The deflated-Welch statistic: a closed-form, guaranteed-level test for heteroscedastic one-way ANOVA William J. Dwyer, MD, MPH, FAAP — Department of Mathematics and Statistics, University of Massachusetts Lowell. ORCID 0009-0004-0855-7222. Concept DOI (always resolves to the latest version): 10.5281/zenodo.21908169. What this is The reproducibility deposit for the deflated-Welch statistic T_BB, a closed-form, guaranteed-level test for heteroscedastic one-way ANOVA (the Behrens–Fisher problem for k ≥ 3 groups). Welch's test becomes liberal under skew and unstable variance weights at small samples; T_BB = Q(s²)·exp(−R) keeps the ordinary group means and buys a guaranteed level by deflating the Welch quadratic by a Berger–Boos scale-inflation radius R. Three operating points are provided: a fixedcalibrated radius (κ_s), a design-adaptive near-guarantee radius (closed-form polygamma Cornish–Fisher with a finite-nkurtosis guard), and a fully proved smallest-eigenvalue radius R_eig (Gaussian, extended under bounded kurtosis). What the deposit contains Manuscript (author + anonymized) and a derivations supplement (DA1–DA13) plus a long-form derivations companion, covering: why Welch fails under skew in closed form; the Berger–Boos deflation and its exact worst-case radius; the polygamma-cumulant Cornish–Fisher radius with saddlepoint-exact normal backbone; the excess-kurtosis tail term with its finite-n upper-confidence guard; the imbalance correction; the fully proved smallest-eigenvalue radius (with the k-group multiplicity fix, free-β optimization, and the proved-under-bounded-kurtosis widening); and the k-sample Behrens–Fisher null distribution. Interactive demonstrator rerun_cochran/honest_anova.html — computes raw-mean Welch, the fixed / adaptive / proved T_BB radii, the estimand-changing transform routes, and the full routing receipt in the browser, reproducing the deposited Python. Its engine is extracted as a standalone Node module (m01A_anova_engine.js) and checked cell-by-cell against Python across an 84-design taxonomy (verify_anova_engine_taxonomy.py/.js, max |Δp| = 0.00000). Reproducibility scripts (rerun_cochran/, rerun/) — every reported number traces to a named, deterministically-seeded script (size/power/surface, the calibration and information-limit decompositions, the proved-radius verification, the imbalance calibration, the skew-router branch, and the figures). Real-data evidence — anova_flip_scan.py scans 2,783 public one-way layouts (254 datasets): guaranteed T_BBwithholds ~41% of Welch-significant calls, concentrated where the weight-instability screen fires, and never manufactures significance (Table 7 / Figure 15). Figures and the deterministic deposit builder (fixed timestamps → stable md5). All evaluation is simulation-based; the one empirical component is the public-dataset scan, which uses only openly distributed data. Code is released under the MIT License; text and figures under CC BY 4.0. Version history (consolidated changelog) Published version DOIs are marked ✅; the concept DOI above always resolves to the latest. Staged versions were rolled into the next published one unless noted. v1.0.77 ✅ 10.5281/zenodo.22167690 (2026-08-30): CSDA guide-for-authors conformance — abstract trimmed to 247 words (from 284), keywords cut to 7 (from 11), the withholding highlight shortened to ≤85 characters, and the arXiv PDF/source regenerated. No change to methods, results, figures, or code. v1.0.76 ✅ 10.5281/zenodo.22167536 (2026-08-30) — AI-disclosure heading aligned to Elsevier. The manuscript's declaration heading is now "Declaration of generative AI and AI-assisted technologies in the manuscript preparation process" (was "Use of generative AI"); the disclosure body is unchanged. Prepared alongside an Elsevier-compliant cover-letter variant and an EM suggested-reviewer sheet (both kept outside the deposit). docx/pdf rebuilt; deterministic md5 refreshed. v1.0.75 ✅ 10.5281/zenodo.22167304 (2026-08-30) — Submission-sharpening pass. Graphical abstract + Elsevier Highlights; figures and tables renumbered into reading order with per-table Source clauses; the validity–power frontier (Figure 8) now carries the proved R_eig operating point (100% validity, size-adjusted power 0.613, merge_tbb_proved_frontier.py); new Section 7 "Recovering power by design" + Table 8 (rc_anova_power_by_design.py); and a live required-n calculator in honest_anova.html (per-group and total n for 80% power, "power now @ total n"), with a numeric-heading CSS fix and the engine re-verified against Python at 0.00000. v1.0.74 ✅ 10.5281/zenodo.22165892 (2026-08-29) — Proved-under-bounded-kurtosis radius (DA12.6). The proved non-normal widening now keys on excess kurtosis, √(1 + κ̂·(n−1)/(2n)), from the exact Var(s²/σ²) = 2/(n−1) + κ/n, so symmetric heavy tails (Student-t) are covered where the old skew form √(1 + 0.75·skew²) under-covered; tbbProvedswitched to the kurtosis form across the demonstrator, engine, and Python truth (re-verified JS-vs-Python at 0.00000); new