Lesson 10: One-Way ANOVA

Objectives

Upon successful completion of this lesson, you should be able to:

  • Explain why it is not appropriate to conduct multiple independent t tests to compare the means of more than two independent groups
  • Use Minitab to construct a probability plot for an F distribution
  • Use Minitab to perform a one-way ANOVA with Tukey's pairwise comparisons
  • Interpret the results of a one-way ANOVA
  • Interpret the results of Tukey's pairwise comparisons

In previous lessons you learned how to compare the means of two independent groups. In this lesson, we will learn how to compare the means of more than two independent groups. This procedure is known as a one-way analysis of variance, or more often as a "one-way ANOVA."

Why not multiple independent t tests?

A frequently asked question is, "why not just perform multiple two independent samples \(t\) tests?" If you were to perform multiple independent \(t\) tests instead of a one-way ANOVA you would need to perform more tests. For \(k\) independent groups there are \(\frac{k(k-1)}{2}\) possible pairs. If you had 5 independent groups, that would equal \(\frac{5(5-1)}{2}=10\) independent t tests! And, those 10 independent t tests would not give you information about the independent variable overall. Most importantly, multiple \(t\) tests would lead to a greater chance of making a Type I error. By using an ANOVA, you avoid inflating \(\alpha\) and you avoid increasing the likelihood of a Type I error.