11: F Distribution and One-Way ANOVA
- Page ID
- 125770
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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
- 11.1: 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.
- 11.2: F Distribution
- Here are some facts and applications of the F distribution.
- 11.3: Multiple Comparisons
- When you perform a large number of statistical tests, some will have P values less than 0.05 purely by chance, even if all your null hypotheses are really true. The Bonferroni correction is one simple way to take this into account; adjusting the false discovery rate using the Benjamini-Hochberg procedure is a more powerful method.
- 11.4: One-Factor ANOVA
- This section shows how ANOVA can be used to analyze a one-factor between-subjects design.
- 11.5: Test of Two Variances
- Another of the uses of the FF distribution is testing two variances. It is often desirable to compare two variances rather than two averages.
- 11.6: Lab- One-Way ANOVA
- A statistics Worksheet: The student will conduct a simple one-way ANOVA test involving three variables.
- 11.E: F Distribution and One-Way ANOVA (Exercises)
- These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.