ABSTRACT
We begin by considering a population of units U = (u 1, u 2,…, uN ). Our objective is to study the effect of a treatment t on these units with respect to a particular response of interest in the context of a randomized experiment. We make use of a model sometimes referred to as a “Potential response model” or as “Rubin model for causal inference.” The model has been used by others to analyze problems associated with estimating a mean treatment effect in both randomized experiments and observational studies.
However, an “average treatment effect” is a meaningful quantity only when it adequately represents the effect of t on each unit. If the effect of t is highly variable from one unit to another, i.e., when the subject-treatment interaction is nonnegligible, then the average treatment effect loses its importance. In fact, a treatment might appear to be a “beneficial” treatment when examining its average effect even though a substantial proportion of the units in the population experience an “unfavorable” effect. This proportion can be calculated or approximated if one knows the variance of the treatment effects along with the mean. Questions concerning the estimation of the variance of treatment effects in a finite population is the subject of this paper.
