A paradox in the interpretation of group comparisons.

It is common practice in behavioral research, and in other areas, to apply the analysis of covariance in the investigation of preexisting natural groups. The research worker is usually interested in some criterion variable (y) and would like to make allowances for the fact that his groups are not matched on some important independent variable or control variable (x). The situation is such that observed differences in the dependent variable might logically be caused by differences in the independent variable, and the research worker wishes to rule out this possibility. It is widely recognized that ideally the research worker should assign cases or individuals at random to the groups that are to be studied by analysis of covariance. In behavioral research and in many other areas, such random assignment is usually difficult or impossible—as, for example, in a com-