Abstract

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. This article first provides general procedures for dimensional analysis prior to statistical design and analysis. The use of dimensional analysis is illustrated with three practical examples. In the first example, the authors 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. The third example shows 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, results obtained via the dimensional-analysis approach are compared to results obtained via conventional approaches. From those, the authors demonstrate the general properties of dimensional analysis from a statistical perspective and recommend its usage based on its favorable performance.