rc_anova_kurtosis_proof.py + deep-dive. v1.0.73 ✅ 10.5281/zenodo.22165709 (2026-08-29) — Reconstructed & verified demonstrator engine (standalone Node module + taxonomy verifier, max |Δp| = 0.00000 across 84 designs; Yuen zero-variance fix; T_BB-routed presets both directions); series-impact deep-dive (the corrected R_eig k-group multiplicity gap also reaches m03 and m01t). v1.0.72 (2026-08-29) — Title set to "The deflated-Welch statistic…"; corrected + optimized proved radius R_eig (β/k multiplicity fix + β-optimization, DA12); real-data Welch-vs-T_BB flip scan (2,783 layouts; Table 7 / Figure 15) + demonstrator imbalance-factor fix; long-form derivations companion. v1.0.71 / v1.0.70 (2026-08-21) — Zhang normal-reference comparator benchmarked on the efficiency frontier (valid on only 24% of designs, in the calibrated-liberal cluster); k = 2 adaptive-radius case-study fold (design-scaling vs shape-keying distinction). v1.0.69 ✅ 10.5281/zenodo.22035826 (2026-08-20) — HTML R1/R2 presentation pass + Figure 9 adaptive per-cluster label merge. v1.0.68 ✅ 10.5281/zenodo.22033737 (2026-08-20) — Companion consolidation into a single six-column Table 6; Figures 11–14 harmonized into one story. v1.0.67 / v1.0.65 / v1.0.60 (2026-08-19/20) — Guarded-reference naming-collision fix; the 40,000-replication expanded-frontier pin (Table 3 + Figure 8) with the symmetric-heteroscedastic skew-router branch; the mean-preserving lightened-R_eig do-not-use fallback. v1.0.59 ✅ 10.5281/zenodo.21995320 (2026-08-18) — Reporting standard + honest_anova.html demonstrator re-aligned to the current T_BB methods paper. v1.0.57 ✅ 10.5281/zenodo.21986847 (2026-08-17) — Reviewer-comprehension pass (multi-paragraph abstract, contributions list, trimmed captions); proved radius R_eig added as a Table 3 scorecard row; corner tail-index correction (N−k)/2 (low-order moments exist in every deployed design). v1.0.56–v1.0.49 (2026-08-16) — The k-sample Behrens–Fisher corner-distribution program: two-moment scaled-χ² corner reference, derived corner cumulants, the secular-eigenvalue law + closed CGF + power-law tail, consolidated into derivations DA13 with a prior-art/novelty audit. v1.0.48 ✅ 10.5281/zenodo.21963458 (2026-08-16) — The unifying λ(z) correction (a smooth instability-keyed deflation strength). v1.0.45 ✅ 10.5281/zenodo.21962965 (2026-08-16) — Atomic sparsity index + bootstrap-t edge hardening + shape-aware pooled standardized-residual bootstrap (SA-PSRB); multivariate transfer to m03. v1.0.44–v1.0.41 (2026-08-16) — Shape-moment re-injection order (skew is the sweet spot), validated and hardened pooled standardized-residual bootstrap, atomic weight-noise probes. v1.0.40 ✅ 10.5281/zenodo.21961667 (2026-08-16) — Log-domain weight-stabilization probe (negative for stabilization; clarifies the size-adjusted oracle ceiling); includes the oracle-power gap decomposition (≈92% conservatism, ≈8% estimation). v1.0.37 ✅ 10.5281/zenodo.21961327 (2026-08-16) — Residual-bootstrap qualification of the shoot-out + the first proved Gaussian smallest-eigenvalue radius R_eig (DA12, the p = 1 specialization of the m03 theorem). v1.0.36 (2026-08-15) — Figure 11 T_BB-region colour fix (amber, matching the routing figures). v1.0.27 ✅ 10.5281/zenodo.21908170 — Earlier published baseline of the deposit. Provenance: every number traces to a named, deterministically-seeded script listed in the manuscript Declarations; the demonstrator engine reproduces the deposited Python to max |Δp| = 0.00000 across the taxonomy verification. License. Code and scripts in the deposit are released under the MIT License; text and figures under CC BY 4.0. Reuse is permitted with attribution to the author and citation of the concept DOI above. How to cite. Dwyer, W. J. The deflated-Welch statistic: a closed-form, guaranteed-level test for heteroscedastic one-way ANOVA. Reproducibility deposit, Zenodo. https://doi.org/10.5281/zenodo.21908169
William Dwyer· Zenodo (CERN European Organi...· 2 citations
Sparse departures from independence in two-way tables: a heteroscedasticity profile and detection boundary, an adaptive higher-criticism gate, and an assumption-lean exact anchor William J. Dwyer, MD, MPH, FAAP — Department of Mathematics and Statistics, University of Massachusetts Lowell. ORCID 0009-0004-0855-7222. Concept DOI (always resolves to the latest version): 10.5281/zenodo.21844797. Published v1.0.0:10.5281/zenodo.21844798. What this is The reproducibility deposit for a single combined manuscript on detecting sparse departures from independence in a two-way contingency table — the regime where dependence hides in a few cells rather than spreading across the table, so the omnibus chi-square is under-powered and a naive per-cell scan mis-calibrates. It is organized in three parts under one set of front/back matter, with a shared derivations supplement (D02): Part I — the heteroscedasticity profile and the detection boundary. The per-cell standardized deviations are heteroscedastic under the margin-conditional null; profiling