continuous/categorical IV in anova


New Member
I understand that ANOVA assumes categorical IVs, and ANCOVA should be used if continuous IVs are included in the model. I am currently analyzing experimental data that contains an ordinal, discrete variable that ranges from 1 to 4 (behavioral response to a stimulus, which I am using to predict another behavior). I am using STATA, and debating whether to specify this variable as a continuous variable (using the specification " continuous()" ) or treat it as a categorical varaible. I am puzzling over this issue, because the variable is significant when treated as categorical, but insignificant when treated as continuous.

Can I justify treating it as a categorical variable (and run ANOVA instead of ANCOVA)? 1-4 doesn't quite seem like a continuous variable, and I know ANOVA can handle both dichotomous and polytomous IVs. I've also looked at the raw data, and the effect of this IV on the DV accords with its ordinality.

Thank you!

You are correct in that ANOVA handles categorical IV's or continuous IV's that have been artificially split into groups. The ANCOVA model assumes the covariate you are controlling for is continuous , not the IV itself.

The bigger issue however, is that if your data is ordinal, you cannot use the standard ANOVA procedure. Look up the Kruskal-Wallis; it's an non-parametric alternative to the ANOVA that can handle ranked data.

Best of luck.


New Member
Thanks for your response!

My deeper question is... when is a variable continuous rather than categorical? If I have a variable with three values, 1,2,3 (or in my case, 1,2,3,4), is that already continuous, even though it is restricted to discrete values (assuming equal intervals)? My sense is that categorical doesn't assume ordinality (ex. allows 1= apple, 2, orange, etc) while continuous does (such that 1<2<3<4). Is that the most fundamental difference?

I know there are many discussions about this in basic stats texts, but I haven't come aross any that makes this distinction. Am I making this up?

Also, what is the mechanical/mathematical difference between how IV and covariates are treated? Is it based on whether one is continuous and the other is not? If so, the researcher still has to specify which variables in the model are to be treated as covariates or IVs, no? That's my basic dilemma.
Variables can be classified as continous or discreet.

Continuous variables can have intermediate values that are sensible between values. I.e, It makes sense that you could weigh 114.5678 pounds. Therefore, gender would be discreet, as you can't be intermediate between male and female -- it doesn't make sense that you can be .75 female and .25 male.

Scales can be either, categorical, ordinal, interval or ratio.

I refer you here for a great explanation of the different types with many examples for clairification:

With Likert Scale data, you can treat it as either ordinal or interval. How you plan to treat your data dictates the subsequent analysis and statistics you are restricted to running.

With respect to the ANCOVA model question, a covariate is usually a continous variable you take into account in order to control for its extraneous effects.

I can give you an example that will hopefully explain it further:

Say I'm interested in looking at the effects of Gender on IQ. I gather a whole bunch of people, split them into male and female groups and give them an IQ test. I find that males significantly out perform females.

However, this result may be due to many other factors related to IQ, but at the same time that we were not interested in measuring. One of those factors might be a person's age. So when I utilize the ANCOVA with age as a covariate, I measure a person's age and enter it into the model. This will allow me to see if the effect of Gender on IQ relationship still holds true after we "account" for the effects of age, or if everybody was the average age.


New Member
thanks, jamesmartin. Just one more Q...

So, if I have a covariate that is discrete (say, how much I like apples, from 1 to 4), does that call for ANCOVA, or anova?

Thanks so much for your help, and sorry I'm being lengthy.
I said the covariate is usually continuous because I've never seen an ANCOVA with a discreet covariate, but as i recall from class, my professor said it is possible. I believe you can in this case, though. Perhaps someone else would like to comment further?


TS Contributor
I think it can be continuous or discrete - I don't think it matters.....its purpose is to reduce error variance so that you have a more sensitive test of the hypothesis - a continuous or discrete variable could fill this role....


Super Moderator
So, if I have a covariate that is discrete (say, how much I like apples, from 1 to 4), does that call for ANCOVA, or anova?

Thanks so much for your help, and sorry I'm being lengthy.

What you might want to consider is a (ANOVA) Randomized Block Design where the covariate, because it is discrete (1,2,3,4), becomes the blocking variable.