Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
Given the concern noted in Section 3.1 regarding the ability to survey 1,000 respondents before the tax declaration deadline, we provide conservative estimates regarding power, estimated using the sampsi command in Stata. With a cell size of 250 observations (pooling both peer and audit treatments to assess whether taxpayers move in any direction), we are powered at the 5 percent level to detect a 0.25 standard deviation effect with a power level of 80 percent. With cells of at least 400 observations, we are powered to detect a 0.2 standard deviation effect. Comparing the minimum sized cell of 150 observations to the control cell of 400 observations, we are able to detect a 0.27 standard deviation effect. While these minimum detectable effect sizes are not small, the change in behavior (increasing declarations above the exemption zone) that we hope to detect embodies an approximate increase of at least 67 percent (on average) for taxpayers below 2 million RWF (if they move to 2 million RWF) and for taxpayers above, if they move below, an effect of similar magnitude if these taxpayers locate where their peers currently locate in the exemption zone. Therefore, we feel confident that this sample size will permit detection of effects on declared taxable income. Likewise, the information provided about audit communicates appreciably high and low levels of audit likelihood, meaning that if the information is credible it would entail updating perceptions to a substantial degree. Therefore, we also feel confident that we will be able to detect changes in the perceived likelihood of audit with this sample size through the survey experiment. For the peer information experiments, we believe these also provide strong information about peers that will be new information to most taxpayers. Their movement to the locations of the peers described in each message would entail the same sized responses as those discussed above, which are within the range of effects we are able to detect.