to the well’s pump-head. Placards displayed both in text and color whether the arsenic concentration was up to 10 ppb (blue), 25 or 50 ppb (green), or above 50 ppb (red). As shown in Figure 1, the placards displayed two hands holding a drinking cups, one hand holding a drinking cup, or a large cross over a hand holding a drinking cup, depending on the arsenic concentration.

The split of the test fee between the tester and supervisor in groups B and C was the same as in group A, but in B the project gave an additional bonus of BDT12 per sale to testers, to compensate for the additional effort necessary to coordinate group formation.<sup>7</sup>

# **2.2 Power Calculation and Study Design**

The trial was not registered, and was not based on a pre-analysis plan. Comparison of demand for and responses to tests between arms A and B was the primary objective of the study. Data from earlier work in neighboring Araihazar subdistrict (see Bennear et al. 2013), were used to estimate an intravillage correlation of _ρ_ = 0 _._ 09 in switching decisions among owners of unsafe wells and a switching rate of about 30%, a rate at the lower end of what observed in previous studies. It was determined that 50 clusters (villages) would be sufficient to detect meaningful impacts with high probability. In particular, assuming a 30% switching rate from unsafe wells with individual sales (arm A), and even using a conservative 0.12 intra-village correlation in switching rates, and with only five unsafe wells identified through the test sales per village, 49 clusters per arm would have been necessary to have 80% power to detect a 15 percentage points difference in switching rates between arms for a two-sided test of equality at the 5% significance level (effect size = 0 _._ 15 _/_<sup>_√_</sup> 0 _._ 3 _×_ 0 _._ 7 = 0 _._ 33). The same number of clusters would have achieved the same power for a smaller 10 percentage points difference (effect size = 0 _._ 10 _/_<sup>_√_</sup> 0 _._ 3 _×_ 0 _._ 7 = 0 _._ 22) with a less conservative _ρ_ = 0 _._ 09 and with higher demand leading to the discovery of 20 unsafe wells per cluster, while 51 clusters per arm and 40 unsafe wells per village would have been necessary with the more conservative _ρ_ = 0 _._ 12.

Given that the available funding allowed the inclusion of a larger number of villages, it was possible to include the additional experimental arm C, for which however sample size was dictated by budget constraints rather than power calculations.

The assignment to treatment arms was done by the principal investigators using random assignment, using the statistical software Stata, after stratification. Strata were determined by whether the share of unsafe wells in the BAMWSP testing campaign carried out years earlier was below or above

> 7The experimental design also included two exploratory arms, with only six villages each, where tests were sold individually either at a village-level price of BDT45 or BDT90, but with payment required only in case of ‘good news’, that is, in case of arsenic level no higher than 50 ppb. The inclusion of these proof-of-concept conditional sales was motivated by the aversion expressed by several members of focus groups to the idea of ‘paying for bad news’. Sales conditional on the results may have thus increased demand (a prediction strongly supported by the observed purchase rates), although the conditional payment also generates a reduction in the (expected) price and a different selection into purchase conditional on beliefs about the safety of the well water. Because of these confounding factors and because of the very small number of villages assigned to these sales, the results are not discussed in detail in this article but they are available upon request from the authors.

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