Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
The planned sample is 400 completed behavioral observations. Participants are individually randomized to the earned-wage payment-timing treatment, with approximately 200 workers assigned to immediate payment of previously earned Day 1 wages and 200 workers assigned to deferred payment of the same earned wages after the Day 2 work session. In the second work session, participants are also individually randomized to the starting production method, with approximately 200 workers assigned to begin with manual shelling and 200 workers assigned to begin with the mechanical sheller. Under balanced assignment, this yields approximately 100 workers in each payment-timing-by-starting-method cell.
The study has two co-primary binary outcomes: initial machine preference before starting-method randomization, and post-assignment machine use after the revision opportunity. The confirmatory family contains two one-sided tests in the pre-specified positive direction. We will control the familywise error rate using the Holm step-down procedure. For conservative planning, power calculations use a one-sided alpha of 0.025 for each primary outcome.
For the first primary outcome, initial machine preference, the benchmark assumes a control-group machine-preference rate of 0.30 and a treatment-group rate of 0.45. This corresponds to a 15 percentage-point increase. With 200 workers per payment-timing arm and a one-sided alpha of 0.025, the design has approximately 88 percent power to detect this effect. The minimum detectable effect for 80 percent power is approximately 13.5 percentage points when the control-group mean is 0.30.
For the second primary outcome, post-assignment machine use, the benchmark assumes that immediate access to previously earned wages increases starting-method-standardized machine use by 15 percentage points. One illustrative case is a 15 percentage-point increase in manual-to-machine switching among participants randomly assigned to begin manually and a 15 percentage-point increase in machine retention among participants randomly assigned to begin with the machine. With approximately 100 workers in each payment-timing-by-starting-method cell, corresponding to 400 completed behavioral observations overall, the design has approximately 89 percent power to detect this starting-method-standardized 15 percentage-point effect using a conservative one-sided alpha of 0.025. The minimum detectable starting-method-standardized effect for 80 percent power is approximately 13.3 to 13.5 percentage points.
The starting-method-specific decomposition estimates are not powered as separate confirmatory hypotheses. With approximately 100 treated and 100 control workers within a given starting-method subgroup, a 15 percentage-point subgroup effect has only about 59 to 62 percent power under a one-sided alpha of 0.025, depending on the baseline rate. The minimum detectable subgroup effect for 80 percent power is approximately 18 to 19 percentage points. For this reason, the manual-starter and machine-starter estimates will be reported as pre-specified decomposition analyses used to interpret the source of the pooled post-assignment effect, not as separate confirmatory tests.
If the scheduled lean-season field period ends before 400 completed behavioral observations are reached, the final analysis will report the realized sample size, the assignment-based study flow, treatment-arm attrition, and updated minimum detectable effects. The study will not report post-hoc power calculations.