UNIVERSAL ADAPTIVE NORMALIZATION SCALE (AMIS): A METHODOLOGY FOR INTEGRATING HETEROGENEOUS SOCIAL AND EDUCATIONAL METRICS

The integration of heterogeneous indicators from diverse sources and units ofmeasurement presents a significant challenge in modern data analysis. Establishednormalization techniques, such as percentage scaling and standardization, suffer fromfundamental limitations: the former disregards the underlying data distribution, whilethe latter compromises interpretability and does not yield a true interval scale. Thispaper introduces the Universal Adaptive Normalization Scale (Adaptive Multi-IntervalScale — AMIS), a novel method designed to address this methodological gap.The key advantage of AMIS is its ability to construct a unified metric space, enablingmathematically sound arithmetic operations between inherently disparate datasets—acapability absent in existing approaches. The method transforms absolute values into aunified 0 to 100 scale through a hierarchical computation of control points, derivedfrom mean values within data distribution intervals. This ensures inherent adaptabilityto the specific shape of any source dataset.In contrast to percentages, which merely represent a position within a fixed range,AMIS defines a value's position relative to the actual statistical distribution, all whilepreserving the rigorous properties of an interval scale. We demonstrate the method'spractical efficacy through two real-world case studies: eliminating aggregation errorswhen averaging student grades across different subjects, and constructing a robust scalefor the heavily skewed global GDP distribution. The results confirm that after AMISnormalization, heterogeneous data become directly comparable and suitable for correctcomputation of averages and weighted indices.The proposed approach holds substantial promise for a wide range of applications,including interdisciplinary research, big data analytics, and machine learning, offeringa fundamentally new pathway for integrating heterogeneous metrics into a coherentmeasurement system.