A calibrated component partition for sparse and skewed contingency tables (m01 Methods): reproducibility deposit

A calibrated component partition for sparse and skewed contingency tables 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.21908473. Published v1.0.27:10.5281/zenodo.21908474. What this is The reproducibility deposit for the m01 Methods paper: a calibrated Lancaster component partition of Pearson's chi-square for sparse and skewed contingency tables, carried out on the variance-stabilized (Anscombe / T_root) scale. The omnibus chi-square answers only "is there association?" and mis-calibrates badly when counts are sparse; decomposing it into interpretable Lancaster components restores the "where, and of what kind" while the standard per-component reference under-covers under sparsity and skew. The paper supplies the correction: margin-conditional per-component referencing, a dependent-cell fourth-cumulant closure that fixes the residual mis-sizing, a failure map locating exactly where the naive partition breaks, and a joint Gaussianization of the components. The published record also carries, as a companion, the honest-by-default reporting standard (the former separate m01r record, folded in) that turns the method into a machine-checkable per-component reporting rule. What the deposit contains Manuscript (author + anonymized; built .docx/.pdf) and the reporting-standard companion (M01r), plus the partition derivations (variance-stabilized Lancaster components, the margin-conditional reference, the exact fourth-cumulant closure, and the joint-Gaussianization construction). Reproducibility apparatus (rerun_cochran/) — the failure-map generator, the closure grid, the exact fourth-cumulant dynamic program (kappa4_exact_dp.py + its JS twin and validator), the per-cell size study, the T_root exact validation, and the locked result CSVs. Every reported number regenerates from these deterministically-seeded scripts. Figures — the failure heatmap and its driver decomposition, the pipeline and closure diagrams, the Cochran partition, the calibration/omnibus/power heatmaps, and the routing figure. Interactive demonstrator honest_partition.html — computes the calibrated per-component partition and its margin-conditional referencing in the browser, reproducing the deposited Python. Deep-dive record (failure-driver decomposition, closed-form application, fourth-cumulant closure, joint Gaussianization, the Cochran/ANOVA/T_root bridge, prior-art / adversarial / reproducibility audits) and the submission apparatus. All evaluation is simulation-based. 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). A calibrated component partition for sparse and skewed contingency tables — reproducibility deposit [Software]. Zenodo. https://doi.org/10.5281/zenodo.21908473 BibTeX: bibtex @software{dwyer_m01_2026, author = {Dwyer, William J.}, title = {A calibrated component partition for sparse and skewed contingency tables --- reproducibility deposit}, year = {2026}, publisher = {Zenodo}, doi = {10.5281/zenodo.21908473}, url = {https://doi.org/10.5281/zenodo.21908473}, 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.21908474 for v1.0.27). 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 On the version numbering. build_m01_deposits.py builds both arms — m01A (the deflated-Welch ANOVA paper) and m01_methods (this partition paper) — from a single shared VERSION constant, deliberately kept shared so both arms are always cut from the identical toolchain state (a reproducibility guarantee). The version number therefore tracks the builder, not either individual deposit. m01_methods was last published at v1.0.27; the intervening churn to v1.0.78 was almost entirely m01A work (proof corrections, flip scans, venue-conformance passes), during which m01_methods was re-cut at the same tag even when its own contents did not change. The jump in the version string is thus expected and cosmetic — the only substantive change to m01_methods across it is the v1.0.78 rendering-only radical refresh below. v1.0.79 — ✅ 10.5281/zenodo.22575729 (2026-09-07): cut in lockstep with the m01A v1.0.79 arm. The two bundled reproducibility scripts (mseries_docx_core.py, build_arxiv_latex.py) were synced to the canonical house versions after a drift audit found the m02e copies were ahead (a fixed-table-width directive the docx core honors and the arXiv builder strips, plus a markdown-emphasis-leak fix). This arm's own manuscript is unchanged from v1.0.78 — no number, figure, table, or word changed; the md5 shift is the bundled tooling only. New version on concept 10.5281/zenodo.21908473 (m01_methods_reproducibility_v1.0.79.zip, md5 6c8cb3492693888ca6ff8647dfc42398, 7,253,146 B, 105 files; deterministic). v1.0.78 — ✅ 10.5281/zenodo.22184651 (2026-08-31): cut in lockstep with the m01A arm — docx/PDF rebuilt through the current math-typography builder so nested-paren radicals render as true Office-math radicals (Partition 0→2, Partition Derivations 7→8 radicals; all math-render clean). No number, figure, table, or claim changed. New version on concept 10.5281/zenodo.21908473 (m01_methods_reproducibility_v1.0.78.zip, md5 9b34a40b731905a8e306b2f2dcc0d888, 7,245,729 B, 104 files). v1.0.27 ✅ 10.5281/zenodo.21908474 (2026-08-12) — published deposit: the calibrated component partition, margin-conditional referencing, the fourth-cumulant closure, the failure map, joint Gaussianization, the honest_partition.html demonstrator, and the folded-in honest-by- default reporting standard companion (M01r). m01_methods_reproducibility_v1.0.27.zip (md5 91f90ba0602242f031c568cfad7348be, 101 files). Provenance: every number traces to a named, deterministically-seeded script under rerun_cochran/; the demonstrator reproduces the deposited Python. Related records: T_root methodology 10.5281/zenodo.21522471; the merged confidence-region record m01cd; the ANOVA-arm sibling m01A 10.5281/zenodo.21908169.