Scales of measurement or levels of measurement were developed by American psychologist Stanley Smith Stevens(November 4, 1906 – January 18, 1973).
He classified variables into four levels: nominal, ordinal, interval, and ratio.
Based on the order of four levels, the usable operators get more and more from nominal to ratio.
Four Scales of Measurement
(1) Nominal scale:
Nominal scales are applied to distinguish objects or abstract definitions.
Therefore, there are only equal or unequal meaning between variables.
Operators: ＝, ≠.
Example: mode, name, blood types, gender, etc.
(2) Ordinal scale:
Ordinal scales are used to rank objects but the distances between each other are not meaningful.
Operators: ＝, ≠, >, <.
Example: median, rank, preference, etc.
(3) Interval scale:
Interval scales can be used to rank objects and the distances between each other are meaningful.
However, the ratios are not meaningful.
Operators: ＝, ≠, >, <, +, -.
Example: mean, Celsius temperature, IQ, etc.
(4) Ratio scale:
Ratio scales possess all the properties of interval scales and meaningful absolute zero.
Therefore, the ratios are meaningful in ratio scales.
Operators: ＝, ≠, >, <, +, -, ×, ÷.
Example: absolute temperature, length, weight, volume, etc.