Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Power calculations assume a two-arm, individual-level randomized trial with no clustering (α=0.05, Power = 80%).
Crucially, our primary hypothesis investigates whether the AI tool democratises tacit knowledge—meaning we are testing an interaction effect (Treatment × Career Stage) rather than just an Average Treatment Effect (ATE).
Our baseline recruitment target of 504 participants is powered under an Optimistic Perspective. Assuming around 50/50 stratified split between PhD students and junior economists, the Minimum Detectable Effect Size (MDES) for the interaction under different enrollment scenarios is as follows:
- Optimistic Target (Moderate Effect, MDES = 0.50 standard deviations): Requires 504 total participants (252 per arm). This is our baseline operational target. (Note: detecting the main ATE alone at this magnitude would require just 126 total participants).
- Reference Scenario (Small-to-Moderate Effect, MDES = 0.30 SD): Requires 1,396 total participants (698 per arm). If recruitment exceeds our baseline target, this is our extended goal.
- Conservative Scenario (Small Effect, MDES = 0.20 SD): Requires 3,140 total participants (1,570 per arm).
Operational Constraints on Power:
These calculations depend on the demographic balance of our strata. Statistical power for an interaction is constrained by the size of the smallest cell, because the variance function p(1−p) is maximized at p=0.5.
If our real-world recruitment pool deviates from a 50/50 split, the required sample size increases significantly to maintain the same MDES. For example, to detect an effect of d=0.50, a 30/70 demographic split increases the required sample from 504 to 524 participants to preserve the necessary minimum cell size. To transparently pre-register our power constraints, we outline the expected sample requirements under varying degrees of demographic imbalance (d=0.5):
- Optimal Split (50/50): Requires 504 total participants (252/arm). The minimum cell size is 126. This is our baseline operational target.
- Mild Imbalance (60/40 or 40/60): Requires 524 total participants (262/arm).
- Moderate Imbalance (70/30 or 30/70): Requires 598 total participants (299/arm).
- Severe Imbalance (80/20 or 20/80): Requires 786 total participants (393/arm).
- Extreme Imbalance (90/10 or 10/90): Requires 1,396 total participants (698/arm).
If the true effect of the AI tool is smaller, the required sample sizes increase drastically (d=0.3).
- Optimal Split (50/50): Requires 1,396 total participants (698/arm).
- Moderate Imbalance (70/30 or 30/70): Requires 1,662 total participants (831/arm).
- Severe Imbalance (80/20 or 20/80): Requires 2,182 total participants (1,091/arm).