principle knowledge could have been shared with others privately. Using geographic coordinates, we estimate that before our pay-for-test campaign the average well owner had about 0.02 wells labeled as safe within 50 m, out of an average of nearly 12 wells within that distance.

The immense public health challenge due to widespread arsenic contamination of well water has been widely discussed and advertised in Bangladesh, and this is reflected in the data. Almost all respondents replied ‘yes’ to the question “[h]ave you ever heard about arsenic in tube well water?” Similarly, all but a handful of respondents replied yes when asked “[a]re you aware of the health risks of drinking tube well water containing arsenic?” On average, wells were shallow (179 feet, or 55 meters) and about nine years old—consistent with many wells having been installed after the BAMWSP blanket testing. The average reported installation cost of wells in the sample was BDT7,560, or about USD100 (USD323 using the PPP exchange rate from World Bank 2015). Well depth is a key predictor of installation costs: in the data, the elasticity of cost with respect to depth is 0 _._ 72 (s.e. 0 _._ 04). The BDT45 price charged for the test in this study thus represented slightly more than one half of a one percent of the installation cost.

Well-sharing was already common in the study area: while the average household had fewer than four members, the average number of individuals using water from a well for drinking was 8.8, and in more than half of the sample wells the number of users was larger than household size.<sup>12</sup>

# **3.2 Variable Balance across Experimental Arms**

Column 5 of Table 1 shows the p-value for the null hypothesis of equality of means across the three treatment arms. The null is rejected in 5 of 26 cases at the 10% level. The differences are due to chance, and because baseline data were collected while offering wells tests, balance on variables measured at baseline could not be enforced through stratification or re-randomization. Some of the differences are substantively important. While overall 19% of household heads in the study area had no schooling, this number drops to 5% in treatment C and is close to 26% in arm A. The fraction of respondents who did not know the status of their well ranged from 68% in arm A to 90% in arm C, while the fraction of wells perceived as safe ranged from 4% in C to 22% in A. Both the group-specific means and the tests of significance are very similar if the estimation is repeated using treatment as initially randomized rather than actual treatment, sometimes not identical due to errors in coding the smartphones used for surveying.<sup>13</sup> The overlap in the distribution of covariates between arms can be gauged more systematically following the approach described in Imbens and Rubin (2015, Ch. 14). First, for each covariate in Table 1, differences between means for each pair of experimental arms normalized by a measure of variance are estimated, see Appendix A.1 for details. While the usual t-statistics used to construct the tests for balance have a denominator that shrinks to zero when sample size grows large (because the standard

> 12Recall households who did not own a well were not surveyed.

> 13In terms of statistical significance, the only differences are that “Wells within 50 m labeled safe” becomes significant at the 10% level (instead of 5) and the fraction of privately owned wells become significant at the 1% level, despite very similar means across arms that range from 97.8 to 99.7%. The full results are available upon request from the authors.

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