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I have a 2x2 experimental design. In the experiment, I also collected the participants' professional qualifications (categorical variable- yes /no). I would like to test the effect of controlling this variable on the MSE. I understand that in ANCOVA, the covariate is either an interval or ordinal variable. So should I refer to the test as an ANCOVA if I include professional qualification as an additional variable? Or should it be a blocking variable since "prof. qualification" is categorical.

kjetil b halvorsen
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LoveExps
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2 Answers2

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ANOVA, ANCOVA and OLS regression are all the same model. In matrix notation they are all

$Y = Xb + e$

where Y is a vector of values on the DV, X is a matrix of values on the IVs, b a vector of parameters to be estimated and e is error.

The main reason these are treated so differently is, I think, historical: ANOVA and regression developed separately.

The usual terminology is that ANOVA is used when all the IVs are categorical, ANCOVA when some are categorical and some continuous. Regression can easily be used for any sorts of IVs.

Peter Flom
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  • But in the context of regression you should not be abbreviating with "IV", which is usually reserved for "instrumental variables", not "independent variables"; at least among economists. – Nameless Jun 19 '13 at 12:35
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    Interesting! Among the people I work with (psychologists, MDs, sociologists, educators), IV is pretty universal as an abbreviation for independent variable – Peter Flom Jun 19 '13 at 12:45
  • +1, I just wanted to add the comment that traditionally ANCOVA is little different from the GLM approach you describe, though in unimportant ways (unless your stats package implements the older method). I think for hand-computational reasons, originally, the covariate was "given" all variance that could be attributed to it (i.e. the type 1 sum of squares), and the remaining variance was partitioned to the rest of the factors. The only difference in results would be the F value for the covariate would be inflated compared to the GLM approach. Like I said, unimportant typically. – le_andrew Jul 10 '15 at 16:25
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As a minor addition, but as I don't have enough points yet to comment it comes as an answer. Reading up on Ancova and how and when to use covariates I had the same question. If you needed a citation for being able to use a categorical covariate: Howell (2016) p593.

In addition, the use of covariates also depends on whether it is a between (independent) or within (repeated) design and what the variables of interest (Baguely, 2012).

Simone
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