# PRE-REGISTRATION ADDENDUM v2 — Bayes-benchmark primary analysis
Written: 2026-08-22T21:40Z, BEFORE examination of any treatment-arm outcome data
(no observation file yet contains a completed my_scores record; verified prior to writing).
Supersedes the PRIMARY outcome in prereg.md (sha256 9744473b117bb9bc5c426cac995fe4ba59a1b4f2f4077dbe313445c5bd75d994);
v1 outcomes retained as descriptive secondary analyses.

## Reason for amendment
Design analysis (not data) shows the v1 primary outcome — absolute standardized deviation
from the frozen context mean, compared across doses — is NOT centred at a constant under
the rational-null hypothesis. A Bayesian reviewer combining an equally-noisy private
signal with n visible signals shifts toward the context mean by the optimal weight
w_B(n) = n/(n+1); the standardized expected deviation follows the closed form

    Y_B(n) = 1 / sqrt( n(n+1) )

which itself falls by a factor sqrt(420/30) ~= 3.74 between dose 5 and dose 20.
A raw dose contrast therefore rejects "no effect" even for perfectly rational reviewers,
and cannot separate information use from social proof. The amended primary estimand makes
the separation explicit.

## Amended PRIMARY estimand
For each (review, dimension) observation with non-degenerate context (>=2 shown scores):

    Effective weight on context mean:  w_eff = 1 - Y_obs / Y_ind,
        Y_obs    = | submitted - context_mean | / sd(shown scores)
        Y_ind(n) = sqrt(1 + 1/n)          (expected standardized deviation of an
                                           independent draw from the same law)

compared against the Bayesian-optimal weight w_B(n) = n/(n+1):
    CONFORMITY GAP  Delta(n) = w_eff(n) - w_B(n).
Primary test: one-sample t-test of H0: Delta = 0 pooled across doses 5 and 20
(reviewer FE, dimension FE, cluster-robust by reviewer), two-sided alpha .05.
Shape tests: (a) Delta(20) - Delta(5) (non-saturation = social-proof signature);
(b) Delta computed within low- vs high-dispersion contexts (information weighting).

Interpretation bands (pre-stated):
    Delta > 0            -> over-conformity (herding beyond Bayesian optimum)
    |Delta| <= 0         -> consistent with rational use of shown evidence
    Delta < -0.05        -> under-use of available information
    w_eff near 1 at both doses -> pure copying (context replaces judgment)
    w_eff near 0 at both doses -> independence (context ignored)

## Model assumptions declared
Equal-variance Gaussian signals around a paper-specific mean; integer-score coarsening
ignored in the standardization (robustness: rank-based variant reported); context mean
treated as exogenous to the focal reviewer (true by platform construction: frozen at
licence issue, excludes own reviews).

## Everything else in prereg.md stands unchanged
(outcomes S1-S5, exclusions, power statement, ethics, locked pipeline file).
analyse_exp.py is amended in step with this addendum; the v1 outputs remain printed
as descriptive tables.