Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Primary outcome:Tax Compliance Rate
Unit: Proportion of declared income per participant(0-1 scale)
1. Pilot Study Foundation
The pilot study was conducted with two network conditions (Control and Complete), providing the crucial baseline data for our power calculations.
Under High Audit Probability:
Control Group (n=28): Compliance Rate Mean = 0.512, Standard Deviation = 0.299
Complete Network Group (n=24): Compliance Rate Mean = 0.4239, Standard Deviation = 0.367
Under Low Audit Probability:
Control Group (n=28): Compliance Rate Mean = 0.416, Standard Deviation = 0.318
Complete Network Group (n=24): Compliance Rate Mean = 0.379, Standard Deviation = 0.327
2. Main Experimental Design
The main experiment will employ a 3 (Network Structure: Control, Chain, Complete) × 2 (Audit Probability: High, Low) mixed design.
Between-Subjects Factor: Network Structure. Each participant is randomly assigned to one of the three network conditions.
Within-Subjects Factor: Audit Probability. Each participant experiences both high and low audit probability conditions.
Total Sample Size: 540 participants, with 180 participants in each of the three network conditions.
3. Power Analysis Calculation
To ensure the study is adequately powered to detect a true effect, we conducted a power analysis using the pooled standard deviations derived from the pilot data for the Control and Complete Network conditions. Based on a conservative two-tailed test with 80% statistical power and a significance level (α) of 0.05.
In the High Audit Probability context, our design can detect a Minimum Detectable Effect Size of 0.098 in compliance rates (0.30standard deviations).
In the Low Audit Probability context, our design can detect a Minimum Detectable Effect Size of 0.095 (0.30standard deviations)
Based on the effect sizes observed in prior studies where audit probabilities were not explicitly disclosed to subjects (e.g., Choo, 2016; Alm, 1992), our target Minimum Detectable Effect (MDE) can be considered both feasible and substantively meaningful.
References
[1] Choo C Y L, Fonseca M A, Myles G D. Do students behave like real taxpayers in the lab? Evidence from a real effort tax compliance experiment[J]. Journal of Economic Behavior & Organization, 2016, 124: 102-114.
[2] Alm J, Jackson B, McKee M. Institutional uncertainty and taxpayer compliance[J]. The American Economic Review, 1992, 82(4): 1018-1026.