In the target article, Banja (2014) argues against alcohol and drug testing for health care professionals and provides several reasons. Most important, there is not much evidence that alcohol or drug abuse has large effects on the performance of health care professionals, and Banja cited evidence that the effects are small. His reasoning, then, is that if alcohol or drug abuse has only small effects on actual performance, it makes little sense to devote resources to alcohol or drug testing.But there are problems with this argument. The obvious problem is that the evidence Banja cites is, as he himself admits, anecdotal. So on the one hand, Pham, Pronovost, and Skipper (2013) suggested a large effect based on primarily anecdotal evidence, whereas on the other hand, Banja suggests a small effect also based primarily on anecdotal evidence. Without solid research with valid numbers, it is difficult to know what to believe.But this is only the tip of a large iceberg. There are relevant mathematical and statistical issues to be considered that place the effect size issue in a broader context. Imagine that a researcher obtains a seemingly unimpressive correlation of -.3 between the abuse of a particular drug and performance, whereby more abuse implies lesser performance. It is possible to square the correlation coefficient to obtain the coefficient of determination, which is .09, and indicates the amount of variance in performance that can be explained by variance in drug abuse. Given that it is theoretically possible to account for 100% of the variance in performance with drug abuse, this 9% value is obviously on the low side and might be taken as supporting the "small effect" that Banja claimed if it were to happen.But interpretation of correlation coefficients is not straightforward. One way is to use a binomial effect size display (Rosenthal and Rosnow 1991;Rosenthal and Rubin 1979;Trafimow 2004). The binomial effect size display makes use of Eq. 1, where r represents the correlation coefficient:Percent performance impairment or nonimpairment D :5 § r 2 (1)In the present example, then, if we imagine the simple case that each health care professional abuses or does not abuse a drug, and either is performance impaired or not, the .3 correlation translates to 65% of the abusers being performance impaired and 35% of the no abusers being performance impaired-an obviously important difference. Of course, the binomial effect display dichotomizes what is likely substance abuse or performance impairment along continua, but the oversimplification is nevertheless useful because it concretizes how a seemingly small effect in correlational or variance-accounted-for terms can translate to an important effect in terms of probability of performance impairment. I might add that Banja himself dichotomized by focusing on specific errors that happen or do not happen, rather than on what might be considered to be a more nuanced view of the total performance of health care professionals along performance continua.But there is more. It is...