Statistical Intervals: A Guide for Practitioners and Researchers, Second Edition.

Description

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 with more than 50 percent new content---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

  and seven new technical appendicies that provide justification and technical details for the various statistical intervals and methods presented in the body of the book.

  Contents

  1 Introduction, Basic Concepts, and Assumptions 1
  2 Overview of Different Types of Statistical Intervals 23
  3 Constructing Statistical Intervals Assuming a Normal Distribution Using Simple Tabulations 37
  4 Methods for Calculating Statistical Intervals for a Normal Distribution 47
  5 Distribution-Free Statistical Intervals 73
  6 Statistical Intervals for a Binomial Distribution 99
  7 Statistical Intervals for a Poisson Distribution 127
  8 Sample Size Requirements for Confidence Intervals on Distribution Parameters 149
  9 Sample Size Requirements for Tolerance Intervals, Tolerance Bounds, andRelated Demonstration Tests 163
  10 Sample Size Requirements for Prediction Intervals 177
  11 Basic Case Studies 185
  12 Likelihood-Based Statistical Intervals 213
  13 Nonparametric Bootstrap Statistical Intervals 245
  14 Parametric Bootstrap and Other Simulation-Based Statistical Intervals 267
  15 Introduction to Bayesian Statistical Intervals 295
  16 Bayesian Statistical Intervals for the Binomial, Poisson, and Normal Distributions 325
  17 Statistical Intervals for Bayesian Hierarchical Models 351
  18 Advanced Case Studies 367
  

  Appendicies

  A Notation and Acronyms 395
  B Generic Definition of Statistical Intervals and Formulas for Computing Coverage Probabilities 403
  C Useful Probability Distributions 423
  D General Results from Statistical Theory and Some Methods Used to Construct Statistical Intervals 447
  E Pivotal Methods for Constructing Parametric Statistical Intervals 473
  F Generalized Pivotal Quantities 489
  G Distribution-Free Intervals Based on Order Statistics 497
  H Basic Results from Bayesian Inference Models 509
  I Probability of Successful Demonstration 523
  J Tables 527
  References 563
  Index 579
  

  
  

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