Empowering Expert Judgment: A Data-Driven Decision Framework for Standard Setting in High-Dimensional and Data-Scarce Assessments

Abstract

A critical methodological challenge in standard setting arises in small-sample, high-dimensional contexts where the number of items substantially exceeds the number of examinees. Under such conditions, conventional data-driven methods that rely on parametric models (e.g., item response theory) often become unstable or fail due to unreliable parameter estimation. This study investigates two families of data-driven methods: information-theoretic and unsupervised clustering, offering a potential solution to this challenge. Using a Monte Carlo simulation, we systematically evaluate 15 such methods to establish an evidence-based framework for practice. The simulation manipulated five factors, including sample size, the item-to-examinee ratio, mixture proportions, item quality, and ability separation. Method performance was evaluated using multiple criteria, including Relative Error, Classification Accuracy, Sensitivity, Specificity, and Youden's Index. Results indicated that no single method is universally superior; the optimal choice depends on the examinee mixture proportion. Specifically, the information-theoretic method QIR (quantile information ratio) excelled in scenarios with a dominant non-competent group, where high specificity was critical. Conversely, in highly selective contexts with balanced proficiency groups, the clustering methods CHI (Calinski-Harabasz index) and sum of squared error (SSE) demonstrated the highest classification effectiveness. Bayesian kernel density estimation (BKDE), however, consistently performed as a robust, balanced method across conditions. These findings provide practitioners with a clear decision framework for selecting a defensible, data-driven standard-setting method when traditional approaches are infeasible.