# What is the difference between “factors” and “covariate” in terms of ANCOVA? [duplicate]

I am a bit confused on the term "covariate". It seems like the term can mean two different things. In ANCOVA, the term is used for the third variable that is not directly related to the experiment. For example, the age or IQ on the performance study (comparing) between male and female in a standardized test, i.e. IQ is used as a covariate.

In ANOVA/regression design, "covariate" just refers to factors/independent variables?

I may have completely misunderstood this.

Can anyone give a simple example of the term "covariate" used in different context?

• See stats.stackexchange.com/questions/61906/covariate-vs-factors In short, there isn't any important theoretical distinction to understand but only a bit of fuzziness in the terminology.
– Gala
Commented Sep 23, 2013 at 17:58
• – Gala
Commented Sep 23, 2013 at 18:03
• Incidentally, the two answers aren't terribly helpful. It's easy to provide some clear-cut definition but since none of them are universally used, it does nothing to dispel the confusion.
– Gala
Commented Sep 23, 2013 at 18:08

This is a frustrating use in terminology that has caused a lot of issues for a lot of people. My understanding is this:

• A factor is categorical variable
• A covariate is a continuous variable

Both of these predict the dependent variable and both have a similar relationship to the dependent variable. Variance from both types of variables are accounted for in a linear model (e.g., regression, ANCOVA). So, a covariate is not just a third variable not directly related to the dependent variable. It is merely a dimensional variable.

The reason statistical packages have options for both of these is because the statistical packages treats them differently. For example, a factor may allow contrasts between groups, while a covariate would not.

When someone asks you to use something as a covariate, make sure you know what they mean. That is the only way you can know, since this misunderstanding is rampant.

• I believe the phrase "dimensional variable" is not a well-known statistical term. What exactly do you mean by it?
– whuber
Commented Sep 23, 2013 at 18:10
• I am not sure about "dimensional variable" either nor the "metric" reference in the previous post. Also, if they act like IVs/factors/predictors, why there is a need for the term "covariate"? If someone says "Use this* variable as a covariate", what do they mean "generally"? Does it depend on the context (ANOVA, ANCOVA, regression)? I guess this question brings back to the original question. Commented Sep 23, 2013 at 18:34
• It seems to me that a covariate is anything added to a given model (linear or generalized linear model) that we want to control or that is to be accounted for. Whether this variable is continuous or not does not really matter. In ANCOVA, though, the covariate is usually continuous (e.g., difference between two groups with pre-post measurements), and we are interested in showing that it is not interacting with the grouping variable.
– chl
Commented Sep 23, 2013 at 19:52
• Is adding a factor to a model not controlling for the factor (e.g., adding group membership in an experimental design)? Commented Sep 23, 2013 at 19:55
• Covariates are primary of second interest, but we think they must be part of a given model, e.g. because they are associated to the outcome and the factor of interest (confounding effect) or because we want to estimate the effect of interest after 'adjusting' for the effect of the covariate itself. This does not limit to DoE, IMO.
– chl
Commented Sep 23, 2013 at 20:03

A covariate is just another independent variable which is metric. In ANOVA you can control for the influence of that variable by adding it to the factors (usually nominal variables).

• Welcome to the site, @Marc Schubert. Please don't sign your posts. You may notice that your username, your identicon, & a link to your userpage are automatically attached to your posts. Since you're new here, you may want to read our about page, which contains info for new users. Commented Sep 23, 2013 at 18:03
• Could you please explain what you mean by "metric"?
– whuber
Commented Sep 23, 2013 at 18:11
• Blocking is an example where we want to reduce response heterogeneity in each treatment group. Usually, it is a categorical variable (e.g., sex, cage, etc.).
– chl
Commented Sep 23, 2013 at 19:55
• Continuous would be a better expression than "metric". Commented Sep 23, 2013 at 20:31
• isqr.uni-freiburg.de/categorical.pdf also gives an example of a categorical covariate. Commented Sep 23, 2013 at 21:05