11.1 Introduction to Statistical Inferences Using the F-Distribution

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One-way ANOVA is used to measure information from several groups. Photo by OpenStax, CC BY 4.0.

Many statistical applications in psychology, social science, business administration, and the natural sciences involve several groups.  For example, an environmentalist is interested in knowing if the average amount of pollution varies in several bodies of water.  A sociologist is interested in knowing if the amount of income a person earns varies according to his or her upbringing.  A consumer looking for a new car might compare the average gas mileage of several models.

For hypothesis tests that compare averages between more than two groups, statisticians have developed a method called “Analysis of Variance” (abbreviated ANOVA).  In this chapter, we will study the simplest form of ANOVA called single factor or one-way ANOVA.  We will also study the [latex]F[/latex]–distribution, used in a one-way ANOVA and the test of two population variances.  This is just a very brief overview of one-way ANOVA.

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Introduction to Statistics Copyright © 2022 by Valerie Watts is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.