# Effect size for ANCOVA

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, η2, which is simply r2.  For Example 1 of Basic Concepts of ANCOVA,

Another commonly used measure of effect size is partial η2 = $\frac{SS_{Treat}}{SS_{Tot}+SS_{Res}}$ 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 = $\sqrt{\frac {t^2}{t^2+df}}$. 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.

### 7 Responses to Effect size for ANCOVA

1. E B Kolawole says:

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

2. Rob says:

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

• Rob says:

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

• Charles says:

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

• Charles says:

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