Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
All figures are at 80% power and alpha 0.05, with a planned total sample of 500 firms, 250 per arm, and are obtained by simulating the experiment on the national bid corpus rather than from a closed-form formula, because the bid count is skewed with a mass at zero and closed-form formulas overstate this design by roughly a quarter for count and share outcomes.
Firm-level number of bids submitted per quarter: Mean in control group: 2.730, Power: 80%, Total sample: 500, Mean difference: 0.683, Standard deviation: 3.043, Cohen's d: 0.224, Alpha: 0.05. The standard deviation is the residual after analysis of covariance on the baseline count; the raw standard deviation is 4.439. Under a proportional rather than an additive effect the same power requires Mean difference: 1.037, Cohen's d: 0.341.
Firm-level probability of submitting any bid: Proportion in control group: 0.564, Power: 80%, Total sample: 500, Proportion in treated group: 0.714, Effect: 0.150, Alpha: 0.05.
Bid-level share of bids on administratively demanding tenders: Proportion in control group: 0.219, Power: 80%, Total sample: 500 firms, clustered by firm, Proportion in treated group: 0.314, Effect: 0.095, Alpha: 0.05.
Firm-level probability of holding a paid subscription: Proportion in control group: 0.100, Power: 80%, Total sample: 500, Proportion in treated group: 0.188, Effect: 0.088, Alpha: 0.05.
Firm-level preparation time per bid: Power: 80%, Total sample: 375 at an assumed 75% endline response, Cohen's d: 0.250, Alpha: 0.05.
Preparation time on tenders where one treated and one control firm bid on the same tender: Power: 80%, Total sample: about 89 matched pairs, Cohen's d: 0.230 to 0.300, Alpha: 0.05.
Bid-level money left on the table: Proportion in control group: 0.263, Power: 80%, Total sample: 500 firms, clustered by firm, Proportion in treated group: 0.308, Effect: 0.045, Alpha: 0.05.
Bid-level win rate: Proportion in control group: 0.412, Power: 80%, Total sample: 500 firms, clustered by firm, Proportion in treated group: 0.502, Effect: 0.090, Alpha: 0.05.
Bid-level probability that a submitted bid is rejected on procedural grounds: Proportion in control group: 0.030. Not detectable at any sample size this study can recruit, declared underpowered in advance and reported descriptively.
These are targets. Recruitment opens only after this registration is approved and the realized sample depends on uptake, so power is re-computed at the realized sample size on the day recruitment closes, before any outcome is observed, and that curve is reported.