Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
To determine the appropriate sample size, we estimated Minimum Detectable Effect (MDE) sizes for Intent-to-Treat (ITT) estimates. We calculated the MDE as the impact divided by the comparison group standard deviation (sqrt(m(1-m)), where m = the proportion of the control group with a “successful” outcome (i.e., reunification). The MDE was calculated assuming a randomization ratio of one treatment (Project Connect) to one control (services as usual) with an alpha level of 0.05anda two-tailed test with 80 percent power. Based on the data from Project Connect and DCYF, Project Connect children were 18 percentage points more likely than comparison group children to be at home by June 30, 2019. This represents a standardized effect size of.40. Under an intent-to-treat (ITT) estimation strategy, where outcomes for all people referred to Project Connect are included, we estimate that to achieve this minimum detectable effect, a sample of roughly 196participants would be necessary, 98 treatment and 98 control.