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

Abstract

Stevens redefined measurement as “the assignment of numerals to objects and events according to a rule.” Using this definition, he defined four scales of measurement (nominal, ordinal, interval, and ratio) and set out criteria for the appropriate statistical tests to be used with each. Stevens’ paper has been influential in statistics for the social sciences, but it is not grounded in either science or mathematics and confuses measurement with labeling and mathematization. Mathematization using set theory obviates the need for Stevens’ ad hoc framework.