Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Power calculation: Minimum Detectable Effect Size (Main Outcomes)
Unit: Individual candidate (first exposure).
Clustering: None (randomization at individual level).
Outcome: Application rate (binary).
Baseline & SD: Baseline application rate 10% with SD = √[0.10·0.90] = 0.300; benchmarked to Hurst, Lee, & Frake (2024, Strategic Management Journal).
Tests: Two‑sided, 80% power. MDEs shown for α = 0.05 (Bonferroni‑adjusted α = 0.0125 in parentheses).
Conservatism: Estimates are conservative because they use only the email outreach pool (N = 10,000; 2,000 per arm) and exclude additional randomized organic traffic. As total N increases, MDEs decline ≈ 1/√N.
MDEs (absolute percentage points):
2,000 vs 2,000 (single arm vs single arm): 2.66 pp (3.20 pp Bonferroni).
2,000 vs 6,000 (degree‑required vs pooled skill‑based arms): 2.17 pp (2.60 pp Bonferroni).
I will recompute MDEs ex post using realized baselines and final sample sizes (including organic traffic).
Second stage
Based on Agan et al. (2025).Expected effect sizes can also be estimated from Agan, Cowgill, and Gee (2025). Their two-sided audit employed 256 Upwork recruiters who each evaluated approximately 8 job applications (over 2,000 total applications). With this sample, they detected statistically significant effects of salary information on multiple outcomes:
- Willingness-to-pay (WTP): Every $1 increase in disclosed salary increased employer WTP by $0.65
- Salary offers: Each $1 disclosed increased salary offers by $0.68
- Beliefs about competing offers: Each $1 disclosed increased beliefs about competing offers by $0.77
- Callback rates: Disclosing workers (especially high-salary disclosers) were significantly less likely to be called back, despite receiving higher salary offers when selected
- Gender differences: Effects varied significantly by gender, with women's disclosures having smaller impacts on callbacks than men's
These effects were detected with 256 recruiters evaluating approximately 2,000 applications total, demonstrating that Upwork recruiters provide reliable, sensitive measures for hiring decisions.
The proposed design plans for approximately 500 recruiters (with each recruiter evaluating 10-15 candidates. This provides several advantages:
Between-recruiter comparisons: With ~167 recruiters per experimental condition (vs. their 256 total across all conditions), I have adequate power to detect main effects of job framing and pool composition on evaluations.
Within-recruiter comparisons: The repeated-measures design (10-15 candidates per recruiter) provides substantially more statistical power than between-subjects comparisons alone. With 500 recruiters × 10-15 candidates = 5,000-7,500 total evaluations (compared to their ~2,000), the design has:
- 95%+ power to detect effects similar in magnitude to those found by Agan et al. on salary-related outcomes
- 85-90% power to detect moderate effects (d = 0.3-0.4) on quality ratings
- High power to detect heterogeneous effects by candidate characteristics. With 5,000-7,500 total evaluations and balanced representation across conditions, the design has 80%+ power to detect whether recruiters rate candidates differently based on gender, race, or education (e.g., whether women receive lower quality ratings than men, or whether non-degree holders are rated lower than degree holders). The design also has adequate power to detect whether such rating differences vary by experimental condition (e.g., whether gender gaps in ratings are larger in certain job framings or applicant pool compositions).
Following their approach, I will measure multiple theoretically-motivated outcomes including quality ratings, salary offers recruiters would make, and callback recommendations. This sample size substantially exceeds what Agan et al. needed to detect meaningful and policy-relevant effects on hiring decisions.