Multiple Hypothesis Testing in Experimental Economics∗

The analysis of data from experiments in economics routinely involves testing multiple null hypotheses simultaneously. These different null hypotheses arise naturally in this setting for at least three different reasons: when there are multiple outcomes of interest and it is desired to determine on which of these outcomes a treatment has an effect; when the effect of a treatment may be heterogeneous in that it varies across subgroups defined by observed characteristics and it is desired to determine for which of these subgroups a treatment has an effect; and finally when there are multiple treatments of interest and it is desired to determine which treatments have an effect relative to either the control or relative to each of the other treatments. In this paper, we provide a bootstrap-based procedure for testing these null hypotheses simultaneously using experimental data in which units are assigned to treatments and control using simple random sampling. Using the general results in Romano and Wolf (2010), we show under weak assumptions that our procedure (i) asympototically controls the familywise error rate – the probability of one or more false rejections – and (ii) is asymptotically balanced in that the marginal probability of rejecting any true null hypothesis is approximately equal in large samples. Importantly, by incorporating information about dependence ignored in classical multiple testing proedures, such as Bonferroni and Holm (1979), our procedure has much greater ability to detect truly false null hypotheses. In the presence of multiple treatments, we additionally show how to exploit logical restrictions across null hypotheses to further improve power. We illustrate our methodology by revisiting the study by Karlan and List (2007) of why people give to charitable causes.