Analysis of Variance

Capstone Project for 2004 ICTCM Short Course on Real-World Applications and Assessment


This project is designed to be used at the end of a first semester introductory statistics courses. To understand this material, you should have the following skill levels.

Computer software that you will need to view these pages includes. Clicking on the software title will take you to a page where you can download the software.

Links that require a special plugin or piece of software to properly view are indicated with the name of that software in brackets after the link. For example, a page that requires Macromedia Flash Player would have [Flash] after the link.

If you are running Windows XP with service pack 2, you will get some warnings when you view the Flash pages. The default settings on service pack 2 warn you before any scripts that open new windows are executed and the Flash animations are opened in a new window. Go ahead and tell it to allow the content or you won't be able to assess yourself.

Goals / Objectives

The purpose of this project is to help you understand the Analysis of Variance (ANOVA) methods. Most of these methods are not in our textbook (Intro Stats by DeVeaux and Velleman) unless you pull them off the CD-ROM that comes with the textbook or the companion website for the text and so these supplements have been developed to help you. For more information, see the rationale behind this project.

Upon completion of this project, you should be able to

Assessment Measurements

If you are one of my students using this module to help understand the Analysis of Variance methods, then you will be given several opportunities to demonstrate your comprehension of the material. The assessment techniques at the end of this document will be used to determine whether or not you have successfully satisified the goals of the project.


Just what is an Analysis of Variance (ANOVA)? What does it look like? How does it function?

Well, the good news is that the ANOVA table works basically the same no matter what you're using it for. That means whether you're doing simple linear regression, multiple linear regression, a one-way ANOVA to compare means, or a two-way ANOVA to compare means, the basics are all the same.

So let's learn the basics of the Analysis of Variance table.

Below is a link to a PowerPoint Presentation introducing you to the terminology behind the Analysis of Variance. It also shows you the table and how it works and then gives you a sample table to complete to see if you understand the workings of the table.

After you've watched (and maybe listened) to the powerpoint presentation, let's see how well your understanding of the concepts are. Click on one of the assessment or feedback links to review or show your understanding of terminology and fundamentals of the ANOVA table or to tell the instructor what you liked or didn't understand from the presentation.


Simple Linear Regression

There are two sources of variation when performing regression; the variation explained by the regression model and the variation that is left unexplained by the regression equation.

Multiple Linear Regression

Multiple linear regression is performed when there is one response (y) and several predictor (x) variables. It builds on the discussion of simple linear regression, so make sure you understand the previous section first.

Analysis of Variance to Test Equality of Means

One-Way Analysis of Variance

The one-way analysis of variance is used to test the equality of several independent means. The two sources of variation are the variation between the groups and the variation within the groups.

Two-Way Analysis of Variance

The two-way analysis of variance conducts two one-way analysis of variance tests and a test for interaction all rolled into one table. We're only going to look at the balanced design, which requires an equal number of samples from each treatment.

Analysis of Variance Assessment

Now that you've completed the entire lesson on Analysis of Variance, it's time to show how much you've learned.

If you make it through all of the material in this project and complete the quizzes, games, and have mastered the tables through the generator, you should be well prepared to tackle the world of the Analysis of Variance (and do well on the exam). There is a little bit more that isn't in these notes simply because I was trying to focus on the ANOVA aspect and not do complete coverage of the topics of regression and comparison of means.