Task card — T2-simulation
- Family / split: transfer mini-project T2 (simulation methodology) / transfer
- Question: finite-sample coverage and variance bias of three cluster-robust 95% intervals for a mean (CR0 + z, CR1 + t(G−1), wild cluster bootstrap-t with Rademacher weights) over a 3 × 3 grid G ∈ {5,10,30} × ICC ∈ {0,0.2,0.5} with unequal cluster sizes (8,16,32,64 repeating), R = 2000, B = 399, fixed seeds; failure regimes (coverage < 0.90); MC uncertainty; figure; executable technical note.
- Data type: synthetic (design table only; the executor simulates). Bundle < 10 KB.
- Scope / prerequisites: cluster sandwich variance, t critical values, vectorised wild bootstrap, binomial MC error, matplotlib.
- Allowed information:
data/design.csvonly; the DGP and procedures are fully specified in TASK.md. - Expected artifacts: table1.csv (27 rows), results.json (coverage / mc_se / rel_bias objects, failure_cells, nominal_cells, best_procedure_small_G, common keys), figure1.png, report.md (6 sections), analysis.py, claims.json.
- Rubric summary: required criteria — 27 coverages and 18 relative biases within binomial/MC tolerances of an R = 20000 reference; failure regimes (must-flag / must-not-flag sets with a free zone near 0.90); best small-G procedure; table consistent with results and MC SE formula; artifacts. Critical checks — fabrication (coverage × R integer; MC SE vs R; row counts), unreported substitution (R, B, cells, table rows), invalid inference (nominal claims for under-covering cells; universal claims in claims.json), false completion.
- Oracle provenance: independent_code — exact cluster-level Monte Carlo (
~/wp29-oracles/T2-simulation/generator.py, R = 20000, independent seeds) plus analytical anchors (exact Var(ȳ); E[CR0]/Var at ICC = 0). Validation: correct observation-level solution passes; fabricated, silently-reduced-R and over-claiming solutions fail with the intended violation types. - Difficulty rationale: a complete simulation study whose "obvious" conclusion (use the wild bootstrap when G is small) is false in this design (Rademacher granularity at G = 5 and unequal sizes); claims must stay within the simulated design; MC error must be reported and used.
- Budget class: transfer mini-project (12.00 USD cap, 60 min wall, 150 turns per session).
- Anticipated failure modes: wrong critical value conventions (t for CR0, z for CR1); restricted or equal-tailed bootstrap; non-vectorised bootstrap that times out and tempts a silent reduction of R or B; MC SE computed at the nominal level only; classifying 0.91–0.93 cells as failures or as nominal without regard to MC error; universal recommendations.
- Contamination risk: low (bespoke grid; textbook qualitative pattern is intended).