that heteroscedasticity gives a closed-form detection boundary separating the sparsity/strength regimes where any test can succeed from those where none can. Part II — an adaptive higher-criticism gate. A higher-criticism statistic tuned to the margin-conditional cell law attains that boundary, with its exact null law and power characterized. Part III — an assumption-lean exact anchor and reporting apparatus. An exact margin-conditional calibration anchor and a routing rule, so a scan that mis-sizes under the asymptotic reference is replaced by one that holds its level: on a corpus of 5,543 real tables the asymptotic per-cell scan mis-sizes about two-thirds of them (mean realized size ≈ 0.33 against a 0.05 target) while the exact anchor holds near 0.01. What the deposit contains Combined manuscript (manuscripts/Dwyer_M02_Combined.{docx,pdf} + M02_Combined_Manuscript.md) and the three part-sources (manuscripts/parts/, provenance for the assembled combined text), plus the D02 derivations companion (derivations/). Verification and study code (code/) — the boundary, exact-anchor, and higher-criticism verification scripts and the power/size study drivers (numpy/scipy, fixed seeds); the docx builder (build_docx.py), the shared math-typography core (mseries_mathtype.py), the inline- and caption-math delimiters, the combined assembler (assemble_combined.py), and the audit gates (structure_audit.py, math_render_audit.py). Locked data (data/) — the study outputs (size/power, boundary, estimated-margins, efficiency) and the higher-replication "big box" runs, so every number regenerates. Figures (figures/), the novelty reviews (novelty_reviews/), the prior-art / adversarial / consistency audits (audits/), and the in-browser detector tools/honest_detection.html. All evaluation is simulation-based; the one empirical component is the public-corpus calibration scan, which uses only openly distributed contingency tables. Code is released under the MIT License; text, figures, and data under CC BY 4.0. How to cite Please cite this deposit if you use the package or the method. Citing the concept DOI references the work in general and always resolves to the latest version; cite a specific version DOI to point at an exact snapshot. Dwyer, W. J. (2026). Sparse departures from independence in two-way tables: a heteroscedasticity profile and detection boundary, an adaptive higher-criticism gate, and an assumption-lean exact anchor — reproducibility deposit [Software]. Zenodo. https://doi.org/10.5281/zenodo.21844797 BibTeX: bibtex @software{dwyer_m02_2026, author = {Dwyer, William J.}, title = {Sparse departures from independence in two-way tables: a heteroscedasticity profile and detection boundary, an adaptive higher-criticism gate, and an assumption-lean exact anchor --- reproducibility deposit}, year = {2026}, publisher = {Zenodo}, doi = {10.5281/zenodo.21844797}, url = {https://doi.org/10.5281/zenodo.21844797}, orcid = {0009-0004-0855-7222} } The DOI above is the concept DOI (resolves to the latest version); to cite a specific release use that version's DOI in place of it (e.g. 10.5281/zenodo.21844798 for v1.0.0). When the accompanying journal article appears, please cite it as the primary reference for the method and this deposit as the reproducibility archive. Version history v1.0.3 — deterministic recut (2026-08-30): the bundle is now cut with the shared mseries_deposit.write_deterministic_zip, so rebuilding the same content yields a byte-identical zip and a stable md5. Every manuscript, derivation, figure, dataset, code file, novelty review, and audit is byte-identical to v1.0.2 (all files SHA-256-matched except the three version-stamped ones). No number, theorem, table, figure, or dataset changed. Publishes as a New Version on concept 10.5281/zenodo.21844797 (build_m02_deposit.py; md5 8f2fa9f7e814ba807710480a7f60cb65, 112 files, 6,044,685 bytes). v1.0.2 — impact-first reframe (2026-08-23): the introduction and abstract reframed to lead with the applied motivation (sparse independence departures in genomics, network/text co-occurrence, pharmacovigilance, ecology, survey cross-tabulation) and the corpus calibration failure, before the detection-boundary theory. No number, theorem, figure, or dataset changed. v1.0.1 — published (2026-08-08): adds the Zenodo concept DOI to the manuscript Availability statement and CITATION.cff, and the widened Figure 8 top box. Content otherwise identical to v1.0.0. v1.0.0 ✅ 10.5281/zenodo.21844798 — first published deposit: the combined three-part manuscript, the D02 derivations, the verification and study code with fixed seeds and locked outputs, all figures, the in-browser detector, and the prior-art / adversarial / consistency audits. Provenance: every number traces to a named, deterministically-seeded script under code/; the combined manuscript is assembled by code/assemble_combined.py and built by code/build_docx.py. Related identifiers: T_root methodology 10.5281/zenodo.21522471; exact conditional engine 10.5281/zenodo.21831680.
