Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
We conducted power analysis for the two primary outcomes, with a significance level of 0.05 and power of 0.8. Using the J-PAL Power Calculator, we computed the Minimum Detectable Effect under different assumptions about sample size and attrition. In all cases we assume the proportion in treatment is 0.5.
Primary Outcome 1: Household disconnected during heating season. We assume an outcome proportion of 0.1 based on the 2024 EIA Disconnections Report. With our target sample size and no attrition, we will be able to detect about a 5 percentage point difference in disconnections between the treatment and control groups. Under more conservative assumptions of a sample of 600 and 20% attrition, we will be able to detect about a 7 percentage point difference.
Sample MDE Attrition (%)
1000 0.0532 0
1000 0.0561 10
1000 0.0595 20
800 0.0595 0
800 0.0627 10
800 0.0665 20
600 0.0687 0
600 0.0724 10
600 0.0778 20
Primary Outcome 2: Household energy spending tradeoffs during heating season. We assume an outcome proportion of 0.2 based on the 2024 EIA Residential Energy Consumption Survey. With our target sample size and no attrition, we will be able to detect a 7 percentage point difference in households trading off energy bills for other expenses between the treatment and control groups. Under more conservative assumptions of a sample of 600 and 20% attrition, we will be able to detect about a 10 percentage point difference.
Sample MDE Attrition (%)
1000 0.0709 0
1000 0.07475 10
1000 0.0793 20
800 0.0793 0
800 0.0836 10
800 0.0886 20
600 0.0915 0
600 0.0965 10
600 0.1024 20