Dimensional Analysis and Its Applications in Statistics

• Activity Number: 131
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Weijie Shen*+ and Dennis Kon-Jin Lin and Christopher J. Nachtsheim
• Companies: The Pennsylvania State University and The Pennsylvania State University and University of Minnesota
• Keywords: Buckingham's $\Pi$ Theorem ; Design of Experiment ; Dimensions ; Statistical Analysis

Abstract

Dimensional Analysis (DA) is a well-developed widely-employed methodology in the physical and engineering sciences. Its use prior to physical experimentation results in reductions of variables and primary insights of their relationships. The application of DA in statistics leads to three advantages: (1) the reduction of the number of potential causal factors that we need to consider, (2) the analytical insights into the relations among variables that it generates, and (3) the scalability of results. The formalization of the DA method in statistical design and analysis would give a clear view on its generality and overlooked significance. In this paper, we first provide general procedures for DA prior to statistical design and analysis. We illustrate the use of DA with three practical examples, demonstrating the basic DA process, its integrations into the regression analysis and its role in developing a superior experimental design. We compare results obtained via the DA approach to those obtained via conventional approaches. From those, we conclude the general properties of DA from statistical perspective and recommend its usage based on its favorable performance.