# When should one use multiple regression with dummy coding vs. ANCOVA?

I recently analyzed an experiment that manipulated 2 categorical variables and one continuous variable using ANCOVA. However, a reviewer suggested that multiple regression with the categorical variable coded as dummy variables is a more appropriate test for experiments with both categorical and continuous variables.

When is it appropriate to use ANCOVA vs. multiple regression with dummy variables and what factors should I consider in selecting between the two tests?

Thank you.

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Which of your variables is a predictor and which a correlate? –  John Aug 14 '11 at 17:35
@John, in the experiment that I mention all of the variables were predictors and were manipulated but I left the description vague because I am hoping for a general answer of what I should consider when choosing between the two types of analysis. –  KennyPeanuts Aug 14 '11 at 17:50
That really changes everything in your question. So you don't really want to select between ANCOVA and regression but ANOVA and regression. –  John Aug 14 '11 at 18:05
@John thanks for your comments. I may not be using the terms correctly. I have an experiment where 2 categorical factors (light/no-light and ambient/elevated CO_2) and one continuous variable ([DOC]) were manipulated. To evaluate the effect of these factors on the response, I used ANCOVA, since there was a mix of categorical and continuous factors. However multiple regression with dummy variable coding can also be used to test the effect of a mixture of cont. and cat. factors on a response. I am hoping to learn more about when it is appropriate to select one or the other. –  KennyPeanuts Aug 14 '11 at 18:25
This is a question about John's answer (as I do not have enough reputation points to write a real comment). The sources I read so far (e.g. if I google for ANOVA ANCOVA or Multiple regression ANCOVA) tell me that ANOVA involves only categorical predictors and ANCOVA involves categorical and continuous predictors, and that both, ANOVA and ANCOVA designs, can be described using a multiple regression model. Does this conflict with John's answer, which sais "ANCOVA and ANOVA are the same, as ttnphns pointed out"? –  klaus se Nov 23 '13 at 17:03

ttnphns is correct.

However, given your additional comments I would suggest that the reviewer wanted the change merely for interpretation. If you want to stick with ANOVA style results just call it ANOVA. ANCOVA and ANOVA are the same, as ttnphns pointed out. The difference is that with ANCOVA you don't treat the covariates as predictors and you definitely appear to want to do just that.

What the reviewer was getting at was that, while you can perform an ANOVA on continuous predictors, it's typical that one perform a regression. One feature of this is that you get estimates of the effects of the continuous variable and you can even look at interactions between it and the categorical (which aren't included in an ANCOVA but could be in an ANOVA).

You may need some help with interpretation of regression results because funny things happen on the way to interactions if you're going to use the beta values to determine the significance of your effects.

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These two are the same thing. For example, in SPSS the procedure where I specify ANCOVA is called GLM (general linear model); it askes to input "factors" (categorical predictors) and "covariates" (continuous predictors). If I recode the "factors" into dummy variables (omitting one redundant category from each factor) and input all those together with the covariates as "independent variables" in REGRESSION procedure (linear regression), I will obtain the same results as with GLM (taken that the dependent variable is the same, of course).

P.S. The results will be identical if the models are identical. If regression contains only main effects then ANCOVA should be specified without factor by factor interactions, of course.

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Multiple linear regression appears to me more appropriate than ANCOVA in this situation, as the journal reviewer recommends.

Try running both a multiple regression and an ANCOVA, and comparing the results. They probably will not be identical.

ANCOVA and multiple linear regression are similar, but regression is more appropriate when the emphasis is on the dependent outcome variable, while ANCOVA is more appropriate when the emphasis is on comparing the groups from one of the independent variables. In the experiment described above, the emphasis seems clearly to be on the outcome variable.

Finally, unless you are really certain that you way of doing things is better than the Reviewer's, and can explain why, then you should probably just concede to the Reviewer's expertise, so you can get your paper published.

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-1, this is incorrect. Did you read the answers by @John or @ttnphns? Both correctly point out that ANCOVA is a multiple regression model. The traditional ANCOVA did not allow for interactions b/t covariates & factors (the so-called 'parallel slopes assumption'), but the term 'ANCOVA' is used sloppily & many people use it to include cases w/ interactions. Moreover, I gather SPSS will run an 'ANCOVA' w/ such. Is that what you had meant here? If so, please clarify. If not I must let the downvote stand. –  gung Jun 27 '12 at 16:48