Dimensional analysis and its applications in statistics

Dimensional analysis (DA) is a well-developed, widely-employed methodology in the physical and engineering sciences. The application of dimensional analysis 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 dimensional-analysis method in statistical design and analysis gives a clear view of its generality and overlooked significance. In this paper, we first provide general procedures for dimensional analysis prior to statistical design and analysis. We illustrate the use of dimensional analysis with three practical examples. In the first example, we demonstrate the basic dimensional-analysis process in connection with a study of factors that affect vehicle stopping distance. The second example integrates dimensional analysis into the regression analysis of the pine tree data. In our third example, we show how dimensional analysis can be used to develop a superior experimental design for the well-known paper helicopter experiment. In the regression example and in the paper helicopter experiment, we compare results obtained via the dimensional-analysis approach to those obtained via conventional approaches. From those, we demonstrate the general properties of dimensional analysis from a statistical perspective and recommend its usage based on its favorable performance.