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?
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1$\begingroup$ 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. $\endgroup$– Glen_bCommented Oct 10, 2019 at 1:09
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$\begingroup$ 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. $\endgroup$– AlexisCommented Nov 19, 2019 at 1:21
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2 Answers
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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).
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$\begingroup$ 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) $\endgroup$ Commented Oct 10, 2019 at 0:39
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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).
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$\begingroup$ 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? $\endgroup$ Commented Oct 10, 2019 at 1:09
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$\begingroup$ 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. $\endgroup$– NoahCommented Oct 10, 2019 at 1:44