5.2 Measurement, scale types, scales, scaling transformations

As we have seen in chapter 2, a measure is a value of a variable, and the variable stands for an attribute representing a characteristic of the referent. The variable can take up many values, each value being designated by a symbol chosen from a suitable symbol system.

Measurement forms a link between the real world of the referent and the model world of the symbol system. There are thus three components to measurement:

• the observations of the chosen characteristics of the referent,

• the chosen symbol system type of the model world, and

• the mapping between the two.

These three give us an understanding of scale type and scale, and leads to the definitions:

scale type

a triple consisting of (i) a system of observations of a characteristic of the referent, (ii) the symbol system type, and (iii) a mapping between the two

and

scale

a scale type adapted to suit the particular domain of observations and the particular range of symbols of the symbol system type

The symbol system type defines the scale type of which there are five common ones:

• Nominal scale, based on symbol system type 1,

• Ordinal scale, based on symbol system type 2,

• Interval scale, based on symbol system type 3,

• Ratio scale, based on symbol system type 4,

• Absolute (counting scale, based on the absolute symbol system type.

Consider a simple example.

Motorists observe that garages up...