# Determining the scale type

I have different functions, that measure characteristics like completeness or reputation. I try to find out on what scale types they are (nominal, ordinal, interval, ratio or absolute).

Most of the functions map to values between $0.0$ and $1.0$. I would assume that they are on a ratio scale. A ratio scale is an interval scale where the values have numerical meaning, so addition and subtraction would work here. This makes somewhat sense.

I represent these numbers as percentage. Is percentage in general a ratio scale?

Then there are measures which map to quite arbitrarily values. For instance one to values between $-355$ and $2214$. Are these on an absolute scale type?

Most of the functions map to values between 0.0 and 1.0. I would assume that they are on a ratio scale. A ratio scale is an interval scale where the values have numerical meaning, so addition and subtraction would work here. This makes somewhat sense.

It actually depends on what your tool was designed for. Some questionnaires return a categorical diagnosis, while some return a properly scaled score. Without knowing what lies between 1 and 0 and what the tools are it's difficult to tell.

Supposed you have no clue what the tools are, some investigation is possible, but beware that you can be wrong. For instance, you can look at the data and see if the numbers in between are very fine with many decimal places, and nearly none of them are alike. If so, then chance is you can treat it as a ratio variable. You can also plot a histogram as well to check the distribution. If you see a very clear comb-shaped distribution (with a lot of "columns" and empty space alternately lined up), then be careful because it could either be a very rough ratio variable with a handful of possible outcomes, or it can be an ordinal scale disguised as continuous.

Anyway, the safest bet is to consult the documentation of your instruments first.

I represent these numbers as percentage. Is percentage in general a ratio scale?

To be called a ratio, a variable needs to have the continuous nature and a meaningful zero. Percentage usually have a meaningful zero so it can be considered as ratio. However, it does not mean percentages can be automatically treated as any other ratio variable. The reason is that most percentage variables are bound at 0 to 100, and time to time if you have very extreme distribution that is siding to either end, your confidence interval can illogically fall into <0% or >100%. Examine your data carefully, and consider using other analysis like beta regression.

Then there are measures which map to quite arbitrarily values. For instance one to values between −355 and 2214. Are these on an absolute scale type?

I'm not sure what do you mean by "absolute scale." If you mean if it's ratio variable or not, then ask yourself:

1. Does a unit increment at any place of the scale means the same amount of increment?
2. Does it have a meaningful zero?

If both are yes, it's a ratio variable. I need to stress again that numbers are just numbers and by them alone it's hard to tell how to treat it; you'd need to provide at least what the variable represents, and what is between the min and the max.

• Thank you for this very comprehensive answer to my rather vague question, it helped me a lot. Interestingly, I find nearly no references, about the scale type 'absolute'. I just found it one book: Software Metrics: A Rigorous and Practical Approach. Simply a ratio scale which is not on a fixed value range like [0,1]. My metrics that return values between 0 and 1 map continuously as they simply count fields from a set of all possible fields, hence ratio seems fine. The one with negative values: the zero does not mean complete absence, so I think it is an interval scale. Oct 1, 2013 at 13:55
• @Mahoni You're welcome. In terms of statistics, I have only come across ratio and interval. And even these two later become very interchangeable (most statistics works for interval also works for ratio variable.) So, I'd think we need not worry too much if it's ratio or interval, just acknowledging it being a continuous variables should suffice. Oct 1, 2013 at 13:57
• In terms of statistics, "nominal" and "ordinal" variables are very common. That said, the deeper you go into statistics, you more you focus on the results of counting them, directly or indirectly. Oct 1, 2013 at 15:18