Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Power Calculation: Minimum Detectable Effect (MDE)Minimum Detectable Effect (MDE): 0.40 Standard Deviations (Cohen's $d$).Statistical Power: 0.80.Significance Level ($\alpha$): 0.05.Explanation and Assumptions:The power calculation was performed for the primary outcome: Reduction in Cash-flow Volatility (Coefficient of Variation of Daily Revenue).Sample Design: The calculation assumes an individual randomization design with a total initial sample of 115 micro-enterprises (58 Treatment, 57 Control).Attrition Adjustment: We accounted for a conservative 30% attrition rate over the 4-month period. This results in a final analytical sample of 80 units (approx. 40 per arm).
Effect Size in Percentage: Based on pilot data and similar behavioral interventions in micro-finance, an MDE of 0.40 SD corresponds to an approximately 12% to 15% reduction in the coefficient of variation of daily revenue.Clustering: Since the randomization is individual and not clustered, the intra-cluster correlation (ICC) is not applicable ($ICC = 0$), which maximizes the power for this specific sample size.Gain from Panel Data: By utilizing 4 waves of data per unit and a Fixed Effects (FE) model, we anticipate a reduction in the standard error of the treatment effect, effectively increasing our ability to detect the specified MDE even with the projected attrition.