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13: F Distribution and One-Way ANOVA

  • Page ID
    20762
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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

    • 13.1: 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.
    • 13.2: 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.
    • 13.3: One-Way ANOVA
      The purpose of a one-way ANOVA test is to determine the existence of a statistically significant difference among several group means. The test actually uses variances to help determine if the means are equal or not.
    • 13.4: F-Tests in One-Way ANOVA
      In this section we will learn to compare three or more population means at the same time, which is often of interest in practical applications. For example, an administrator at a university may be interested in knowing whether student grade point averages are the same for different majors. In another example, an oncologist may be interested in knowing whether patients with the same type of cancer have the same average survival times under several different competing cancer treatments.
    • 13.5: Facts About the F Distribution
      Here are some facts and applications of the F distribution.
    • 13.6: 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.
    • 13.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.

    Contributors and Attributions

    Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/30189442-699...b91b9de@18.114.


    This page titled 13: F Distribution and One-Way ANOVA is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.