We begin by considering various measurements of effect size for Example 1 of Basic Concepts of ANCOVA (using the results of the analysis as summarized in Figure 3 of Regression Approach to ANCOVA).

A commonly used measure of effect size, despite it being positively biased, is eta squared, *η ^{2}*, which is simply

*r*For Example 1 of Basic Concepts of ANCOVA,

^{2}.Another commonly used measure of effect size is partial *η ^{2}* = which for Example 1 of Basic Concepts of ANCOVA is

We can also use these measures of effect size for the covariate.

This shows that the covariate explains a larger part of the variance (either total or unattributed to other variables) than the method.

For the contrasts we can use the usual measure *r* = . For the comparison in Example 1 of Contrasts for ANCOVA, we have

which is a relatively large effect.

We can also compute the effect size of the covariate using the regression coefficient information in Figure 5 of Regression Approach to ANCOVA (cell U36), and see that it is a very large effect.

The write up of the subject matter is good and well presented

Hello,

I want to echo the thanks for this great resource.

I am running the ACNOVA on 4 categories, and want to be able to tell if the categories are different from each other (or what categories are statistically similar to one another)

I am able to run your tool to get the SS, slope, adj mean, and determine the r^2 for each treatment. Is is possible to use this analysis to determine if the categories are statistically different or similar to one another?

Thanks, and happy to clarify,

Rob

Sorry, Just to amend. I didn’t see the “Contrasts” section, which is definitely what I am looking for.

However, in that section I am having trouble finding figure 23.3. (I checked all figure 3 for the ACNOVA sections and none seem to line up). Any clue to where it is?

Thanks again,

Rob

Rob,

Thanks for catching this. I have now updated the Contrasts webpage so that you can see what the cell reference is.

Charles

Rob,

Glad you like the website.

I see from your subsequent comment that you have now found the webpage which shows how to conduct the analysis that you are looking for.

Charles

Thank you for the quick response!

Also I thought I would let you know that the following link is down:

http://www.real-statistics.com/wp-content/uploads/2013/01/Real-Statistics-Examples-Part-2.xlsx

Please let me know if you get it back up and THANKS AGAIN!

Rob,

Thanks for the heads/up. It should be working now.

Charles