Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
We estimate power calculations for several assumptions. First, given the current PARR service level from February 2024, and a four month treatment window, we would expect a total sample of 544. Based on this sample size, we expect an intent-to-treat (ITT) minimum detectable effect (MDE) on the main outcomes of interest of 14-15 percentage points (95% confidence, 80% power). Release from detention: population mean 0.72, MDE 0.14; Days to Release: population mean 28.6, MDE 8.9; Dismissal: population mean 0.32, MDE 0.14, Conviction: population mean 0.36, MDE 0.15. Expanding the treatment window to 6 months lowers the MDEs to between 11 and 12 percentage points (7.2 days to release), and to 9 months lowers the MDEs to between 9 and 10 percentage points (5.6 days to release).
If the PARR program is able to serve a larger share of eligible clients per month (e.g. 317 clients), the MDEs for the 4 month timeline closely mirror those for the 9 month timeline cited above. MDEs for a six month treatment window range from 7 to 8 percentage points (4.7 days to release).
All of these MDEs are well below the impact estimates generated from the pilot study.