The psychophysicist Stanley Smith Stevens defined nominal, ordinal, interval, and ratio scales.
Nominal measurements do not have meaningful rank order among values, and permit any one-to-one transformation.
[4] The issue of whether or not it is appropriate to apply different kinds of statistical methods to data obtained from different kinds of measurement procedures is complicated by issues concerning the transformation of variables and the precise interpretation of research questions.
"The relationship between the data and what they describe merely reflects the fact that certain kinds of statistical statements may have truth values which are not invariant under some transformations.
[5] The following table classifies the various simple data types, associated distributions, permissible operations, etc.