William Dwyer· Zenodo (CERN European Organi...· 0 citations
A guaranteed-coverage confidence interval for the two-sample standardized effect William J. Dwyer, MD, MPH, FAAP — Department of Mathematics and Statistics, University of Massachusetts Lowell. ORCID 0009-0004-0855-7222. Concept DOI (always resolves to the latest version): minted on first publication. What this is The reproducibility deposit for the m01te methods paper: a guaranteed-coverage confidence interval for the two-sample standardized effect (Cohen's d) at the skewed, unequal-variance, small-n corner where the textbook interval silently under-covers. The noncentral-t inversion assumes normal data and equal variances; at a lognormal, four-to-one variance-ratio, n = 10 design its realized coverage falls to 0.81 against a nominal 0.95, and a naive percentile bootstrap of dfalls further, to 0.78 — a joint failure of the mean-difference reference and the variance estimate that standardizes it, which resampling does not repair. The paper gives a three-tier recommendation, mirroring the companion two-sample test and the one-way effect-size paper: Classical — the noncentral-t / normal-approximation interval, the everyday default, liberal at the corner. Calibrated middle tier — the guaranteed two-sample test T_BB inverted for the mean difference at the full level, divided by the plug-in pooled scale. Closed-form and deterministic (no resampling), with near-nominal worst-case coverage 0.93 at about 1.6× the classical width. It keeps the mean-difference deflation that repairs the actual under-coverage while treating the scale at its point estimate; the over-covering numerator and the under-covering plugged-in scale roughly cancel to near nominal. Guaranteed floor — a Bonferroni combination of the T_BB-inverted mean-difference interval with a distribution-free bootstrap scale interval, carrying a proved finite-sample coverage floor (worst-case 0.97) at about 4× the classical width. What the deposit contains Manuscript (author + anonymized markdown; built .docx/.pdf, including a cross-reference–hyperlinked variant) and the derivations (D1–D6): the estimand and its d_av scale; the T_BB-inverted mean-difference interval; the exact Bonferroni coverage floor of the ratio interval; why the classical standard error under-covers off its normal/equal-variance premise; the deterministic-simulation confirmation; and the calibrated middle tier with its compensation argument. Reproducibility runner — rerun/rc_m01te_coverage.py computes, for each design cell across the parent-distribution × sample-size × variance-ratio × effect grid, the realized coverage and mean width of all four intervals (classical, percentile-bootstrap, calibrated middle, guaranteed floor). Every number regenerates from this deterministically-seeded script (seed 20260826); its locked output CSV is deposited. Figure — figures/m01te_coverage.png (built by make_m01te_figure.py): the four coverage curves cell by cell across the grid, the classical and bootstrap curves sliding below nominal at the corner, the calibrated curve tracking near it, and the guaranteed curve holding above it. All evaluation is simulation-based. Code is released under the MIT License; text and figures under CC BY 4.0. How to cite Please cite this deposit if you use the package or the method. Citing the concept DOI references the work in general and always resolves to the latest version; cite a specific version DOI to point at an exact snapshot. Dwyer, W. J. (2026). A guaranteed-coverage confidence interval for the two-sample standardized effect: reproducibility deposit (Version 1.0.0) [Software]. Zenodo. https://doi.org/⟨concept DOI⟩
William Dwyer· Zenodo (CERN European Organi...· 0 citations
A guaranteed-coverage confidence interval for the two-sample standardized effect William J. Dwyer, MD, MPH, FAAP — Department of Mathematics and Statistics, University of Massachusetts Lowell. ORCID 0009-0004-0855-7222. Concept DOI (always resolves to the latest version): 10.5281/zenodo.22114522. Published v1.0.0:10.5281/zenodo.22114523 (2026-08-26, the earlier two-tier construction). The three-tier update described below is staged as a pending new version (v1.1.0) on the same concept DOI. What this is The reproducibility deposit for the m01te methods paper: a guaranteed-coverage confidence interval for the two-sample standardized effect (Cohen's d) at the skewed, unequal-variance, small-n corner where the textbook interval silently under-covers. The noncentral-t inversion assumes normal data and equal variances; at a