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.

- Intermediate Algebra, especially the ability to solve simple equations and plug values into formulas.
- Introductory Statistics, especially the concepts of variance and hypothesis testing and the ability to evaluate simple statistical formulas.

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.

- Microsoft PowerPoint Viewer version 2000 or later (you can also use the full version of PowerPoint if it is loaded on your machine). This link downloads the 2003 viewer but the presentations will work with the 2000 viewer.
- Microsoft Excel. There is a link provided by Microsoft on the page they created, but the link is to a non-existent location so you can't download the web components using that link.
- Macromedia Flash Player version 6.0 or later.

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.

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

- Know the terminology used with the ANOVA
- Understand the workings of the ANOVA table
- Understand how ANOVA is used in regression and multiple regression
- Understand how the one-way ANOVA and two-way balanced design ANOVA can be used to test equality of means.
- Know how to find the degrees of freedom for the various ANOVA tables
- Complete an ANOVA table when the sum of squares are supplied
- Finish a partially completed ANOVA table

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.

- Introduction to Analysis of Variance without sound (small - 180 KB) [PowerPoint]
- Introduction to Analysis of Variance with sound (large - 2476 KB) [PowerPoint]
- Assessment of ANOVA Fundamentals [Flash]
- One Minute Feedback on the ANOVA Fundamentals

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.

- Introduction to correlation and regression - uses real data from the men's 400m race at the 2004 Olympic games. No regression is performed since there is no signficant linear correlation
- Using the ANOVA to conduct regression analysis - uses real data from the weightlifting competition at the 2004 Olympic games
- One Minute Feedback on using the ANOVA to perform Simple 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.

- Multiple linear regression using the ANOVA table - uses real data from the weightlifting competition at the 2004 Olympic games.
- One Minute Feedback on using the ANOVA to perform Multiple Linear Regression

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.

- Introduction to One-Way Analysis of Variance (small 215KB) [ Powerpoint ]
- Application to Compute a One-Way Analysis of Variance Table from Summary Statistics [Excel] - this spreadsheet starts off with the same data used in the PowerPoint presentation but allows you to modify the summary statistics and see how the ANOVA table is changed.
- One Minute Feedback on the One-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.

- Introduction to Two-Way Analysis of Variance
- One Minute Feedback on the Two-Way Analysis of Variance

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

- ANOVA assessment [Flash] - take a multiple choice quiz or challenge another person.
- WebQuest Technology Project - Gather real data from the Internet and conduct a one-way and two-way analysis of variance to analyze the data.
- ANOVA Generator - this application will generate partially completed ANOVA tables and ask you to complete the rest of the values.

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.