Proof of Data Weigher Analysis (DWA) and Its Application to Dynamic Meta Data Weigher

Abstract

Data Weigher Analysis (DWA) addresses the persistent problem of objectively quantifying whether the values in a data set lean more heavily toward the left or right side, a challenge that becomes increasingly complex in irregular or large-scale data sets. Motivated by the need for a simple yet rigorous quantitative framework, this study compares two DWA techniques—the data weighting method and the data mean difference method—designed to compute balance points in a sequence. The data weighting method assigns balanced linear weights to left and right subsets, whereas the data mean difference method calculates first- and second-order mean differences to capture asymmetry in data distribution. We provide a theoretical proof of equivalence between these two formulations, showing that the mean difference approach produces the same linear weighting as the original data weighting scheme. Building on this theoretical result, we introduce a sliding-window algorithm to operationalize DWA on large, dynamic data streams, allowing automated detection of local imbalances in real time. Empirically, we validate our approach on real-world metadata and trade datasets, comparing it against baseline descriptive statistics to assess efficiency and precision. Quantitative findings show that the mean difference method reduces computation processes without loss of accuracy compared with manual weighting. Overall, this work contributes to a unified theoretical foundation, a lightweight algorithmic implementation, and evidence of practical benefits for using DWA in decision-making contexts such as questionnaire analysis, market dynamics, and trade flow monitoring.