I would say no :)

And it is also not my topic. So take this advise carefully (aa always! hopefully).

Actually I'd say that the answer depends on two things:

1) what is the precise research question and

2) what is the precise definition of "intellectual disability" and "IQ".

Regarding the second point: if "intellectual disability" is just another word for "having a low IQ", then the two variables almost measure the same kind of information. In this case it makes no sense to use IQ as a co-variate (therefor my answer above).

But consider that these are really different concepts, measuring a different kind of information. Then the research question will be important. Is it relevant for the question to "adjust" for differences in the IQ? Is so, then IQ should be used as a covariate, and if not, then not. This can be answered only by the researcher, by the expert in the field, and not by a statistician.

Dear Haris,

I would say yes. Even though this is not entirely my topic (IQ and Intelectual disabilities) covariates are very useful because it remains in this case IQ constant. So, if you already know that IQ will be different then it can be a bigger argument to use it as a covariate. If you don't control for this variable it is not easy to know if really the difference or relationship (for that matter) of motor skills and IT are as a result of this two variables or maybe IQ is having an interaction effect that you are not taking into account. 

Hope this helps

Regards

I would say no :)

And it is also not my topic. So take this advise carefully (aa always! hopefully).

Actually I'd say that the answer depends on two things:

1) what is the precise research question and

2) what is the precise definition of "intellectual disability" and "IQ".

Regarding the second point: if "intellectual disability" is just another word for "having a low IQ", then the two variables almost measure the same kind of information. In this case it makes no sense to use IQ as a co-variate (therefor my answer above).

But consider that these are really different concepts, measuring a different kind of information. Then the research question will be important. Is it relevant for the question to "adjust" for differences in the IQ? Is so, then IQ should be used as a covariate, and if not, then not. This can be answered only by the researcher, by the expert in the field, and not by a statistician.

Hi,

Kindly see the follwoing:

covariates can be used BEFORE the experiment to experimentally control for pre-existing differences:

1.  Use score on a covariate as a way to assign subjects to groups

2.  Match different groups based on score on a covariate measure

3.  Match different treatment groups on age, or gender, or IQ

covariates can be used AFTER the experiment to “statistically” adjust for pre-existing differences:

1.  Allow for variation in the concomitant variable both within and between groups

2.  During the analysis, statistically account for the effect of the covariate on

the dependent variable

(Echoing Jochen's great comment but with one additional comment)

Echo: The important thing to remember is that the meaning of the coefficient is different. Most stats packages show what they say is the coefficient for Intellectual disability, but if it is after using IQ as a covariate it is not this. It is it AFTER conditioning on IQ. It is NOT the coef. for Intellectual disability!  It IS the coef. only after conditioning. Whatever this is may or may not make sense, but it is very different. I assume IQ and intellectual disability are highly associated, which means the meaning of the coefficient changes A LOT.

New comment: I suggested in a seminar that people make their regression coef tables listing each variable and all that it is conditioned upon. The comment was, as expected, this makes the table look a mess when there are even a couple of predictor variables, and a complete mess when there are lots. I replied "good", that's what it should look like.

Lesson: consider the results from any multiple regression carefully when variables are correlated.

Analysis of covariance (ANCOVA) is a general linear model which blends ANOVA and regression.

The ANCOVA (analysis of covariance) can be thought of as an extension of the one-way ANOVA to incorporate a "covariate". Like the one-way ANOVA, the ANCOVA is used to determine whether there are any significant differences between the means of two or more independent (unrelated) groups (specifically, the adjusted means). However, the ANCOVA has the additional benefit of allowing you to "statistically control" for a third variable (sometimes known as a "confounding variable"), which may be negatively affecting your results. This third variable that could be confounding your results is the "covariate" that you include in an ANCOVA. 

Maybe I didnot choose the best example as the intellectual disability and IQ are very related (the first almost exclusively depending on the second). Another example: we want to assess the effectiveness of an math educational program on two groups of children: group 1 and group 2. The effects were much better in group 1 (without covariate). Now we want to assess math skills adjusting for their parent level of education (covariate). And now we found no differences between the groups. But we KNOW for a fact that these two groups differ regarding their parents level of education and that the educational level of, say, group 2 parents cannot be increased to a level that was used in covariation (and in the future studies these differences will still exist among these two groups parents education). So how to report these findings?

Andrew Rutherford has a couple of good books and papers on the topic.

http://www.amazon.com/By-Andrew-Rutherford-ANOVA-ANCOVA/dp/B00N4GOK26

He argues that if you have randomly allocated people to conditions then with variables that are associated but not super associated conditioning on the covariate increases statistical power. However, often researchers have not allocated people to conditions at random, and then the issues raised above again occur. It sounds like your groups are very different on the covariate. Are they? If so, no matching procedure is great. It sounds like, if possible, an alternative design should be used where you have people in each group with similar values on the covariates.

It also depends also why you are doing the analyses. If your groups related to an intervention and a control condition, you are probably interested in causation.

I recommend consulting a statistician before you design this study so that you can address the question efficiently.

Daniel hit the mark:

It also depends also why you are doing the analyses.

That's it. Your aim tells you if it is the coefficient for the "adjusted" effect or for the "unadjusted effect". These are different things, answers for different questions, and the difference is related to the kind of correlation and the whole scientific (not statistical!) matter. You must get your question right, and then look for the model.

Reading the comments I finally realized the right question. I guess you should not use (or at least be very careful about using) covariate when the groups are naturally different on the covariate (not randomly assigned to the group). Thank you for clarifying this concept.

next example:  you are comparing communication skills between two different types of syndromes that course with intellectual disability (i.e Down syndrome and Fragile X) and they are matched on age but not on IQ, then does it make sense to  use NONVERBAL IQ as a covariate?