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F Distribution and ANOVA: Introduction

Module by: Dr. Barbara Illowsky, Susan Dean

Summary: This module provides a brief introduction on handling hypothesis tests with two means by the one-way Analysis of Variance (ANOVA), F Distribution, and the Test of Two Variances statistical analysis.

Student Learning Objectives

By the end of this chapter, the student should be able to:

  • Discuss basic ideas of linear regression and correlation.
  • Create and interpret a line of best fit.
  • Calculate and interpret the correlation coefficient.
  • Calculate and interpret outliers.

Introduction

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 involving more than two averages, 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 ANOVA, and the test of two variances. This is just a very brief overview of ANOVA. You will study this topic in much greater detail in future statistics courses.

Note:

ANOVA, as it is presented here, relies heavily on a calculator or computer.

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