October 6, 2025

Fragility Metrics as Legal Standards in Gun Control Research

In this article, I propose two statistical fragility diagnostics for evaluating gun policy evidence in legal proceedings. The Percent Fragility Index (PFI) indicates the minimum percentage of outcomes that would need to change to reverse a study’s statistical significance. In contrast, the Risk Quotient (RQ) indicates the percentage that would need to change to eliminate any policy benefit. Applied to published gun policy survey data examining concealed carry support by race, the analysis demonstrates that studies achieving statistical significance (P < 0.001) may remain fragile to minor perturbations. The worked example showed a PFI of 5.8% and an RQ of 9.9%, indicating that conventional P-values alone fail to convey evidentiary stability and magnitude—critical factors for courts applying the preponderance standard. These metrics enable judges and policymakers to distinguish robust findings from fragile ones without relying on opaque models, translating statistical uncertainty into legally relevant information about reliability and probative value.

Citation: Heston, Thomas F, Fragility Metrics as Legal Standards in Gun Control Research (September 26, 2025). Available at SSRN:  https://ssrn.com/abstract=5534939 or http://dx.doi.org/10.2139/ssrn.5534939