# A09 · Prospective analysis specification

Version 1.0. No participant outcomes have been collected. The actual completed analyses are the NASA feasibility audit and artificial-data design sensitivity. Tools implement audit, geometry, assignment and **complete-cohort** contrasts; they do not implement the missing-data model below.

## Design, units and identifiers

Target 32 schools, one instructor in each school, four distinct science sections per instructor, 24 fixed baseline-cohort participants per section. Each block receives one section in each cell (I,R)=(0,0),(0,1),(1,0),(1,1). I is offer of immersive delivery with accessible alternatives; R is structured prediction–evidence–revision instruction. Baseline roster, consent and assessment precede allocation. Record seed after roster lock and keep the real allocation concealed until required.

School IDs and instructor IDs are one-to-one in this design. Section IDs and pseudonymous student IDs are globally unique. A learner cannot appear in multiple randomized sections. If a school's structure requires a different design, amend and register it before allocation; do not force it into this tool's assumptions.

## Primary outcome and estimand

Mean of two blinded human raters' 0–20 delayed-transfer total scores at calendar day 21 (±3 school days). Keep every baseline-cohort learner in the assigned offer group regardless of actual headset use. No-headset use is not an exclusion. No study score determines course grades.

For block b, define cell mean μ_bir across its 24 baseline-cohort learners. Primary block contrast d_b=μ_b11−μ_b10−μ_b01+μ_b00. Primary estimate is mean(d_b), with equal weights for schools/blocks rather than for nominal class enrollment. Variance estimate is sample variance of d_b divided by B. Use approximate t(B−1) 95% interval and two-sided α=.05 test. Variability across heterogeneous block contrasts makes this estimate conservative under independent randomizations and no interference; it is not an exact finite-sample weak-null test. Common school/instructor intercepts cancel within block. Treatment-specific cross-section interference does not cancel and threatens identification.

A naïve permutation of observed outcomes tests a sharp global no-effect null, not a composite no-interaction null in the presence of unknown main effects. No exact interaction permutation claim is made. Report cell means and all simple effects with uncertainty to make the interaction interpretable.

## Secondary analysis and multiplicity

Revision main contrast: (μ_b01+μ_b11−μ_b00−μ_b10)/2. Immersion main contrast: (μ_b10+μ_b11−μ_b00−μ_b01)/2. Apply Holm correction to this two-test secondary family. Immediate transfer, presence, effort, symptoms, attendance, implementation and cost are exploratory estimates with clearly labeled intervals. Do not select the best endpoint after viewing results.

A prespecified secondary baseline-adjusted model includes baseline total and fixed task form sequence, allocation main effects and interaction, with section nesting and school-block intercepts. Use appropriate section/school correlation handling and small-sample correction, report the model formula and software/version, and retain the primary block contrast. Relationships between process records and outcomes are descriptive, not identified causal mediation.

## Missing data: planned, not implemented in the complete-cohort utility

Document missingness by cell, school, baseline score, access route and reason. Offer accessible make-up assessment within the fixed window without changing the task. Do not replace a missing learner with a newly recruited learner.

Before primary analysis, fit a joint multilevel normal model for immediate and delayed scores with 50 imputations, section random intercepts and school-block fixed intercepts. Delayed predictors include baseline score (centered), immediate score, fixed form sequence, I, R, I×R, attendance (0–3 sessions), actual access route and pre/post symptom indicators. Impute missing immediate scores jointly using the same fully observed predictors without conditioning on delayed scores that are themselves absent. Use weakly regularizing normal priors scaled to the 0–20 range (intercept N(10,10²); standardized-predictor slopes N(0,5²)) and half-normal(0,5) residual/section SD priors. Draw missing outcome values from the bounded predictive distribution [0,20]. If necessary, adapt computation rather than dropping hierarchical terms silently.

Run at least four chains, require rank-normalized R-hat<1.01 and bulk/tail effective sample sizes>400 for reported parameters, inspect predictive score distributions by condition and block, and increase draws or revise an explicitly documented model when diagnostics fail. This is a planned model and requires a separately reviewed implementation; its fit is not claimed here.

For each completed dataset calculate block contrasts and their within-imputation variance. Pool Q̄=mean(Q_l), Ū=mean(U_l), between-imputation variance B_MI=sampleVar(Q_l), T=Ū+(1+1/L)B_MI. Use the Barnard–Rubin small-sample reference (Biometrika86(4):948–955;doi10.1093/biomet/86.4.948) with complete-data df ν_com=B−1. Let λ=(1+1/L)B_MI/T; ν_old=(L−1)/λ² (infinite when λ=0);ν_obs=((ν_com+1)/(ν_com+3))ν_com(1−λ);ν=(1/ν_old+1/ν_obs)^−1. Use t(ν) for pooling, flag nonpositive/undefined variance cases, and disclose software and validation against a hand-worked example before main analysis. Normal intervals are a reported sensitivity, not an unannounced replacement. Imputation under missing-at-random is an assumption, especially after device discomfort or whole-section loss.

Perform pattern-mixture sensitivity shifting missing delayed scores by −2,−1,+1,+2 rubric points within each cell separately, clipping to [0,20], plus adversarial shifts opposing the estimated interaction. Report tipping patterns and cell-specific missing fractions. Report worst-case bounded contrasts using missing outcomes assigned 0 or 20 in the directions maximizing/minimizing the interaction. If an entire cell/section is absent, explicitly show the interval's reliance on imputation. No complete-case estimate is the sole analysis when outcomes are missing.

## Design sensitivity already executed

Seed20261016;10,000 replicates per scenario; blocks16/32/48;four sections per block;24learners per section;classICC.05/.10/.15. Standardized class-mean residual variance v=ICC+(1−ICC)/24. Four independent Gaussian residuals per block generate the interaction residual, whose variance is4v. Add constant interactionδ=.40. Test using the same across-block t statistic. Report null rejection and MonteCarlo SE=sqrt(p(1−p)/10000). Normal-approximation80% MDE=(z_.975+z_.80)sqrt(4v/B). Independent errors, complete outcomes, constant interaction and no floor/ceiling effects are assumptions. These are artificial observations, not primary findings from learners.

## Source audit rules

Use the exact query in research_tools.py and retrieval.json. Audit unique names, explicit solution types, finite/missing values and sequential filters. Core: PublishedConfirmed;pl_controv_flag0;sy_snum1;cb_flag0;discoverymethod in Transit/RadialVelocity/TransitTimingVariations;positive finite period and semi-major axis;0≤e<.95;all three limit flags0;reference present. Enhanced: positive upper and negative lower errors for period, axis and e;positive lower period/axis;0≤lower e and upper e<1. Error bars are marginal reported bounds, not a joint posterior. No missing e is set to zero. No imaging/microlensing projected separation enters as an orbital axis.

## Deviations and release

Freeze forms, manifest and smallest important difference before allocation. Publicly version amendments with dates and whether outcome information had been seen. Participant records require separately approved access; no individual records are included in this package. Original source CSV and third-party text/images are not redistributed. A later TAP response is a new snapshot, not automatically a reproduction of the hash-pinned response.