appendix C: Useful Probability Distributions

Appendix D: General Results from Statistical Theory and Some Methods Used to Construct Statistical Intervals
 Introduction
 D.1 The Cdfs and Pdfs of Functions of Random Variables
 D.2 Statistical Error Propagation—The Delta Method
 D.3 Likelihood and Fisher Information Matrices
 D.4 Convergence in Distribution
 D.5 Outline of General Maximum Likelihood Theory
 D.6 The Cdf Pivotal Method for Obtaining Confidence Intervals
 D.7 Bonferroni Approximate Statistical Intervals

Appendix E: Pivotal Methods for Constructing Parametric Statistical Intervals
 Introduction
 E.1 General Definition and Examples of Pivotal Quantities
 E.2 Pivotal Quantities for the Normal Distribution
 E.3 Confidence Intervals for a Normal Distribution Based on Pivotal Quantities
 E.4 Confidence Intervals for two Normal Distributions Based on Pivotal Quantities
 E.5 Tolerance Intervals for a Normal Distribution Based on Pivotal Quantities
 E.6 Normal Distribution Prediction Intervals Based on Pivotal Quantities
 E.7 Pivotal Quantities for LogLocationScale Distributions

Appendix F: Generalized Pivotal Quantities
 Introduction
 F.1 Definition of a Generalized Pivotal Quantity
 F.2 A Substitution Method to Obtain Generalized Pivotal Quantities
 F.3 Examples of Generalized Pivotal Quantities for Functions of LocationScale Distribution Parameters
 F.4 Conditions for Exact Confidence Intervals Derived from Generalized Pivotal Quantities

Appendix G: DistributionFree Intervals Based on Order Statistics
 Introduction
 G.1 Basic Statistical Results Used in this Appendix
 G.2 DistributionFree Confidence Intervals and Bounds for a Distribution Quantile
 G.3 DistributionFree Tolerance Intervals to Contain a Given Proportion of a Distribution
 G.4 DistributionFree Prediction Interval to Contain a Specified Ordered Observation from a Future Sample
 G.5 DistributionFree Prediction Intervals and Bounds to Contain at Least k of m Future Observations from a Future Sample
 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
Product information
 Title: Statistical Intervals, 2nd Edition
 Author(s):
 Release date: April 2017
 Publisher(s): Wiley
 ISBN: 9780471687177
You might also like
book
Probability, Random Variables, Statistics, and Random Processes
Probability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications is a comprehensive undergraduatelevel textbook. With …
book
HandsOn Machine Learning with ScikitLearn, Keras, and TensorFlow, 2nd Edition
Through a series of recent breakthroughs, deep learning has boosted the entire field of machine learning. …
book
Introduction to Probability
Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding …
book
Bayesian Analysis with Python  Second Edition
Bayesian modeling with PyMC3 and exploratory analysis of Bayesian models with ArviZ Key Features A stepbystep …