Title: Lurking Variable Detection via Dimensional Analysis,
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.