Universal Adaptive Normalization Scale (Amis): A Methodology For Integrating Heterogeneous Social And Educational Metrics

The integration of heterogeneous indicators from diverse sources and units of measurement presents a significant challenge in modern data analysis. Established normalization techniques, such as percentage scaling and standardization, suffer from fundamental limitations: the former disregards the underlying data distribution, while the latter compromises interpretability and does not yield a true interval scale. This paper introduces the Universal Adaptive Normalization Scale (Adaptive Multi-Interval Scale — AMIS), a novel method designed to address this methodological gap. The key advantage of AMIS is its ability to construct a unified metric space, enabling mathematically sound arithmetic operations between inherently disparate datasets—a capability absent in existing approaches. The method transforms absolute values into a unified 0 to 100 scale through a hierarchical computation of control points, derived from mean values within data distribution intervals. This ensures inherent adaptability to 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 while preserving the rigorous properties of an interval scale. We demonstrate the method's practical efficacy through two real-world case studies: eliminating aggregation errors when averaging student grades across different subjects, and constructing a robust scale for the heavily skewed global GDP distribution. The results confirm that after AMIS normalization, heterogeneous data become directly comparable and suitable for correct computation 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, offering a fundamentally new pathway for integrating heterogeneous metrics into a coherent measurement system.