Statistical Convergence and Uncertainty in Electrocatalytic Benchmarking of Ir and Ru Oxygen Evolution Catalysts

Abstract

Electrocatalytic oxygen evolution reaction (OER) catalysts are often benchmarked using a small number of measurements, with performance differences commonly assessed based on calculated mean activity and standard deviation (SD). However, dispersion metrics alone do not quantify the uncertainty of the estimated mean and, therefore, cannot support statistically robust comparisons between catalyst systems. In this work, we aim to elucidate the convergence of statistical variables with the specific goal of estimating the sample size required to achieve a certain level of significance. We begin by demonstrating a medium-throughput workflow combining parallel hydrothermal synthesis with multi-working-electrode (MWE) screening to generate more than sixty independent measurements of two OER catalysts, i.e., IrOx and RuOx nanoparticles supported on antimony-doped tin oxide (ATO). The resulting datasets reveal markedly different statistical behaviors between the two catalysts. IrOx/ATO exhibits narrow distributions, near-normal profiles, and consistent activity across synthesis batches. In contrast, RuOx/ATO shows broader dispersion, deviations from normality, and statistically significant batch-to-batch differences that are not adequately captured by the calculated SD alone, largely due to the presence of outliers. Using simulated normal-distributed datasets with and without outliers, we evaluate statistical variables as a function of sample size and compare simulations with the experimentally obtained dataset. The results show that approximately seven measurements are required to obtain a reliable estimation of the underlying activity data. Our findings establish a statistically rigorous framework for electrocatalytic benchmarking and provide practical guidance for sample-size selection and data reporting in acidic OER studies.