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,

Eta squared ANCOVAAnother 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

Partial eta squared ANCOVA

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

Effect size 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

Effect size contrast ANCOVA

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:

    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,

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