6. Basic Statistical Inference

• Published in: Methods in Experimental Physics Vol. 28; pp. 155 - 186
• Main Author: Kitchin, John
• Format: Book Chapter
• Language: English
• Published: Elsevier Science & Technology 1994
• ISBN: 0124759734; 9780124759732
• ISSN: 0076-695X
• DOI: 10.1016/S0076-695X(08)60256-2

This chapter discusses the problem of making inferences, or more generally, answering questions based on observations subject to randomness. It builds a framework for statistical inference. The chapter introduces the basic concepts of classical inference under a parametric model and illustrates these concepts through simple, though real, examples in a way that demonstrates what is possible with classical statistical inference. The chapter also includes brief discussions of some of the weaknesses of classical statistical inference and reference to other approaches to inference that are in competition with classical statistical inference. Using a statistical model, the chapter discusses the methods to estimate the population parameters or functions of them (estimation), to establish the precision of such estimates (confidence intervals), and to formally answer questions about the population (statistical testing). The chapter also shows the way in which precision in statistical estimation can be obtained. Confidence intervals and other interval and “region” estimation methods based on the confidence interval concept provide a special type of initial precision for inference under uncertainty.