lognormal, four-to-one variance-ratio, n = 10 design its realized coverage falls to 0.81 against a nominal 0.95, and a naive percentile bootstrap of dfalls further, to 0.78 — a joint failure of the mean-difference reference and the variance estimate that standardizes it, which resampling does not repair. The paper gives a three-tier recommendation, mirroring the companion two-sample test and the one-way effect-size paper: Classical — the noncentral-t / normal-approximation interval, the everyday default, liberal at the corner. Calibrated middle tier — the guaranteed two-sample test T_BB inverted for the mean difference at the full level, divided by the plug-in pooled scale. Closed-form and deterministic (no resampling), with near-nominal worst-case coverage 0.93 at about 1.6× the classical width. It keeps the mean-difference deflation that repairs the actual under-coverage while treating the scale at its point estimate; the over-covering numerator and the under-covering plugged-in scale roughly cancel to near nominal. Guaranteed floor — a Bonferroni combination of the T_BB-inverted mean-difference interval with a distribution-free bootstrap scale interval, carrying a proved finite-sample coverage floor (worst-case 0.97) at about 4× the classical width. What the deposit contains Manuscript (author + anonymized markdown; built .docx/.pdf, including a cross-reference–hyperlinked variant) and the derivations (D1–D6): the estimand and its d_av scale; the T_BB-inverted mean-difference interval; the exact Bonferroni coverage floor of the ratio interval; why the classical standard error under-covers off its normal/equal-variance premise; the deterministic-simulation confirmation; and the calibrated middle tier with its compensation argument. Reproducibility runner — rerun/rc_m01te_coverage.py computes, for each design cell across the parent-distribution × sample-size × variance-ratio × effect grid, the realized coverage and mean width of all four intervals (classical, percentile-bootstrap, calibrated middle, guaranteed floor). Every number regenerates from this deterministically-seeded script (seed 20260826); its locked output CSV is deposited. Figure — figures/m01te_coverage.png (built by make_m01te_figure.py): the four coverage curves cell by cell across the grid, the classical and bootstrap curves sliding below nominal at the corner, the calibrated curve tracking near it, and the guaranteed curve holding above it. All evaluation is simulation-based. Code is released under the MIT License; text and figures under CC BY 4.0. How to cite Please cite this deposit if you use the package or the method. Citing the concept DOI references the work in general and always resolves to the latest version; cite a specific version DOI to point at an exact snapshot. Dwyer, W. J. (2026). A guaranteed-coverage confidence interval for the two-sample standardized effect: reproducibility deposit (Version 1.0.0) [Software]. Zenodo. https://doi.org/10.5281/zenodo.22114522
William Dwyer· Zenodo (CERN European Organi...· 0 citations
Sparse departures from independence in two-way tables: a heteroscedasticity profile and detection boundary, an adaptive higher-criticism gate, and an assumption-lean exact anchor William J. Dwyer, MD, MPH, FAAP — Department of Mathematics and Statistics, University of Massachusetts Lowell. ORCID 0009-0004-0855-7222. Concept DOI (always resolves to the latest version): 10.5281/zenodo.21844797. Published v1.0.0:10.5281/zenodo.21844798. What this is The reproducibility deposit for a single combined manuscript on detecting sparse departures from independence in a two-way contingency table — the regime where dependence hides in a few cells rather than spreading across the table, so the omnibus chi-square is under-powered and a naive per-cell scan mis-calibrates. It is organized in three parts under one set of front/back matter, with a shared derivations supplement (D02): Part I — the heteroscedasticity profile and the detection boundary. The per-cell standardized deviations are heteroscedastic under the margin-conditional null; profiling that heteroscedasticity gives a closed-form detection boundary separating the sparsity/strength regimes where any test can succeed from those where none can. Part II — an adaptive higher-criticism gate. A higher-criticism statistic tuned to the margin-conditional cell law attains that boundary, with its exact null law and power characterized. Part III — an assumption-lean exact anchor and reporting apparatus. An exact margin-conditional calibration anchor and a routing rule, so a scan that mis-sizes under the asymptotic reference is replaced by one that holds its level: on a corpus of 5,543 real tables the asymptotic per-cell scan mis-sizes about two-thirds of them (mean realized size ≈ 0.33 against a 0.05 target) while the exact anchor holds near 0.01. What the deposit contains Combined manuscript (manuscripts/Dwyer_M02_Combined.