Analysis of Variance Tutorial

Analysis of variance (ANOVA) refers to a collection of statistical methods that researchers use to determine whether mean scores differ significantly across treatment groups.

About the Tutorial

This tutorial explains how to use analysis of variance to assess the effect of one or more factors on a single interval- or ratio-scale variable. The tutorial focuses on four classic experimental designs:

  • Single-factor independent groups design.
  • Full factorial independent groups design.
  • Randomized block design with independent groups.
  • Repeated measures design (aka, within-subjects design).

Who Is This For?

This tutorial is designed for students and researchers who have some familiarity with introductory statistics (e.g., a high school statistics course or Advanced Placement Statistics).

What Will You Learn?

By the end of the tutorial, you will be able to judge whether analysis of variance is the right tool for the study you are conducting. You will be able to choose the right design for your research. You will be able to conduct an appropriate analysis of variance for the design you have chosen, by hand or with software. And, most important, you will be able to correctly interpret the outputs you produce.

Note: In the real world, you will most likely use a software package (e.g., SAS, SPSS, Excel) to generate outputs from analysis of variance. Examples in this tutorial use Excel, since it is widely available. Outputs from Excel are similar to outputs from other statistical packages; so if you can interpret outputs from Excel, you should be able to interpret similar outputs from other packages.

How to Use This Tutorial

Individual lessons are accessible through the table of contents, which can be found in the vertical column on the left side of the page. You should work through lessons in the order in which they appear; because some lessons build on previous lessons.

Individual lessons are accessible through the table of contents, which can be accessed by tapping the "Analysis of Variance: Table of Contents" button at the top of the page. You should work through lessons in the order in which they appear; because some lessons build on previous lessons.

Additional Helpful Resources

As you progress through the tutorial, take advantage of the following helpful resources.

  • Online calculators. The F distribution calculator, the chi-square calculator, and the Bartlett's test calculator are useful for interpreting outputs from analysis of variance. They can be found in the appendix section of the table of contents.
  • Sample problems. Many of the lessons include sample problems and solutions. The sample problems expand your knowledge. The solutions explain how to correctly interpret analytical outputs.
  • Online help. Stat Trek's online Statistics Dictionary takes the mystery out of statistical jargon. If any term or concept is unclear, visit the dictionary for additional explanation.

Note: The dictionary can be accessed by clicking the Help tab in the main menu (located at the top of this web page).