# Stevens’ levels of measurement

This is about Stevens’ 1946 largely unhelpful categorisation of scales into categorical/nominal, ordinal, interval and ratio. Stevens argued, correctly, that there is an ordinal scale of scaling: nominal/categorical scaling, ordinal scaling, interval scaling and ratio scaling.

#### Details #

Stevens started this with his paper Stevens, S. S. (1946). On the theory of scales of measurement. Science, 103, 677–680, probably one of the most influential papers in the psychological realm and still powerful though largely, in my view, unhelpfully. Stevens’ levels were as follows:

1. nominal “scaling” has no scaling: there is not implicit ordering of any of the values
2. ordinal scaling has order but no (implicit) mathematical relationships: “rarely”, “sometimes” and “often” have a pretty clear sequence but you can’t say how much “sometimes” is more than “rarely” nor how much “often” is more than “sometimes” nor anything about how the differences relate to each other, is “often” more different from “sometimes” than “sometimes” is from “rarely”?
3. interval scaling: the intervals are mathematical but the ratios are not. The only example in our realm (and hardly) is temperature in Celsius/centigrade or Fahrenheit. Each has the property that a temperature of 30 degrees is as much hotter than 20 degrees as 20 degrees is hotter than 10 degrees but in neither scale is 20 degrees twice as hot as 10 degrees: because the zero values are arbitrary.
4. ratio scaling: is what it says. Being 40 years old really does mean you’ve been out of the womb twice as long as someone who is 20 years old (but see age), weighing 70kg is twice 35kg, a 50 minute session is 5/9ths of a 90 minute group session duration. (Temperature in Kelvin has ratio scaling: 273 degrees Kelvin (zero in Celsius, 32 degrees in Fahrenheit) is twice as hot as 136.5 degrees, but that’s getting us way away from ROM!)

Does this matter? Stevens argued it did and said you can only compute a mean for interval or ratio scaling and not for ordinal scaling and argued that pretty much any psychological scales only have ordinal scaling. That’s true and it led to the idea that “parametric statistics”: based on the assumption of Gaussian distributions and in turn on the mean and variance being “real” couldn’t be used for psychological scales. Certainly there are issues but how much they really matter for our data is a moot point however, scaling level, which is “real” is actually rather separate from the issue of whether parametric statistical methods can be applied to our data, and the arrival of bootstrap methods probably makes the issue even less persuasive. Perhaps more importantly, the whole idea seduces us away from thinking about what our variables actually mean to individuals and to social groups. But that’s a monograph!

#### Try also … #

Nominal/category scaling
Ordinal scaling
Interval scaling
Ratio scaling
Parametric versus non-parametric statistics
Bootstrap methods & bootstrapping

#### Chapters #

Mostly chapter 4 but also pertinent to chapter 10.

Created 2/11/21