Beyond the Mean: A Weighted k-Sample Omnibus Variance-Ratio Statistic for Covariate Balance Diagnostics
Abstract
Rubin's variance ratio (VR) complements the standardized mean difference by detecting covariate imbalance in spread, but no purpose-built omnibus extension exists for more than two groups. We introduce FVR, a size-weighted quadratic combination of pairwise log-variance-ratios that generalizes VR to k groups, together with geometric-mean and maximum pairwise variance-ratio comparators. FVR has an exact relationship to Rubin's VR at k = 2 and a mathematical structure directly parallel to Cohen's f. In Monte Carlo simulations spanning four variance-driven bias mechanisms, k = 3, 4, 6, and sample sizes from 200 to 10,000, FVR and the geometric-mean statistic generally tracked downstream estimation bias at least as well as the maximum statistic. FVR retained substantially more signal when many groups shared a very small sample, while absolute-bias thresholds were unstable at N = 200. Across mechanisms, FVR < 0.10 was reasonably reassuring, values above approximately 0.30 generally indicated concern, and intermediate values were context-dependent. The statistic is implemented for arbitrary analysis weights in the Stata command varatio and illustrated using a multivalued-treatment application.
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BibTeX
@misc{linden2026beyond,
title = {{Beyond the Mean: A Weighted k-Sample Omnibus Variance-Ratio Statistic for Covariate Balance Diagnostics}},
author = {Ariel Linden},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27772},
eprint = {2609.27772},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27772},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Beyond the Mean: A Weighted k-Sample Omnibus Variance-Ratio Statistic for Covariate Balance Diagnostics
AU - Ariel Linden
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.27772
UR - https://arxiv.org/abs/2609.27772
AB - Rubin's variance ratio (VR) complements the standardized mean difference by detecting covariate imbalance in spread, but no purpose-built omnibus extension exists for more than two groups. We introduce FVR, a size-weighted quadratic combination of pairwise log-variance-ratios that generalizes VR to k groups, together with geometric-mean and maximum pairwise variance-ratio comparators. FVR has an exact relationship to Rubin's VR at k = 2 and a mathematical structure directly parallel to Cohen's f. In Monte Carlo simulations spanning four variance-driven bias mechanisms, k = 3, 4, 6, and sample sizes from 200 to 10,000, FVR and the geometric-mean statistic generally tracked downstream estimation bias at least as well as the maximum statistic. FVR retained substantially more signal when many groups shared a very small sample, while absolute-bias thresholds were unstable at N = 200. Across mechanisms, FVR < 0.10 was reasonably reassuring, values above approximately 0.30 generally indicated concern, and intermediate values were context-dependent. The statistic is implemented for arbitrary analysis weights in the Stata command varatio and illustrated using a multivalued-treatment application.
ER -