Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
All minimum detectable effects (MDEs) use the two-arm formula MDE ≈ 2.8 x SD x sqrt(2/n) for continuous outcomes (SD = sqrt(p(1-p)) for binary outcomes), at alpha = 0.05 two-sided and 80% power, using moments from prior, already-delivered CES waves (no Wave 81/82 data used). Figures below are conservative post-only upper bounds; registered ANCOVA specifications will shrink them further once baseline-endline correlations are estimated. Selected main outcomes:
- Personal wage-catch-up belief (H2/H6), n ≈ 9,500/arm: MDE ≈ 0.041 SD (no directly comparable prior-wave item; reported in SD units).
- Standard 12-month wage-growth expectation, employees (H7), n ≈ 5,083/arm: SD = 5.49 pp (winsorized 2%); MDE ≈ 0.31 pp.
- Horizon-conditioned catch-up outcome (H8), n ≈ 9,500/arm: MDE ≈ 0.041 SD (new item; reported in SD units).
- Any large-ticket purchase (H4), n = 9,112/arm: base rate 42.9%, SD = 0.499; MDE ≈ 2.1 pp.
- Total household consumption (H4), n = 9,112/arm: SD = EUR 5,030 (winsorized 1%); MDE ≈ EUR 209 (≈0.042 SD).
- Realized on-the-job search, all respondents (H5), n = 9,107/arm: base rate 13.87%, SD = 0.346; MDE ≈ 1.4 pp.
- Own wage-growth persistence, employees, arms A vs C (H3), n = 2,542/arm: SD = 5.49 pp (winsorized); MDE ≈ 0.43 pp.