Ordinal, Interval & Ratio Scales

In his influential 1946 paper "On the Theory of Scales of Measurement," S. S. Stevens proposed that all measurement can be classified into four scale types, each permitting a progressively richer set of mathematical operations. This taxonomy — nominal, ordinal, interval, and ratio (often abbreviated NOIR) — remains foundational in psychology and the social sciences, guiding which statistical operations are appropriate for different kinds of data.

The Four Scale Types

A nominal scale assigns labels to categories with no inherent order — jersey numbers, diagnostic categories, or stimulus types. An ordinal scale preserves rank order but says nothing about the size of differences — Mohs hardness, preference rankings. An interval scale has equal differences between scale values, but lacks a true zero point — temperature in Celsius, IQ scores. A ratio scale has both equal intervals and a meaningful zero — reaction time, weight, length.

Permissible Statistics

Stevens argued that the scale type constrains which statistics are meaningful. For nominal data, only mode and frequency counts are appropriate. Ordinal data permit medians and percentiles. Interval data allow means and standard deviations. Ratio data additionally permit geometric means and coefficients of variation. While this prescriptive view has been debated — some statisticians argue that the validity of a statistic depends on the research question, not the scale type — the framework remains a valuable heuristic for thinking about what numerical operations on psychological data actually mean.

Connection to Measurement Theory

In representational measurement theory, scale type is determined by the uniqueness theorem: the set of admissible transformations that preserve the measurement's validity. Stevens' taxonomy is thus a classification of uniqueness classes, connecting his practical framework to the deeper axiomatic foundations developed by Krantz, Luce, Suppes, and Tversky.