A Statistical Framework for Probabilistic Assessment of Data Consistency in Single-Molecule Conductance Measurements

Single-molecule break junction techniques have become essential tools for nanoscale characterization and ultrasensitive chemical sensing, where resolving minute analytical differences is crucial. However, due to the inherent stochastic nature of molecule-electrode contacts, this high sensitivity makes the rigorous assessment of data consistency across measurements a critical challenge. Current practices predominantly rely on comparing Gaussian-fitted conductance histogram peak positions, a point-estimate approach that often conflates intrinsic molecular variance with the statistical precision of the mean. Consequently, in high-throughput experiments, relying solely on such deterministic point estimates frequently leads to the misinterpretation of negligible systematic drifts due to the lack of an objective equivalence criterion. To move beyond the limitations of single-value comparisons, we introduce a statistical framework integrating an interval-based boundary evaluation method (two one-sided tests, TOST) and robust Bayesian inference to quantitatively discriminate physical equivalence. Using the nickel bis(dithiolene) molecular junction as a model system, we demonstrate that while null hypothesis significance testing is sensitive to large sample sizes, TOST provides a definitive judgment of physical equivalence within defined bounds. Importantly, the Bayesian module complements this binary judgment by quantifying the continuous certainty of such equivalence via the posterior probability. Furthermore, we show that this probabilistic perspective enables a dynamic stopping rule by continuously monitoring evidence as data is collected, determining optimal sample sizes based on evidence convergence. This framework transitions the evaluation of data consistency from deterministic parameter estimation to probabilistic inference, establishing a rigorous statistical foundation for both nanoscale characterization and advanced sensing in single-molecule studies.