Dimensional analysis in statistics

Alex Reinhart – Updated August 4, 2022 notebooks · refsmmat.com

When I was a physics major, I was taught dimensional analysis: physical quantities have units (like length or mass), and any formula combining physical quantities had to have correct units. You cannot, for instance, add mass to velocity: the units are incompatible.

In statistics, however, we routinely build models relating physical quantities with units, and do not think very carefully about the units at all. Thinking about units would help with interpretation (e.g. regression coefficients have units, and these help us interpret what the coefficient means), but may also suggest what model types are viable: models that do not preserve units cannot be correct, in some fundamental way. But I have seen very little exploration of units in statistics or what they might mean for modeling.