# Can ratio data have negative values?

I get the concept of a "true zero" value, but I'm not sure why this implies that there cannot be any negative values—at least that's what most sources say that I found only, with only few exceptions.

But what about a variable like account_balance? To me, it ticks off all requirements for ratio data, and negative values are meaningful to indicate debt. I can even say that one person has twice as much debt as another person, and a balance of 0 still feels like a "true zero" expressing the absence of any money.

If account_balance is not a ratio data, what else should it be then? And why?

• Two questions: (1) can you point to a definition of/set of criteria for ratio data that you're using ("... it ticks all of the requirements ...") and (2) why do you care? what is the context? (IMO definitions are created because they make useful distinctions. In order to decide whether account balance is ratio-valued, I think we need to know what you want to do with it and how your procedures will change if you decide that it is or isn't ratio-valued ... Apr 13, 2021 at 2:06
• @BenBolker Regarding (1), I was referring to the commonly used criteria: (a) meaningful order, (b) measurable difference, and (c) having a "true zero". Regarding (2), mainly curiosity and to improve my understanding. Apr 13, 2021 at 2:12
• I agree it's an interesting example, but I'm not sure (in the absence of concrete applications) that there will be a definitive answer. I'll be curious to see someone try. Apr 13, 2021 at 2:15

Yep, ratio data can have negative values. These lecture notes even describe your specific case of account balance. Your intuitions were right.

Your bank account balance is another [example of ratio-scale data]. Although you can have a negative or positive account balance, there is a definite and nonarbitrary meaning of an account balance of 0.

I don't know of any text arguing that negative values are forbidden because of the presence of a true zero. For example, Reid's Introduction to Statistics makes no claim about a non-negativity requirement for ratio data.

• Yes, this was one of the source I've found that say ratio data can have negative values. It's just that there are many other sites that say otherwise. Hence my confusion. Apr 14, 2021 at 2:27
• There are other typologies for levels of measurement, e.g. by Mosteller and Tukey. Theirs distinguishes amounts (non-negative real) from balances (real). Apr 15, 2021 at 1:43