发表机构
University of Massachusetts Lowell（马萨诸塞大学洛厄尔分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对列联表效应量在独立下为正的偏差，提出精确逐表噪声底限 V_0.95 作为报告门限，并在 4129 个真实表中发现 21.8% 的效应无显著关联。
AI 中文摘要
Cramer's V 及其他卡方族效应量在精确独立条件下为正，因此报告值可能小于同一统计量在无关联表上产生的值。这种向上偏差是经典的（Tschuprow 1925; Bartlett 1937; 由 Bergsma 2013 修正），并且以一般形式推荐在观测值旁边报告边界值（临界效应量）（Perugini et al. 2025）；我们不主张这些。我们的贡献是一般性建议无法提供的两件事。第一，精确的逐表报告门限：噪声底限 V_0.95，即在独立条件下效应量有 5% 的时间偶然达到的值，根据精确的边际条件分布而非渐近临界值计算。渐近底限在报告风险最高的地方校准不当：在异质表上，其误报率达到 0.10，而目标是 0.05，而精确底限保持名义水平。第二，一项测量：在来自 291 个公共数据集的 4,129 个真实二维表中，21.8% 的标记效应（聚类稳健 95% 置信区间 17% 至 27%）位于无显著关联的表上。我们建议在稀疏或异质表上，以精确形式报告 V_0.95，并置于每个关联度量旁边，且在设计阶段进行。
英文摘要
Cramer's V and the other chi-square-family effect sizes are positive under exact independence, so a reported value can be smaller than what the same statistic produces on a table with no association at all. The upward bias is classical (Tschuprow 1925; Bartlett 1937; corrected by Bergsma 2013), and reporting the boundary value, the critical effect size, beside the observed one has been recommended in general form (Perugini et al. 2025); we claim neither. Our contribution is two things a general recommendation does not supply. First, an exact per-table reporting gate: the noise floor V_0.95, the value the effect size reaches by chance 5% of the time under independence, computed from the exact margin-conditional law rather than the asymptotic critical value. The asymptotic floor miscalibrates where reporting is riskiest: on heterogeneous tables its false-alarm rate reaches 0.10 against a 0.05 target, while the exact floor holds nominal. Second, a measurement: across 4,129 real two-way tables from 291 public datasets, 21.8% of labeled effects (cluster-robust 95% CI 17 to 27%) sit on tables with no significant association. We recommend reporting V_0.95, in exact form on sparse or heterogeneous tables, beside every association measure and at the design stage.
Comments27 pages, 6 figures. Under review at Journal of Applied Statistics. Reproducible code, data, and the derivation companion are openly archived on Zenodo: https://doi.org/10.5281/zenodo.21664321. Part of a contingency-table effect-size series (companions on the point estimate, the confidence interval, and the exact conditional distribution engine)