{docx,pdf} + M02_Combined_Manuscript.md) and the three part-sources (manuscripts/parts/, provenance for the assembled combined text), plus the D02 derivations companion (derivations/). Verification and study code (code/) — the boundary, exact-anchor, and higher-criticism verification scripts and the power/size study drivers (numpy/scipy, fixed seeds); the docx builder (build_docx.py), the shared math-typography core (mseries_mathtype.py), the inline- and caption-math delimiters, the combined assembler (assemble_combined.py), and the audit gates (structure_audit.py, math_render_audit.py). Locked data (data/) — the study outputs (size/power, boundary, estimated-margins, efficiency) and the higher-replication "big box" runs, so every number regenerates. Figures (figures/), the novelty reviews (novelty_reviews/), the prior-art / adversarial / consistency audits (audits/), and the in-browser detector tools/honest_detection.html. All evaluation is simulation-based; the one empirical component is the public-corpus calibration scan, which uses only openly distributed contingency tables. Code is released under the MIT License; text, figures, and data under CC BY 4.0. How to cite Please cite this deposit if you use the package or the method. Citing the concept DOI references the work in general and always resolves to the latest version; cite a specific version DOI to point at an exact snapshot. Dwyer, W. J. (2026). Sparse departures from independence in two-way tables: a heteroscedasticity profile and detection boundary, an adaptive higher-criticism gate, and an assumption-lean exact anchor — reproducibility deposit [Software]. Zenodo. https://doi.org/10.5281/zenodo.21844797 BibTeX: bibtex @software{dwyer_m02_2026, author = {Dwyer, William J.}, title = {Sparse departures from independence in two-way tables: a heteroscedasticity profile and detection boundary, an adaptive higher-criticism gate, and an assumption-lean exact anchor --- reproducibility deposit}, year = {2026}, publisher = {Zenodo}, doi = {10.5281/zenodo.21844797}, url = {https://doi.org/10.5281/zenodo.21844797}, orcid = {0009-0004-0855-7222} } The DOI above is the concept DOI (resolves to the latest version); to cite a specific release use that version's DOI in place of it (e.g. 10.5281/zenodo.21844798 for v1.0.0). When the accompanying journal article appears, please cite it as the primary reference for the method and this deposit as the reproducibility archive. Version history v1.0.3 — deterministic recut (2026-08-30): the bundle is now cut with the shared mseries_deposit.write_deterministic_zip, so rebuilding the same content yields a byte-identical zip and a stable md5. Every manuscript, derivation, figure, dataset, code file, novelty review, and audit is byte-identical to v1.0.2 (all files SHA-256-matched except the three version-stamped ones). No number, theorem, table, figure, or dataset changed. Publishes as a New Version on concept 10.5281/zenodo.21844797 (build_m02_deposit.py; md5 8f2fa9f7e814ba807710480a7f60cb65, 112 files, 6,044,685 bytes). v1.0.2 — impact-first reframe (2026-08-23): the introduction and abstract reframed to lead with the applied motivation (sparse independence departures in genomics, network/text co-occurrence, pharmacovigilance, ecology, survey cross-tabulation) and the corpus calibration failure, before the detection-boundary theory. No number, theorem, figure, or dataset changed. v1.0.1 — published (2026-08-08): adds the Zenodo concept DOI to the manuscript Availability statement and CITATION.cff, and the widened Figure 8 top box. Content otherwise identical to v1.0.0. v1.0.0 ✅ 10.5281/zenodo.21844798 — first published deposit: the combined three-part manuscript, the D02 derivations, the verification and study code with fixed seeds and locked outputs, all figures, the in-browser detector, and the prior-art / adversarial / consistency audits. Provenance: every number traces to a named, deterministically-seeded script under code/; the combined manuscript is assembled by code/assemble_combined.py and built by code/build_docx.py. Related identifiers: T_root methodology 10.5281/zenodo.21522471; exact conditional engine 10.5281/zenodo.21831680.
