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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