Statistical Intervals, 2nd Edition

Chapter 2 Overview of Different Types of Statistical Intervals

Objectives and Overview

This chapter introduces different kinds of statistical intervals and their applications. A discussion of the procedures for constructing such intervals is postponed to subsequent chapters. We begin with some general comments about the choice of a statistical interval. We end the chapter with discussions of some practical issues concerning the use of statistical intervals.

This chapter explains:

• Reasons for constructing a statistical interval and some examples (Section 2.1).
• Different types of confidence intervals and one-sided confidence bounds (Section 2.2).
• Different types of prediction intervals and one-sided prediction bounds (Section 2.3).
• Tolerance intervals and one-sided tolerance bounds (Section 2.4).
• The selection of an appropriate statistical interval (Section 2.5).
• The selection of a confidence level (Section 2.6).
• The difference between two-sided intervals and one-sided statistical bounds (Section 2.7).
• The advantages of using confidence intervals instead of significance tests (Section 2.8).
• The use of simultaneous statistical intervals (Section 2.9).

2.1 Choice of a Statistical Interval

The appropriate statistical interval for a particular application depends on the application. Thus, the analyst must determine which interval(s) to use, based on the needs of the problem. The following comments give brief guidelines for this selection. Table 2.1 categorizes the statistical ...