design with 40 clusters per arm and 25 households with children < 5 per years cluster. After the baseline survey, we decided to additionally power the study to detect differences between groups in height-for-age Z-scores based on a hypothesis published on the possible effects of improved hygiene and sanitation on child growth [15]. We reviewed measures of variability and withincluster correlation of height-for-age Z-scores (SD=2.09, intra-class correlation=0.17), and chose to increase the within-cluster sample sizes from 25 to 38 households to ensure the study had 80% power to detect differences of +0.2 Z in height-for-age.

# **3.2  Sample Selection and Randomization**

**Village selection** : Due to the large-scale implementation of TSC in Madhya Pradesh at the beginning of the study in 2009, we did not include a random sample of villages and instead enrolled villages in administrative areas that were willing to participate in the study. The evaluation selected _Gram Panchayats_ (hereafter referred to as “villages”)<sup>11</sup> in three stages.  First, the state government and WSP selected two districts out of the 50 in Madhya Pradesh – Dhar and Khargone – who were willing to work with WSP to implement the TSC. Second, the evaluation included 11 of 13 blocks from Dhar district and 8 of 9 blocks from Khargone; the remaining blocks were excluded from the evaluation because block officials were unwilling to maintain control villages for the length of the study. Third, in each block the government identified villages where they were indifferent about implementing the TSC program. We selected 40 villages in each district with between 2 and 8 villages from each block (larger blocks contributed more villages).

**Household selection** :  In each selected village the field team listed and mapped 200 households and used systematic random sampling to select 25 households with at least 1 child < 24 months of age in the baseline. The field team focused survey efforts in the most populous parts of each village.  We visited the same households again at follow-up, and expanded the study to include 38 households per cluster due to sample size considerations (described above). Because we conducted the follow-up survey 21 months after the baseline, the eligibility criteria for newly enrolled households was that they had at least one child between the ages of (0 + 21 =) 21 months and (24 + 21 =) 45 months and were living in the village at the time of the baseline survey to be commensurate with the eligibility criteria for the original cohort.

**Randomization** : The 80 study villages ( _Gram Panchayat_ s) were the independent units and were randomly allocated in equal proportion to intervention or control. The randomization was stratified at the administrative block level. We stratified the randomization because TSC implementation was coordinated at the block level and we wanted to ensure that the treatment arms were evenly allocated between districts and geographically stratified within districts. The randomization took place in a public lottery in each of the 19 blocks. In each lottery, eligible

> 11 A _Gram Panchayat_ could include one large village or a group of villages; on average, a _Gram Panchayat_ included 2 to 3 villages in the study region.

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