Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
The study exploits a factorial design. Importantly, we will not primarily analyze this as a ten-arm experiment requiring pairwise comparisons. Instead, the 5×2 factorial structure lets us estimate the marginal effect of each intervention component — the redesigned notice, the case documents access, the e-filing tool, and SMS reminders — by pooling across the other dimension.
The table below reports minimum detectable effects (MDEs) at 80% power (α = 0.05, two-sided) for Answer filing in percentage points (pp), which has a baseline rate of approximately 40% under the current notice.
Estimate | What it Captures | Effective N Per Group | MDE
Redesign Effect | New notice vs current notice | ~4,000 | 3.1 pp
Document Access | New notice with vs without access link | ~4,000 | 3.1 pp
E-Filing | New notice with vs without e-filing link | ~4,000 | 3.1 pp
SMS | Text reminders vs no reminders | ~10,000 | 1.9 pp
Pairwise (any single arm vs control) | Individual arm comparison | ~2,000 | 4.3 pp