ABSTRACT
A small lack of balance can often be satisfactorily dealt with by some ad hoc modification of the procedures for balanced data. In general, however, and certainly with the present data, this is either unsatisfactory or impossible. These data illustrate in very simple form some of the issues in analysing unbalanced data such as arise commonly, although by no means exclusively, in observational studies. The calculations for the analysis are those of least-squares theory that is multiple regressions. If the data show clear evidence of interaction, estimates and interpretation of main-effect parameters will be relevant only in those rather rare circumstances in which one is for some clear practical reason interested in effects of one factor averaged over the levels of the other factor, columns. In some narrowly technological situations one may be concerned with the average treatment effect over a population of individuals with specified proportions of males and females.
