I agree with the other respondents' posts. Just to add something that might clarify, this kind of situation in these studies is common, and the natural desire of the investigator is to "regress out" the variable of no (or less) interest, in order to allow us to make an inference about the differences between groups. But if there's not considerable overlap, in principle it cannot be done. This was well explained in the article "Misunderstanding Analysis of Covariance," Miller and Chapman, J. Abnormal Psychology, 2001, Vol. 110, No. 1,40-48.
From the admittedly polemic introduction of that article: "In this article, we discuss why attempts to control statistically for such differences are, in general, inappropriate. For example, consider a data set consisting of age as a potential covariate, grade in school as the grouping variable, and basketball performance as the dependent variable. An analysis of covariance (ANCOVA) might be run in hopes of asking whether 3rd and 4th graders would differ in performance were they not different in age. This might seem to be a reasonable question, in that one could ask whether some maturational change at that age makes a nonlinear contribution to basketball ability. However, in fact it makes no sense to ask how 3rd graders would do if they were 4th graders. They are, inherently, not 4th graders, and ANCOVA cannot 'control for' that fact. Age is so intimately associated with grade in school that removal of variance in basketball ability associated with age would remove considerable (perhaps nearly all) variance in basketball ability associated with grade. The results of the ANCOVA would be meaningless. As a complement to this problem of the covariate removing too much of the independent variable of interest, a problem can arise when preexisting groups differ systematically on more than the covariate. The covariate will leave those differences intact, thus biasing the estimate of the treatment effect (Reichardt and Bormann, 1994), which has been called specification error."