What should you do if you have vastly different sample sizes across levels of a categorical variable you are including as a covariate in an ANCOVA? For example, if you are controlling for gender with 4 categories (i.e., man, woman, prefer to self-describe, prefer not to say), is there a citation that supports either collapsing the last gender categories or even excluding them from the analysis because of their extremely small sample size to avoid skewing results? If the sample sizes are so small, however, even with collapsing, you could still run into the same sample size problem. Is there a general consensus about how to handle this type of issue?
I would suggest an ancova model of the form post= a +b1pre +b2gender +... + error the structure of the X (also called design) matrix automatically takes care of the sample sizes. See:
https://www.amazon.com/Introduction-Linear-Models-Analysis-Experiments/dp/0534364829/ref=sr_1_1?s=books&ie=UTF8&qid=1534969062&sr=1-1&keywords=mendenhall+design+and+analysis+of+experiments
For examples. Best wishes,David Booth
Hello Tasha,
Since the covariate is nominal, be sure that you recode it into (k - 1) dummy variates if you choose to include it in your model (as David Booth suggested).
There may be specific guidance about minimal numbers of cases per level for a nominal covariate, but I've not seen it. The usual admonitions about n per level would apply to levels of the fixed or random effects factors in the design. If it were the case that a small subgroup (on your covariate) was wildly different in their scores on the dependent variable (see below), that could bias the explanatory power of the covariate in your sample to a level that potentially didn't match that for the population.
What governs the "impact" of inclusion of a covariate is: (a) the strength of correlation between scores on the covariate and scores on the dependent variable; and (b) the degree to which treatment groups differ on the covariate. If there is no relationship and groups do not differ, inclusion of a covariate will only reduce error df, and will not affect the the results in any other material sense.
Good luck with your work!
For your instance, gender with four levels appears to be more of a categorical predictor than a covariate per se. A covariate is normally and in most cases a continuous variable. Like what was mentioned, apply dummy / binary coding (see https://blogs.perficient.com/2012/04/25/dummy-coding-with-ibm-spss/). Also, to add on to the two assumptions of the covariate mentioned what David Morse said, (a) is a pre-requisite and much more important than (b). In some cases, you will find that your treatment / test groups differ w.r.t. the covariate but that the covariate do not correlate significantly with the DV(s) of interest. In that case, you may consider choosing that variable as a covariate since it have minimal impact on your DV(s). This normally happens with categorical IVs/predictors.
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