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I want to use ANCOVA to test whether means on a dependent variable (DV) differ between 3 groups (the independent variable, IV) while adding 3 variables as covariates (CV).

One assumption of ANCOVA is that the regression slopes of a covariate should be homogeneous across levels of the IV.

I learned that when having one covariate you could test this assumption, by running the model with the main effects of the IV and CV while also adding the interaction effect best of the IV and CV to the model an check, whether the interaction is indeed not significant.

Here an example in SPSS:

SPSS example 1

1. How should this assumption be tested with multiple covariates? (2. and why?)

Could you do it by running one model including the IV, all CVs and all IV*CV interaction terms?

SPSS example:

SPSS example 2

Or should this assumption better be tested separately for each covariate? Thus testing the model with main effects for the IV and CV1 and interaction of IV and CV1 repeat this with CV2 and CV3?

Thus repeating the following with CV2 and CV3:

SPSS example3

I assumed that you should test it using a model with all CVs and CV*IV interaction effects since you already assume that all CVs are related to your DV and therefore need to be accounted for when testing whether the effect of a particular CV on the DV is equal across levels of the IV. Unfortunately all sources I looked up until now discuss testing this assumption in contexts where only one covariate is used.

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    $\begingroup$ You may get a faster response if you write out your model in mathematical notation. See the linear model below the second paragraph en.wikipedia.org/wiki/Analysis_of_covariance. Your question is hard to interpret as is. $\endgroup$
    – Eli
    Mar 25, 2020 at 19:26
  • $\begingroup$ Thank you for your suggestion @EliK . I tried to make the question more clear by referring to the procedure in SPSS including some example pictures. $\endgroup$
    – Max
    Apr 28, 2020 at 16:45
  • $\begingroup$ This might attract close votes because it looks like a software question. Please reformulate to focus on the statistical question! $\endgroup$ Oct 29, 2020 at 11:11

1 Answer 1

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Since you're planning to use all three covariates in the same model, including them all in testing homogeneity of slopes is generally preferred, for the reason you mentioned.

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