ABSTRACT
Measurement is typically defined as an assignment of numerals to objects according to certain rules. Stevens (1951) classified measurement into four types: nominal, ordinal, interval and ratio. Nominal measurement. An example of nominal measurement is the numbering of athletes, such as 3, 5, 7 and 10, where these numbers are used for identification or as labels. The only mathematical rule to govern nominal measurement is one-to-one correspondence. If two objects have different numbers or labels, they are considered different. Ordinal measurement. An example of ordinalmeasurement is the ranking of movies, such as 1, 2 and 3, where 1 indicates the best, 2 the second best and 3 the last one, without providing any information how much the best is better than the second best. Here the mathematical rules are oneto-one correspondence and order relations for which only a monotone transformation is permissible. Interval measurement. An example of interval measurement is temperature in Celsius or Fahrenheit, where the difference is meaningful (e.g., the difference between 3 and 5 degrees is considered the same as the difference between 10 and 12 degrees). However, the measurement does not have the rational origin and thus cannot be used in such a way that the temperature of 20 degrees is twice as hot as 10 degrees. Imagine what happens if we change the temperature from Celsius to Fahrenheit. Here the mathematical rules are one-to one correspondence, ranking and equality of the unit. Ratio measurement. An example of ratio measurement is distance, say between Toronto and Montreal, where the measurement has the absolute origin (i.e., “0” means nothingness of the attribute under consideration). The existence of the origin allows the ratio to be a meaningful quantity. For instance, we can now say that the distance of 10 km is twice the distance of 5 km. Here the permissible mathematical operations are oneto-one correspondence, ranking, equality of the unit and the division and multiplication.
