How Many Subjects Show the Effect? 1 How Many Subjects Show the Effect? a Sharp Lower-bound Estimator with Examples from Behavioral Economics

Computing the average 'effect', the difference in means of the dependent variable between conditions, is by far the most common way of analyzing experimental data. In many settings, however, the proportion of people individually exhibiting the effect in question (or the opposite one) is of interest also. This paper puts forward an assumption-free and computationally efficient algorithm that estimates a sharp lower-bound for such a statistic. Its use and usefulness are demonstrated by reanalyzing data from various behavioral economics experiments. Lower bounds of the share of subjects behaving contrary to standard economic theory in those experiments are shown to be sufficiently high and estimated with enough precision to be considered informative. Promising applications in behavioral economics more broadly, in experimental development economics, and in clinical medical trials are discussed.