William Dwyer· Zenodo (CERN European Organi...· 0 citations
Reproducibility package for the interval-estimate paper of the contingency-table effect-size arc, the companion to the point-estimate paper M0f. It regenerates every result behind the exact conditional confidence interval for phi^2 (and Cramer's V): the pre-registered Berger-Boos simulation (C1 passed, C2 and C3 failed) frozen before the run; the post-registration exact conditional (mid-p) interval that turns the two failures into a positive result; its characteristic-function / cosine (CF/COS) extension to larger and denser tables; the certified 2x2 coverage floor; the exact conditional median-unbiased point estimate (the fold) that resolves the residual; the shape-by-effect factorial decomposition of the small-effect coverage dip into its additive mechanisms (mid-p atom, estimand gap, discreteness residual); and the direct exact-coverage sweeps. Includes the manuscript and Additional File 1 (docx + pdf), all figures and their black-and-white-safe generators, the derivation companions, the pre-registration, a prior-art audit, the shared estimator/interval code with its exact dynamic-programming tail engines (verified to ~3e-15), and a null-coverage regression self-test. Every reported number regenerates under recorded seeds; runs are staged, resumable, and memory-capped. MIT License for code; CC BY 4.0 for documents and data.
William Dwyer· Zenodo (CERN European Organi...· 0 citations
The deflated-Welch statistic: a closed-form, guaranteed-level test for heteroscedastic one-way ANOVA William J. Dwyer, MD, MPH, FAAP — Department of Mathematics and Statistics, University of Massachusetts Lowell. ORCID 0009-0004-0855-7222. Concept DOI (always resolves to the latest version): 10.5281/zenodo.21908169. What this is The reproducibility deposit for the deflated-Welch statistic T_BB, a closed-form, guaranteed-level test for heteroscedastic one-way ANOVA (the Behrens–Fisher problem for k ≥ 3 groups). Welch's test becomes liberal under skew and unstable variance weights at small samples; T_BB = Q(s²)·exp(−R) keeps the ordinary group means and buys a guaranteed level by deflating the Welch quadratic by a Berger–Boos scale-inflation radius R. Three operating points are provided: a fixedcalibrated radius (κ_s), a design-adaptive near-guarantee radius (closed-form polygamma Cornish–Fisher with a finite-nkurtosis guard), and a fully proved smallest-eigenvalue radius R_eig (Gaussian, extended under bounded kurtosis). What the deposit contains Manuscript (author + anonymized) and a derivations supplement (DA1–DA13) plus a long-form derivations companion, covering: why Welch fails under skew in closed form; the Berger–Boos deflation and its exact worst-case radius; the polygamma-cumulant Cornish–Fisher radius with saddlepoint-exact normal backbone; the excess-kurtosis tail term with its finite-n upper-confidence guard; the imbalance correction; the fully proved smallest-eigenvalue radius (with the k-group multiplicity fix, free-β optimization, and the proved-under-bounded-kurtosis widening); and the k-sample Behrens–Fisher null distribution. Interactive demonstrator rerun_cochran/honest_anova.html — computes raw-mean Welch, the fixed / adaptive / proved T_BB radii, the estimand-changing transform routes, and the full routing receipt in the browser, reproducing the deposited Python. Its engine is extracted as a standalone Node module (m01A_anova_engine.js) and checked cell-by-cell against Python across an 84-design taxonomy (verify_anova_engine_taxonomy.py/.js, max |Δp| = 0.00000). Reproducibility scripts (rerun_cochran/, rerun/) — every reported number traces to a named, deterministically-seeded script (size/power/surface, the calibration and information-limit decompositions, the proved-radius verification, the imbalance calibration, the skew-router branch, and the figures). Real-data evidence — anova_flip_scan.py scans 2,783 public one-way layouts (254 datasets): guaranteed T_BBwithholds ~41% of Welch-significant calls, concentrated where the weight-instability screen fires, and never manufactures significance (Table 7 / Figure 15). Figures and the deterministic deposit builder (fixed timestamps → stable md5). All evaluation is simulation-based; the one empirical component is the public-dataset scan, which uses only openly distributed data. Code is released under the MIT License; text and figures under CC BY 4.0. Version history (consolidated changelog) Published version DOIs are marked ✅; the concept DOI