# Ratio Measurement Scale and Absolute Zero

Levels of measurement are: Nominal, ordinal, interval and ratio.

What happens when the absolute zero of a data set using the ratio scale is a negative number? I.E when the absolute zero is -25,000? How does this impact related math. Or does it?

• Note that the levels of measurement typology you refer to ({Stevens' typology](en.wikipedia.org/wiki/Level_of_measurement)) is just one of many; the way your question is phrased it sounds like you think it's the only way to categorize variables. Commented Oct 10, 2019 at 1:09
• Emphasis on the just one of many! For example: there are also (among others) discrete modular, and continuous modular, rank, and continuous, and complex measures. Commented Nov 19, 2019 at 1:21

If you use the absolute scale, for which 'absolute 0' is the $$0,$$ then that's a ratio scale.

For example, $$0^o$$ Kelvin is the same as $$-273.15^o$$ C. On the Kelvin scale you can make sense of the statement $$100^0$$ K is half as 'hot' as $$200^0$$ K. [Half is a ratio.]

In cooking, you couldn't make sense of "$$100^0$$ C (boiling water) is half as 'hot' as $$200^0$$ C" (baking bread).

• And 15 degrees celcius is one degree hotter than 14 degrees celcius - so celcius is an interval scale (and as @BruceET inferred Kelvin is a ratio scale) Commented Oct 10, 2019 at 0:39

If the absolute zero on your scale is -25,000, by which I presume you mean observing a score of -25,000 implies that there is none of the construct of interest, then you have an interval scale, not a ratio scale.

A ratio scale is one in which a score of 0 corresponds to having none of the construct, and doubling the score corresponds to doubling the amount of the construct. Counts and amounts are ratio; most other numerical measurements (e.g., IQ score, SAT score, score on visual analog scale, etc.) are interval. If you could shift the entire scale by a constant and the new values would have the same meaning as the old values, then you have an interval scale (e.g., measuring on a scale from -3 to 3 is the same as measuring on a scale from 1 to 7).

• This is helpful. Thank you for your time. One follow-on questions using temperature as an example of an interval scale-- these is no decipherable meaning to "zero temperature". As I understand it, Ratio scales have an absolute zero beyond which there is nothing (no construct nor value). So what happens when there is a point beyond which there is nothing (no value) but that point is a negative number. Is it still an interval scale when there is an point beyond which there is no value, but that point is less than zero? Commented Oct 10, 2019 at 1:09
• Yes, it is still interval. Temperature measures the thermal motion in matter; if there is no motion, temperature is at its absolute minimum. In Celcius, this is −273.15°. Celcius is an interval measure. In Kelvin, this is 0°; Kelvin is a ratio measure.
– Noah
Commented Oct 10, 2019 at 1:44