Definition:Scale of Measurement/Linear Interval
Definition
A linear interval scale is a scale of measurement which has an arbitrary zero, but measurements of a quantity such as $x$ and $y$ performed on two such scales satisfy a relationship of the form:
- $y = m x + c$
Hence, in addition to the relationship of equality and ordering, measurements on a linear interval scale are such that for any two quantities the ratios of the differences for each scale is constant.
Examples
Fahrenheit and Celsius
The Fahrenheit and Celsius scales for the measurement of temperature are linear interval scales.
Warning
It makes no sense to discuss multiples of values on a linear interval scale.
Thus, for example, to say that a temperature of $20 \cels$, measured on the celsius scale, is twice as hot as a temperature $10 \cels$ is meaningless.
On the Fahrenheit scale, these temperatures are $68 \fahr$ and $50 \fahr$ respectively, which immediately shows up the fallacious nature of that reasoning.
Also see
- Results about linear interval scales can be found here.
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): scales of measurement