12: F Distribution and One-Way ANOVA
For hypothesis tests comparing averages between more than two groups, statisticians have developed a method called "Analysis of Variance" (abbreviated \(ANOVA\)). In this chapter, you will study the simplest form of \(ANOVA\) called single factor or one-way \(ANOVA\). You will also study the \(F\) distribution, used for one-way \(ANOVA\), and the test of two variances. This is just a very brief overview of one-way \(ANOVA\). You will study this topic in much greater detail in future statistics courses. One-Way \(ANOVA\), as it is presented here, relies heavily on a calculator or computer
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- 12.1: Prelude to F Distribution and One-Way ANOVA
- 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.
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- 12.3: The F Distribution and the F-Ratio
- The distribution used for the hypothesis test is a new one. It is called the F-distribution, named after Sir Ronald Fisher, an English statistician. The F-statistic is a ratio (a fraction). There are two sets of degrees of freedom; one for the numerator and one for the denominator.
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