An Honest Effect Size for Contingency Tables: Why Nothing Can Be Unbiased, Where to Put the Error Instead, and How to Route the Report (m0f)

Abstract

An Honest Effect Size for Contingency Tables: Why Nothing Can Be Unbiased, Where to Put the Error Instead, and How to Route the Report 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.21783660. What this is The reproducibility deposit for the point-estimate paper of the contingency-table effect-size arc. The everyday workflow reports Cramér's V and reads it against Cohen's labels; that workflow is biased at the null (Jensen's inequality makes an unbiased estimator of the square-root scale impossible) and treats a noisy point as if it were exact. The paper puts the unavoidable error where it belongs and routes the report: a closed-form O(RC) delete-one jackknife for V² that is nearly unbiased everywhere (at most 0.008 across the 180-design grid, 0.013 as a supremum), a projected confidence interval (conservative but asymptotically valid, any R×C) with an exact-conditional companion for tight coverage, a noise-floor verdict (V_{0.95}) that refuses labels a table cannot support, and a single routing rule that selects the reference (by sparsity and margin heterogeneity), the verdict, the point estimate (by purpose), the scale (always V², negatives permitted and meaningful), and the interval (by whether a guarantee is required). What the deposit contains Manuscript — the built article with the house-standard Key-points box, 8 figures, and 12 numbered/captioned tables (every table carrying an APA bold-label/italic caption and a substantive in-text callout), plus a novelty review companion. Derivations — the compressed derivations ladder and the proof-complete long-form Derivations Companion(Dwyer_M0f_Derivations_Companion_LongForm, ~38 pp, D11–D17 written out in full): the φ² non-U-estimability remark (attributed, with its self-correction), the projected interval as the projection principle instantiated, the affine-link uniqueness, the O(RC) closed-form jackknife, the Bergsma-vs-jackknife crossover equation, and the over-dispersion / two-moment interval fix. Interactive demonstrators — honest_point_estimate.html (the m0f effect-size router: computes the naive V, the jackknifed V², the noise-floor verdict, and the routed report in the browser) and honest_interval.html (the m0g guaranteed-interval sibling), both to the house flip-interpretation standard with a per-cell flip-incidence panel and a seeded null-calibration strip. Reproducibility scripts + locked outputs — every reported number traces to a named, deterministically-seeded script (the bias frontier vs Bergsma's prior, the pooling/meta-analysis collapse, the link/affine-scale test, the projected-interval benchmark, the routing grid, and the figure generators), with the analyzable public-table corpus (effect_size_tables_analyzable.csv) and the routing/flip-incidence scans (rerun/taxonomy_flip_incidence.py, taxonomy_grid_sim.py, and the m0g interval scans) included so the embedded numbers are traceable from the deposit. Real-data evidence — across 4,129 public contingency tables the label-vs-noise-floor recalibration runs both ways (615 forward / 450 reverse); the guaranteed-interval sibling withdraws a claimed resolution on 312 of 2,391 tables (13%, near-pure one-directional deflation). Figures and the deterministic deposit build (fixed timestamps → stable md5; a SHA-256 MANIFEST.txt listing every file). All evaluation is simulation-based; the one empirical component is the public-table scan, which uses only openly distributed data. 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). An Honest Effect Size for Contingency Tables: Why Nothing Can Be Unbiased, Where to Put the Error Instead, and How to Route the Report — reproducibility deposit [Software]. Zenodo.https://doi.org/10.5281/zenodo.21783660 BibTeX: bibtex @software{dwyer_m0f_2026, author = {Dwyer, William J.}, title = {An Honest Effect Size for Contingency Tables: Why Nothing Can Be Unbiased, Where to Put the Error Instead, and How to Route the Report --- reproducibility deposit}, year = {2026}, publisher = {Zenodo}, doi = {10.5281/zenodo.21783660}, url = {https://doi.org/10.5281/zenodo.21783660}, 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 and add version = {v1.2.NN}. When the accompanying journal article is published, please cite it as the primary reference for the method and this deposit as the reproducibility archive. 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. v1.2.11 ⏳ (staged 2026-09-01) — Live availability-DOI link + deepened table callouts (documents-only; no result, number, figure, or datum changed). The manuscript's Availability of data and materials statement now renders the concept DOI as a functional, clickable hyperlink in the built docx/pdf (was literal [...](...) text) — the m0-family docx builder was taught to render markdown [text](url) as a real hyperlink, resolving the reason the Behavior Research Methods editorial office returned the submission. The Table 11 and Table 12 callouts were deepened to point the reader at specific rows/values (float_callout substantive 0.35 → 0.45). Manuscript docx/pdf rebuilt from unchanged source; MANIFEST regenerated. v1.2.10 ✅ 10.5281/zenodo.22151244 (2026-08-28) — Long-form Derivations Companion added (~38 pp, D11–D17 written out in full) alongside the compressed ladder; documents-only, structure + math-render audits pass. v1.2.9 ✅ 10.5281/zenodo.22139670 (2026-08-28) — Routing-domain validation. Both browser demonstrators resolve flip incidence across the routing taxonomy (m0f: 615 forward / 450 reverse label-vs-floor recalibrations over 4,129 public tables; m0g: 312 of 2,391 guaranteed-interval withdrawals), with new reproducible scans, deposited JSON/CSV outputs, the analyzable public-table corpus, and two taxonomy deep-dives. v1.2.8 (2026-08-28) — De-bolded for verbal emphasis; Key-points highlights; refreshed novelty review.Emphasis-bold minimized (170 → ~42 spans; all 744 numeric tokens verified byte-identical), a house-standard seven-bullet Key-points box added after the abstract, and the novelty review rewritten to the clean strand-by-strand form. Presentation only; rolled into v1.2.9. v1.2.7 (2026-08-28) — Tables numbered, captioned, and called out. All 12 tables numbered (Table 1–12), given APA bold-label/italic captions, and referenced in the body (float_callout depth 1.00). Organization only; rolled into v1.2.9. v1.2.6 ✅ 10.5281/zenodo.22135868 (2026-08-27) — Routing-flowchart polish. Consistent ①–⑤ stage numbering (the scale stage is now a numbered pass-through in the figure too), vertical centering of decision-box titles, STOP-box clearance, rounded modal corners, and a legible star default marker. Presentation only. v1.2.1–v1.2.5 (2026-08-27) — The routing flowchart brought to a single house edge-label spec (figure + pop-up generated from one source), box-sizing / no-touching-boxes overlap guard, the pop-up flowchart aligned to the manuscript figure's visual style, and the browser tool taken to the flip-interpretation standard. Presentation + tooling; no result changed; rolled into v1.2.6. v1.2.0 ✅ 10.5281/zenodo.22003886 (2026-08-18) — Over-dispersion interval. The over-dispersion mechanism for the noncentral-interval drift and the derived two-moment ρ-interval (ρ_ci tight + ρ_ci_guard conservative, any R×C, JS-ported), rewriting Section 6.3 + Figure 6 and derivation D17 and superseding the earlier endpoint patch. v1.1.1 ✅ 10.5281/zenodo.21784544 (2026-08-04) — Earlier public release of the point-estimate package. Provenance: every number traces to a named, deterministically-seeded script listed in the manuscript Declarations; the two browser demonstrators reproduce the deposited Python, and the deposit build is deterministic (fixed timestamps → stable md5, SHA-256 MANIFEST).