Lurking Variable Detection via Dimensional Analysis

TL;DR

This paper introduces formal hypothesis tests based on Dimensional Analysis and a modified Buckingham Pi theorem to detect lurking variables in physical phenomena, enabling algorithm-driven detection beyond visual inspection.

Contribution

It presents a novel, structured approach for lurking variable detection using hypothesis testing and Dimensional Analysis, addressing limitations of traditional visual methods.

Findings

Developed hypothesis tests for lurking variable detection

Created procedures for complex cases of lurking variables

Applied methods to engineering problems demonstrating effectiveness

Abstract

Lurking variables represent hidden information, and preclude a full understanding of phenomena of interest. Detection is usually based on serendipity -- visual detection of unexplained, systematic variation. However, these approaches are doomed to fail if the lurking variables do not vary. In this article, we address these challenges by introducing formal hypothesis tests for the presence of lurking variables, based on Dimensional Analysis. These procedures utilize a modified form of the Buckingham Pi theorem to provide structure for a suitable null hypothesis. We present analytic tools for reasoning about lurking variables in physical phenomena, construct procedures to handle cases of increasing complexity, and present examples of their application to engineering problems. The results of this work enable algorithm-driven lurking variable detection, complementing a traditionally inspection-based approach.