Sample size confounded with factors (ANOVA) What do you suggest doing when sample size is confounded with factors in an ANOVA?
"For example, in a two-way ANOVA, let’s say that your two independent variables (factors) are Age (young vs. old) and Marital Status (married vs. not).
Let’s say there are twice as many young people as old. So unequal sample sizes.
And say the younger group has a much larger percentage of singles than the older group.  In other words, the two factors are not independent of each other.  The effect of marital status cannot be distinguished from the effect of age.
So you may get a big mean difference between the marital statuses, but it’s really being driven by age." (Thank you to the analysis factor for this example)
If I am interested specifically in the interaction (age*marital status), how can I address the issue of an uneven distribution of marital status across age?
 A: I notice that you research Alzheimer's disease, including its factors. So let's suppose you want to know the causal influence of age on a particular factor. You've mentioned that you think age influences marital status (surely not the reverse, except perhaps figuratively!), and perhaps you're also thinking that marital status influences the Alzheimer's factor. In that case, you would have a causal diagram like this:

This situation is known as a mediator: marital status is a mediator of the causal effect of age on the Alzheimer's factor. In this scenario, marital status is NOT a confounder, because it does not set up a backdoor path from Age to the Alzheimer's factor. If you were to regress the Alzheimer's Factor on Age, and you were to include the marital status, you'd be conditioning on marital status and you would get an incorrect causal effect of age on the Alzheimer's factor. Conclusion: regress the Alzheimer's factor solely on age, without including marital status.
On the other hand, you might be interested in investigating the causal effect of marital status on the Alzheimer's factor. Using the same causal diagram, but re-arranging it a bit yields this quite different picture:

Now age sets up a backdoor path from marital status to the Alzheimer's factor. If you want the correct causal effect of marital status on the Alzheimer's factor, you must condition on age (include in your regression).
I've made some assumptions in this answer which might be quite different from what you're really trying to accomplish, but I wanted to show you how the New Causal Revolution can really help clarify what to do when, particularly when it comes to confounding variables. Indeed, I view understanding confounding variables as one of the most important advances of the New Causal Revolution.
