Mathematization, Not Measurement: A Critique of Stevens’ Scales of Measurement

Abstract

In the early 1900s, physics was the archetypical science and measurement was equated with mathematization to real numbers. To enable the use of mathematics to draw empirical conclusions about psychological data, which was often ordinal, Stevens redefined measurement as “the assignment of numerals to objects and events according to a rule.” He defined four scales of measurement (nominal, ordinal, interval, and ratio) and set out criteria for the permissible statistical tests to be used with each. Stevens' scales of measurement are still widely used in data analysis in the social sciences. They were revolutionary but flawed, leading to ongoing debate about the permissibility of the use of different statistical tests on different scales of data. Stevens implicitly assumed measurement involved mapping to real numbers. Rather than rely on Stevens' scales, researchers should demonstrate the mathematical properties of their data and map to analogous number sets, making claims regarding mathematization explicit, defending them with evidence, and using only those operations that are defined for that set.