Paper 3, Study 2 — predeclared plan v1.0: does modelling the skewness remove the directional failure of small-sample intervals for a difference in means? (Behrens–Fisher programme)

Description (paste): Prospective registration of the predeclared plan (v1.0, frozen 6 Nov 2026) for Study 2 of Paper 3 in a programme on the direction of small-sample interval failure for a difference in arithmetic means. Study 2 asks whether intervals that model the skewness escape the directional failure, and at what cost when the model is wrong. The intervals compared are posterior intervals from lognormal, gamma, Weibull and skew-normal likelihoods (correct and misspecified), stacking over candidate models, and informative shape priors. They are compared with the fiducial interval, the Bayesian bootstrap, Welch, bootstrap-t and a two-sample beta-bootstrap-t. The design has 156 settings of positive-valued populations (13 group pairings, 6 sample-size pairs, 2 mean differences). Hypotheses T1–T7 are stated with criteria, including a primary and two sensitivity bars for T2. The package contains the frozen plan (with a typeset PDF copy) and its SHA-256 fingerprint, all code including the frozen confirmatory analysis, grid-accuracy and leave-one-out validations, the Monte Carlo endpoint check that set the draw counts, and the pilot runs on non-study seeds used only for code checks and timing. No Study 2 computation on study data had been run at the time of deposit. AI-use note (paste, or use the programme's final wording): The code and checks were developed with Claude (Anthropic) as a computational assistant under the author's direction; the author developed the design decisions and hypotheses and is responsible for the registration.