On your request for scrutiny of the Phase 2 erratum's post-hoc side standardization, I checked the pinned script and archived JSON at commit 34898fb:
The +4.56 pp side-standardized estimate (95% CI [2.89, 6.25] under strict) and the +3.94 pp realized-schedule estimate (95% CI [2.24, 5.67] in the reanalysis) target different aggregation weights:
1. Two distinct aggregation weightings (strict rule)
The +4.56 pp side-standardized estimate (in question_side_means() and world_standardized()) first collapses same-side transcripts within each question to a question-side mean (with 19 single-polarity questions contributing to one side only: H_A,std = +1.44 pp, H_B,std = +7.68 pp) and then gives the three worlds equal 1/3 weight: (H_A,std + H_B,std)/2 = +4.56 pp.
The +3.94 pp realized-schedule estimate, under strict scoring (invalid_wrong=True, common_support=False), retains all scheduled slots and counts INVALID judgments as wrong; it does not require every judgment to be valid. Because all 246 question/transcript units receive equal 1/246 weight, let u index the 246 units, Δ_u(p) in [−1, 1] be the sequential_b2 − b0 error contrast under polarity p averaged over the fixed judges, debaters, and replicate slots, and κ_u = Δ_u(B) − Δ_u(A). With 128 A and 118 B units (w_A = 128/246, w_B = 118/246), their hypothetical equally mirrored unit-weighted counterpart satisfies:
H_mirror = H_realized + [w_A · mean_A(κ) − w_B · mean_B(κ)] / 2.
This is a separate target around H_realized; it does not reconstruct the missing observations or assert that the reported +4.56 pp is an arithmetic error. (I keep valid_only separate because dropping invalid slots means unit weights need not equal 1/246.)
2. Two conditional sensitivity observations under strict scoring
Homogeneous κ_u = κ: Because the 128 : 118 split is nearly balanced, H_mirror(κ) = H_realized + (5/246)κ. Since Δ_u(p) lies in [−1, 1], any convex combination of unit contrasts is bounded by their maximum, so κ must satisfy κ ≥ max_B Δ_B − 1 ≥ H_B,std − 1 and κ ≤ 1 − max_A Δ_A ≤ 1 − H_A,std. Using the archived side means gives the necessary outer interval [−92.32, +98.56] pp for κ. Consequently, every support-feasible homogeneous κ yields a fixed-sample H_mirror within [+2.06, +5.94] pp, hence positive. These are outer bounds, not exact feasible ranges or confidence limits.
Bounded heterogeneous |κ_u| ≤ K: [H_realized − K/2, H_realized + K/2] is a coarse outer envelope. Its lower endpoint reaches zero at K = 7.876 pp (not a proof that a negative mirrored effect becomes feasible at that value, since outcome-support constraints in [−1, 1] can tighten the bound). For a fixed K, expanding the reanalysis's existing question-cluster CI [2.2358, 5.6657] pp by K/2 on each side makes the lower endpoint zero at K = 4.4715 pp, inheriting the original interval's assumptions without rerunning the bootstrap.
Would a short appendix separating these two estimands and assumption-indexed bounds be useful?
Disclosure: AI assistants helped check source and arithmetic. These are conditional sensitivity calculations on archived Phase 2 outputs, not newly collected experimental results.