Probably Not, 2nd Edition

16Introduction to Frequentist Statistical Inference

Introduction

In previous chapters we introduced the distinction between frequentist and Bayesian concepts of probability, and in Chapters 11 and 12 developed the basics of Bayesian statistics. There are many situations where the frequentist approach is appropriate, and for that matter most discussions of “Statistics” or “Statistical Inference” refer to frequentist statistics.

Both frequentist and Bayesian statistics are enormous fields of knowledge. In this introductory book, we have only scratched the surface of Bayesian statistics; similarly, here we will only scratch the surface of frequentist statistics.

Sampling

Suppose we have a population of something that we want to learn about. A good example is the distribution of lifetimes of light bulbs that some manufacturer produces. This example is mathematically equivalent to the average weight of bottles of juice, the average amount of sugar in bottles of soda, etc. A related but not quite identical example is the incidence rate of broken cashew nuts in jars (of cashew nuts), or of nails without heads in boxes of nails. All of these examples are important to manufacturers (and purchasers) of these items.

Related to the above is the problem of measurement. No measurement instrument is perfect. In addition, measurements of weights and volumes tend to vary with ambient temperature and humidity, neither of which are easy to control precisely. A large manufacturer of some product ...