ANCOVA controversy?

[jhdc]

Hello all,

I have a question regarding ANCOVA, which seems straightforward, however an answer has eluded me. The question is:

Can a dichotomous variable be used as a covariate in ANCOVA?

I've consulted several textbooks (Stevens, Tabachnick, Munro, Norman), some of which indicate that the covariate must be continuous level, while others are ambiguous on the subject.

To add to the confusion, I have seen several studies using ANCOVA to control for the effects of gender.

Any help on this would be appreciated. If possible, I would love to have a good citation clarifying this issue.

Thank you in advance.

[Dragan]

Originally Posted by jhdc

Hello all,

I have a question regarding ANCOVA, which seems straightforward, however an answer has eluded me. The question is:

Can a dichotomous variable be used as a covariate in ANCOVA?

I've consulted several textbooks (Stevens, Tabachnick, Munro, Norman), some of which indicate that the covariate must be continuous level, while others are ambiguous on the subject.

To add to the confusion, I have seen several studies using ANCOVA to control for the effects of gender.

Any help on this would be appreciated. If possible, I would love to have a good citation clarifying this issue.

Thank you in advance.

Winer, Brown, and Michels (1991) on page 787 give an example of where a covariate was used as a classification factor (1's,2's,3's, and 4's).

However, to make more sense out of this situation, I think it would be wiser to use the dichotomous (covariate) variable as a second factor and thus create a two-factor experiment....which is what the authors of this textbook do.

[jhdc]

Thank you Dragon,

I understand that nominal level variables which are not dichotomous cannot be used as covariates in ancova, however my understanding is that dichotomous variables are different. Since this aspect of ANCOVA uses multiple linear regression, which permits the use of dichotomous (but not other discrete) variables, it makes no sense to me that gender could not be used as a covariate. Any other ideas?

Thanks again!

[Dragan]

Originally Posted by jhdc

Thank you Dragon,

I understand that nominal level variables which are not dichotomous cannot be used as covariates in ancova, however my understanding is that dichotomous variables are different. Since this aspect of ANCOVA uses multiple linear regression, which permits the use of dichotomous (but not other discrete) variables, it makes no sense to me that gender could not be used as a covariate. Any other ideas?

Thanks again!

Well, ask yourself what the purpose of ANCOVA is.

Answer: The primary purpose of including a covariate into the model is to

(statistically) control or reduce the error term associated with the Mean

Square of Error (MSE).

Whether the covariate is continuous or dichotomous, to make sense, the

covariate should be correlated with the dependent variable (within groups).

And, the within group regression slopes should be statistically the same – by

assumption.

So, (1) check your assumption of homogeneity of regression coefficients and

(2) look at the regression weight associated with the covariate and see if it statistically significant.

If you get past these two tests, then I would say you’re fine and use the dichotomous variable.