# A11 analysis specification · prospective protocol v1.0

No participant-data analysis, allocation, ethics approval or registration has occurred. This specification is for independent statistical review, implementation checking and registration before recruitment. The implemented Python functions cover only the completed metadata audit, artificial-data simulations and complete-pair diagnostics.

## Population, assignment and estimand

96 stable mentor-course clusters, 48 pairs, 12 consenting baseline-cohort learners per cluster, target1,152. Pair before assignment within institution/educational stage/course domain using baseline cluster transfer score and paid support. One mentor team cannot span both conditions. A fair independent binary draw assigns one cluster per pair. Independent custodian locks roster/pairs/baseline before disclosure. Seed is access-controlled until irrevocable allocation, then auditable; no participant allocation is supplied.

Primary: equal-cluster average assigned-policy effect on baseline-to-week20 transfer change, irrespective of submission, editorial decision, public release or treatment adherence. Each cluster mean weights the fixed baseline cohort equally; each pair equal weight. The effect concerns the offer, not publication itself or an individual complier effect. No instrumental-variable publication analysis is planned.

## Outcomes and observation schedule

Baseline and week20 parallel, counterbalanced 0–24 transfer tasks; primary mean of two masked human total ratings. Week20 0–16 provenance mastery uses unfamiliar case records. Week26 delayed transfer, time diaries, access failures and unwanted exposure secondary/exploratory. Technical eight-item export/import index is a process measure. Pilot outside main sample must freeze forms, anchors, accommodations and scoring before assignment.

## Complete-outcome estimator

For pair p with clusters t,c, D_p = mean_i(Y20_i−Y0_i)_t − mean_i(Y20_i−Y0_i)_c. Estimate = mean_p(D_p). SE = sampleSD(D_p)/sqrt(P). Approximate95% t interval uses P−1 degrees of freedom (47 under target design). This is an equal-cluster estimand; with unequal cluster sizes it is not a student-weighted estimand. Pair-to-pair effect heterogeneity can make this variance conservative relative to the finite-population allocation variance; finite-sample normality is not guaranteed.

The complete-pair diagnostic tool implements the mean/SE/t interval and a Monte Carlo sign-flip test of the Fisher sharp null,9999 flips,seed20261016, p=(1+#permuted absolute statistics≥observed)/(B+1). The test assumes assignments independent and equally likely within frozen pairs and outcomes fixed under the sharp null. It is not the primary missing-data analysis and must not silently discard a missing cluster. A readout from a list of differences does not validate allocation, consent, blinding or cohort integrity.

## Missing outcomes: specified but not implemented here

Record reason and timing; continue assessment after intervention discontinuation where consent allows. No grade/publication outcome is imputed as a learning score. Planned primary working analysis uses50 multilevel posterior-predictive imputations of missing endline scores, bounded0–24, with all baseline cohort members retained. Baseline missingness is resolved by assessment before allocation; later discovered invalid baselines require a recorded amendment and sensitivity analysis.

Working model: latent Gaussian endline response, observed/imputed values truncated to[0,24], conditional on centered baseline transfer, assignment, baseline×assignment interaction, educational stage, counterbalanced task form, baseline self-reported access barrier and authorized accommodation indicator; fixed pair intercepts and a mentor-cluster random intercept. Predictors are coded and standardized before outcome unmasking. Centered continuous coefficients have Normal(0,6) priors in rubric-point units; pair intercepts Normal(12,6); random-intercept and residual SDs half-Normal(0,6). Missing secondary provenance scores use a separate bounded0–16 model and corresponding baseline task evidence; do not borrow an invented pretest.

Use four MCMC chains,2000 warmup+2000 retained iterations each; require R-hat<1.01, effective sample size>1000 for assignment and variance parameters, no divergent transitions after tuning, and posterior predictive checks for boundary mass and arm/cluster distributions. Draw50 well-separated posterior predictive completed datasets after convergence. Diagnostics and model code must be independently checked before registration. If fit fails, report the failure; do not choose a replacement after seeing treatment estimates. A prespecified amendment before unmasking may simplify interaction terms with justification.

For each completed dataset compute the same equal-pair contrast and complete-data variance. Pool estimates with Rubin total variance Ubar+(1+1/M)B and Barnard–Rubin small-sample degrees of freedom, using complete-data df=P−1. The reference is Barnard and Rubin(1999), DOI10.1093/biomet/86.4.948. Model-based imputation adds assumptions to randomization; resulting inferences are not presented as assumption-free design results.

Pattern-mixture sensitivity: shift treatment-arm imputed values−1 and−2points from the working model, clamp to[0,24], repeat corresponding comparator shifts and symmetric adverse/favorable combinations. Report0/24 bounds for all missing outcomes, a tipping-point map and numbers missing per arm/pair. A wholly missing cluster cannot be deleted with its partner to recover nominally complete pairs. Differential missingness/privacy withdrawals limit causal certainty even if the working-model estimate is positive.

## Multiplicity and reporting

Two-sidedalpha.05 primary. Only if primary rejects, test provenance mastery at.05 as fixed-sequence secondary; otherwise interval descriptive. All other outcomes/interactions exploratory, with intervals and clear labels. Student-weighted, unadjusted complete-case and per-protocol contrasts are sensitivity descriptions with distinct estimands/selection assumptions. No subgroup is declared benefited from an interaction-insensitive overall trial.

Record course stage, domain and access accommodations only under consent/ethics plan. Suppress disclosure-risk cells under institutional rules determined before collection. Do not use trial results to advertise Stanford/AERA endorsement or guaranteed acceptance.

## Completed DataCite audit

Inputs exactly three frozen first-page100-record queries in frozen-query.json. Normalize DOI URL prefixes and case, enforce uniqueness and publicationYear2024/2025. Audit public metadata-projection.json with research_tools.py audit. Group by declared resourceTypeGeneral and ALL; count fields/relationships, not people. ORCID scheme entries are checked for syntax/checksum only; no OAuth information is available. Keep resource version distinct from metadataVersion, Issued from registered/created/published, and metadata CC0 from resource rights. No inferential prevalence CI, learning estimate, content-access claim or ingestion-readiness count is produced. Missing values mean absent in this response.

## Completed simulation

research_tools.py simulate: NumPy2.3.5/SciPy1.17.0,seed20261016,20,000 independent replicates/scenario. P48,m12. Conditional within-pair individual change variance1; cluster residualvarianceρ∈{.05,.12,.20},individual residualvariance1−ρ. Independent retained n~Binomial(12,r),r∈{1,.85,.70},clamped≥1. Cluster means = independentNormal(0,ρ) + independentNormal(0,(1−ρ)/n). Difference treated−control; shared pair intercept cancels. Compare t statistic against t47. Effect added to treated meanδ=.30. Calculate null rejection, power, MCSE=sqrt(p(1−p)/20000),95% interval coverage. No cluster loss, informative missingness, heterogeneous effects, instrument error, baseline imbalance or spillover; no empirical learning effects. All reported scenario numbers are in design-analysis.json. Conditional residual ICC differs from a marginal ICC that includes matched-pair variance.