Statistical mirroring-based ordinalysis: A sensitive, robust, efficient, and ordinality-preserving descriptive method for analyzing ordinal assessment data

This study introduces statistical mirroring-based ordinalysis (SM-based ordinalysis), a novel, model-free, assumption-free, peer-independent, and descriptive statistical methodology for analyzing ordinal data at the individual level. The approach addresses key limitations of classical methods such as mean, median, and summed score techniques, particularly in terms of sensitivity, ordinality preservation, robustness, and interpretability. By integrating Kabirian-based isomorphic optinalysis with statistical mirroring, SM-based ordinalysis enhances the estimation process. Python code, packages, and a dedicated software application have been developed to promote accessibility and reproducibility. SM-based ordinalysis was validated through Monte Carlo simulations using data generated from normal, categorical, and multivariate model distributions. The proposed descriptive estimators demonstrated improved sensitivity to distributional variation, stronger ordinal preservation, probabilistic interpretability, scale robustness, and accuracy, especially in contexts with skewed data. SM-based ordinalysis is broadly applicable to fields such as clinical ordinal assessment, psychometrics, public health, market research, and survey analysis.•SM-based ordinalysis incorporates adaptive customization and optimization of parameters, statistical mirroring, and Kabirian-based isomorphic optinalysis to refine the analysis of ordinal scores within a set of composite assessments.•The descriptive estimators focus on analyzing statistical proximity or deviation of ordinal assessment scores from the highest positive ordinal scale point, unlike classical methods that rely mainly on descriptive positions of ordinal scores.