A review of dimensional assessment for statistics and probability

• Published in: Journal of statistical theory and practice Vol. 10; no. 4; pp. 639 - 655
• Main Author: Hughes, Gary B.
• Format: Journal Article
• Language: English
• Published: Cham Taylor & Francis 01.10.2016; Springer International Publishing
• Subjects: Dimensional homogeneity; dimensioned linear algebra; dimensions of probability density; dimensions of statistics; Mathematics and Statistics; Probability Theory and Stochastic Processes; Statistical Theory and Methods; Statistics; unit cancelation; dimensions of statistics; unit cancelation; Dimensional homogeneity; dimensioned linear algebra; dimensions of probability density; 00A73
• ISSN: 1559-8608; 1559-8616
• DOI: 10.1080/15598608.2016.1214852

Numeric values that are meant to describe physical attributes are given a precise context by association with measurement units. Units define the quantification of the attribute's dimension within a specific measurement system. Science and engineering disciplines have long relied on measurement systems and dimensional reasoning. This article explores the (long-held) notion that dimensional awareness can also stimulate unique insight into statistics and probability concepts. Linear algebra developed for dimensioned physical quantities provides a rigorous framework for analyzing applied equations. Units associated with descriptive statistics can be determined by dimensional assessment of basic definitions. Dimensioned linear algebra can be used to trace units through more advanced statistical constructs. Any dimensional context precludes a non-dimensionless probability unit, and requires probability density to have a dimension that is reciprocal to that of the random variable. The physical meaning of distribution parameters becomes clear in a dimensional context, and several pervasive inconsistencies in graphics and basic equations are clarified. The ideas presented in this article are not new. Dimensional awareness also contributes to a broader system-level foundation for utilizing statistics and probability concepts as tools in applied scenarios.