SCALES OF MEASUREMENT
Level of measurement or scale of measure is a classification that describes the nature of
information within the numbers assigned to variables. Psychologist Stanley Smith Stevens
developed the best known classification with four levels or scales of measurement: nominal,
ordinal, interval, and ratio.
Stevens proposed his typology in a 1946 Science article titled "On the theory of scales of
measurement". In this article, Stevens claimed that all measurement in science was conducted
using four different types of scales that he called "nominal" "ordinal" "interval" and "ratio"
unifying both "qualitative" (which are described by his "nominal" type) and "quantitative" (all
the rest of his scales). The concept of scale types later received the mathematical rigor that it
lacked at its inception with the work of mathematical psychologists Theodore Alper (1985,
1987), Louis Narens (1981a, b), and R. Duncan Luce (1986, 1987, 2001).
As Luce (1997, p. 395) wrote;
S. S. Stevens (1946, 1951, and 1975) claimed that what counted was having an interval or ratio
scale. Subsequent research has given meaning to this assertion, but given his attempts to invoke
scale type ideas it is doubtful if he understood it himself ... no measurement theorist I know
accepts Stevens’ broad definition of measurement ... in our view, the only sensible meaning for
'rule' is empirically testable laws about the attribute.
1. Nominal Scale:
A nominal scale of measurement deals with variables that are non-numeric or where the numbers
have no value. The lowest measurement level you can use, from a statistical point of view, is a
nominal scale. A nominal scale, as the name implies, is simply some placing of data into
categories, without any order or structure.
A physical example of a nominal scale is the terms we use for colours. The underlying
spectrum is ordered but the names are nominal.
In research activities a YES/NO scale is nominal. It has no order and there is no distance
between YES and NO.
