What is the word to describe a variable whose value does not relate to any absolute unit of measure?

Question

What the title says. I know there's a word but can't remember it.

To explain in more detail, I'm trying to state that while the variable is quantitative, the quantity is not referring to an objectively measurable concept. For example something like "happiness" - I can say that happiness is variable linear on an integer scale from 1 to 10, but that does not prevent someone else to define it as logarithmic on a real scale between 0 and 1.

I'm then looking for an adjective to say that: "happiness is a/an ... variable".

I've tried non-parametric, non-unitary, non-measurable, but they all mean something different.

Answer 1

For the variable:

dimensionless (adj.)

Of a physical quantity or its unit: having no dimensions (dimension n. 3c); of the nature of a pure number or ratio, and therefore having a value independent of the choice of units for other quantities. (OED)

For the scale used to measure it:

arbitrary (adj.)

Based on or determined by individual preference or convenience rather than by necessity or the intrinsic nature of something m-w

Answer 2

It sounds like you're referring to an ordinal scale.

Ordinal data is a categorical, statistical data type where the variables have natural, ordered categories and the distances between the categories are not known.[1]: 2  These data exist on an ordinal scale, one of four levels of measurement described by S. S. Stevens in 1946. The ordinal scale is distinguished from the nominal scale by having a ranking. It also differs from the interval scale and ratio scale by not having category widths that represent equal increments of the underlying attribute.[2]

You can categorize some amount of happiness as being "more" than another amount, but things such as "twice as much happiness" don't have any clear meaning.