Precomputed grid headline
On the same cohort of 2,000 students, 5 papers, and 10 replications, rank recovery against true ability barely moves across the whole marking grid: 0.948 at worst and 0.966 at best. Measurement quality is not where the marking scheme earns its keep.
The guess rate is all or nothing. Which side a cell falls on turns on a single line: a blind shot pays whenever the correct mark is more than three times the penalty. The interactive controls below let you poke at that cliff yourself.
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Technical appendix: long-run measurement targets
These long-run IRT targets sit beyond the near-term normalization design.
| Parameter | Target | Note |
|---|---|---|
| Target reliability | ≥ 0.92, stretch 0.95 | Marginal reliability |
| Discrimination a | 0.8 to 2.0, reject < 0.5 | Avoid uniformly maximal discrimination |
| Difficulty b | -0.5 to +2.0 logits | Denser near merit cutoffs |
| Point-biserial | ≥ 0.20, prefer ≥ 0.30 | Screening threshold |
| Guessing c | ~0.10 to 0.25 | 3PL range for four options |
| Anchors | ≥ 20 to 25% | For equating and drift monitoring |
| Annual refresh | ~0.30 | Exposure-driven retirement |
| Pretest N per item | 200-500 (1PL), 500-1,000 (2PL), 1,000-2,000+ (3PL) | Calibration sample |
Iᵢ(θ) = D²·aᵢ²·Pᵢ(1−Pᵢ) ; I(θ) = Σ Iᵢ(θ) ; SE(θ) = 1/√I(θ) ; ρ ≈ σ²θ / (σ²θ + SĒ²)At 20 to 30 lakh candidates, pretest breadth is the constraint, not per-item sample size.