Statistical mirroring-based ordinalysis: A sensitive, robust, efficient, and ordinality-preserving descriptive method...

Area of Science:

• Statistics
• Data Analysis

Background:

• Classical statistical methods for ordinal data (mean, median, summed scores) have limitations in sensitivity, ordinality preservation, robustness, and interpretability.
• Analyzing ordinal data at the individual level requires methods that are model-free, assumption-free, and peer-independent.

Purpose of the Study:

• Introduce statistical mirroring-based ordinalysis (SM-based ordinalysis) as a novel, descriptive statistical methodology for individual-level ordinal data analysis.
• Address limitations of classical methods by enhancing sensitivity, ordinality preservation, robustness, and interpretability.

Main Methods:

• Developed a novel, model-free, assumption-free, peer-independent, and descriptive statistical methodology: SM-based ordinalysis.
• Integrated Kabirian-based isomorphic optinalysis with statistical mirroring to enhance estimation.
• Created Python code, packages, and a software application for accessibility and reproducibility.
• Validated through Monte Carlo simulations using normal, categorical, and multivariate distributions.

Main Results:

• SM-based ordinalysis demonstrated improved sensitivity to distributional variation and stronger ordinal preservation.
• The method offers enhanced probabilistic interpretability, scale robustness, and accuracy, particularly with skewed data.
• Descriptive estimators analyze proximity to the highest positive ordinal scale point, differing from classical methods.

Conclusions:

• SM-based ordinalysis is a broadly applicable statistical methodology for analyzing ordinal data across various fields like clinical assessment, psychometrics, public health, market research, and survey analysis.
• The approach provides a robust and interpretable alternative to traditional methods for ordinal data analysis.
• Adaptive customization and optimization of parameters, statistical mirroring, and Kabirian-based isomorphic optinalysis refine ordinal score analysis.