above always resolves to the latest. Staged versions were rolled into the next published one unless noted. v1.0.74 (2026-08-29) — Proved-under-bounded-kurtosis radius (DA12.6). The proved non-normal widening now keys on excess kurtosis, √(1 + κ̂·(n−1)/(2n)), from the exact Var(s²/σ²) = 2/(n−1) + κ/n, so symmetric heavy tails (Student-t) are covered where the old skew form √(1 + 0.75·skew²) under-covered; tbbProved switched to the kurtosis form across the demonstrator, engine, and Python truth (re-verified JS-vs-Python at 0.00000); new rc_anova_kurtosis_proof.py + deep-dive. v1.0.73 ✅ 10.5281/zenodo.22165709 (2026-08-29) — Reconstructed & verified demonstrator engine (standalone Node module + taxonomy verifier, max |Δp| = 0.00000 across 84 designs; Yuen zero-variance fix; T_BB-routed presets both directions); series-impact deep-dive (the corrected R_eig k-group multiplicity gap also reaches m03 and m01t). v1.0.72 (2026-08-29) — Title set to "The deflated-Welch statistic…"; corrected + optimized proved radius R_eig (β/k multiplicity fix + β-optimization, DA12); real-data Welch-vs-T_BB flip scan (2,783 layouts; Table 7 / Figure 15) + demonstrator imbalance-factor fix; long-form derivations companion. v1.0.71 / v1.0.70 (2026-08-21) — Zhang normal-reference comparator benchmarked on the efficiency frontier (valid on only 24% of designs, in the calibrated-liberal cluster); k = 2 adaptive-radius case-study fold (design-scaling vs shape-keying distinction). v1.0.69 ✅ 10.5281/zenodo.22035826 (2026-08-20) — HTML R1/R2 presentation pass + Figure 9 adaptive per-cluster label merge. v1.0.68 ✅ 10.5281/zenodo.22033737 (2026-08-20) — Companion consolidation into a single six-column Table 6; Figures 11–14 harmonized into one story. v1.0.67 / v1.0.65 / v1.0.60 (2026-08-19/20) — Guarded-reference naming-collision fix; the 40,000-replication expanded-frontier pin (Table 3 + Figure 8) with the symmetric-heteroscedastic skew-router branch; the mean-preserving lightened-R_eig do-not-use fallback. v1.0.59 ✅ 10.5281/zenodo.21995320 (2026-08-18) — Reporting standard + honest_anova.html demonstrator re-aligned to the current T_BB methods paper. v1.0.57 ✅ 10.5281/zenodo.21986847 (2026-08-17) — Reviewer-comprehension pass (multi-paragraph abstract, contributions list, trimmed captions); proved radius R_eig added as a Table 3 scorecard row; corner tail-index correction (N−k)/2 (low-order moments exist in every deployed design). v1.0.56–v1.0.49 (2026-08-16) — The k-sample Behrens–Fisher corner-distribution program: two-moment scaled-χ² corner reference, derived corner cumulants, the secular-eigenvalue law + closed CGF + power-law tail, consolidated into derivations DA13 with a prior-art/novelty audit. v1.0.48 ✅ 10.5281/zenodo.21963458 (2026-08-16) — The unifying λ(z) correction (a smooth instability-keyed deflation strength). v1.0.45 ✅ 10.5281/zenodo.21962965 (2026-08-16) — Atomic sparsity index + bootstrap-t edge hardening + shape-aware pooled standardized-residual bootstrap (SA-PSRB); multivariate transfer to m03. v1.0.44–v1.0.41 (2026-08-16) — Shape-moment re-injection order (skew is the sweet spot), validated and hardened pooled standardized-residual bootstrap, atomic weight-noise probes. v1.0.40 ✅ 10.5281/zenodo.21961667 (2026-08-16) — Log-domain weight-stabilization probe (negative for stabilization; clarifies the size-adjusted oracle ceiling); includes the oracle-power gap decomposition (≈92% conservatism, ≈8% estimation). v1.0.37 ✅ 10.5281/zenodo.21961327 (2026-08-16) — Residual-bootstrap qualification of the shoot-out + the first proved Gaussian smallest-eigenvalue radius R_eig (DA12, the p = 1 specialization of the m03 theorem). v1.0.36 (2026-08-15) — Figure 11 T_BB-region colour fix (amber, matching the routing figures). v1.0.27 ✅ 10.5281/zenodo.21908170 — Earlier published baseline of the deposit. Provenance: every number traces to a named, deterministically-seeded script listed in the manuscript Declarations; the demonstrator engine reproduces the deposited Python to max |Δp| = 0.00000 across the taxonomy verification. License. Code and scripts in the deposit are released under the MIT License; text and figures under CC BY 4.0. Reuse is permitted with attribution to the author and citation of the concept DOI above. How to cite. Dwyer, W. J. The deflated-Welch statistic: a closed-form, guaranteed-level test for heteroscedastic one-way ANOVA. Reproducibility deposit, Zenodo. https://doi.org/10.5281/zenodo.21908169
William Dwyer· Zenodo (CERN European Organi...· 0 citations