Statistical Intervals, 2nd Edition

Chapter 1 Introduction, Basic Concepts, and Assumptions

Objectives and Overview

This chapter provides the foundation for our discussion throughout the book. Its emphasis is on basic concepts and assumptions. The topics discussed in this chapter are:

• The concept of statistical inference (Section 1.1).
• An overview of different types of statistical intervals: confidence intervals, tolerance intervals, and prediction intervals ( Section 1.2).
• The assumption of sample data (Section 1.3) and the central role of practical assumptions about the data being “representative” (Section 1.4).
• The need to differentiate between enumerative and analytic studies (Section 1.5).
• Basic assumptions for inferences from enumerative studies, including a brief description of different random sampling schemes (Section 1.6).
• Considerations in conducting analytic studies (Section 1.7).
• Convenience and judgment samples (Section 1.8).
• Sampling people (Section 1.9).
• The assumption of sampling from an infinite population (Section 1.10).
• More on practical assumptions (Sections 1.11 and 1.12).
• Planning the study (Section 1.13).
• The role of statistical distributions (Section 1.14).
• The interpretation of a statistical interval (Section 1.15).
• The relevance of statistical intervals in the era of big data (Section 1.16).
• Comment concerning the subsequent discussion in this book (Section 1.17).

1.1 Statistical Inference

Decisions frequently have to be made from limited sample data. For example:

• A television ...