Interpreting audit saturation without mistaking assignment for observation¶

Methods companion to W3 R90 · 22 October 2026

Estimand and what the word “sharp” means¶

The analysis conditions on the realized set of originally missing records, whose membership is represented by the first-stage missingness mask. The target is the finite-population mean of the prespecified bounded response \(Z=\operatorname{clip}((Y+1)/2,0,1)\) among those records, not the original unbounded gaze response or a functional regression coefficient.

If there are \(N\) originally missing records, and outcomes for \(n\) are actually measured by secondary validation or completed follow-up audits, the unknown bounded outcomes may collectively contribute anywhere from 0 to \(N-n\). With no restrictions beyond \(0\le Z\le1\), both endpoints are attainable. Consequently the finite-population mean has sharp interval

where \(S\) contains actually measured records, not simply assigned records. Its width \((N-n)/N\) is a deterministic fraction of unavailable data. It has no guaranteed 90% or 95% confidence interpretation.

For a positive-minus-negative predictor-group contrast, subtract opposite bound endpoints in the two disjoint observed groups. This contrast bound can be wider than one; it is sharp under no additional constraints on unreturned data.

Saturation identities and their limits¶

The five nested randomized assignments are q=0, 0.25, 0.50, 0.75 and 1. Assignment uses common uniforms; therefore a record assigned at q=0.25 is also assigned at higher q, with actual-return uniforms held fixed. With identical underlying masks, the number of truly observed outcomes cannot decrease, so the bound width is nonincreasing.

Under the ideal complete-return policy, q=1 forces every initially missing record either to be recovered in secondary validation or returned in its assigned audit, making \(n=N\). Bound width zero and point identification of the realized finite mean are then tautological. They do not establish a universal method for field-data MNAR identification.

Under the outcome-selective return policy, even q=1 need not make \(n=N\). The nonzero remaining interval width is the realized fraction of unreturned records, specific to the synthetic return law, sources and target definition—not a general or irreducible law of missing data.

At q=0, no third-stage audit is assigned; both return policies must coincide exactly. This provides a negative control against accidental policy-driven changes before assignment.

Thresholds are descriptive decisions, not significance tests¶

For each independent generating block and policy, the original study computes the earliest of the five assignment levels whose bounded-mean width is at most 0.10 or 0.05, or records that the threshold is never reached. These cutoffs are descriptive information-width criteria. They are not hypothesis-test thresholds, confidence levels or a quality standard validated for actual eye-tracking data.

At q=1, all 32 sources per fixed cell cross both thresholds under complete return, while none cross under the frozen selective-return law. This is observed conditional on the source generator, not an uncertainty claim about a population of users.

The number of independent source conditions is 64: 32 primitive blocks in each native design. MAR/MNAR, return law and five assignment levels are paired reanalyses of those sources. The 1,280 resulting records must not be counted as 1,280 independent experimental replications. Repeated trials and within-trajectory time points are also not independent source blocks.

Original and independently reconstructed scientific evidence¶

The original R90 run #39746751227 completed 12/12 dedicated scientific jobs, including eight fresh-source shards and a SHA256-checked original ledger. The independent R90-A run #39747852468 completed 4/4, including mandatory replay of all 1,280 original source records with separately coded generation and bounded estimands.

The first independent real-archive run failed because the replay checked an inherited R89 summary field instead of R90's frozen field name. The audit was corrected without changing the source generating process, archived outcomes or interval computations, and the subsequently rerun immutable original replay passed. Preserve both the failed and corrected runs in the evidence ledger.

Agreement between original and independent implementations is evidence of software/numerical reproducibility only. It does not show that selectively missing real-world outcomes are identified, that a return propensity is estimable, or that W3 simultaneously covers true functional slopes with nominal 90% frequency.

Release boundary¶

The experimental R90 and R90-A implementations remain unmerged draft PRs. Only articles and source-derived SVG plots may enter protected main after their own strict CI and Pages deployment. Issues #296 (response-dependent gaze loss) and #289 (simultaneous-band coverage) are still open. Stable 1.1.0 remains unchanged, and v1.2 GitHub/PyPI publication is on hold.