Why Experimental Balance is Still a Reason to Randomize

Experimental balance is usually understood as the control for the value of the conditions, other than the one under study, which are liable to affect the result of a test. We will discuss three different approaches to balance. ‘Millean balance’ requires to identify and equalize ex ante the value of these conditions in order to conduct solid causal inferences. ‘Fisherian balance’ measures ex post the influence of uncontrolled conditions through the analysis of variance. In ‘efficiency balance’ the value of the antecedent conditions is decided ex ante according to the efficiency they yield in the estimation of the treatment outcome. Against some old arguments by John Worrall, we will show that in both Fisherian and efficiency balance there are good reasons to randomize the allocation of treatments, in particular when there is no agreement among experimenters as to the antecedent conditions to be controlled for.