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I am looking at a set of statistics slides and came across the following question and answer: Quiz: Temperature. What is it, interval scale or ratio scale? Temperature can be seen as both! Interval scale: an increase from 5$^\circ$C to 10$^\circ$C is the same (in some aspects) as an increase from 10$^\circ$C to 15$^\circ$C. Ratio scale: if temperature is in Kelvin (relative to $-$273$^\circ$C).

Would it not be appropriate to argue that temperature is always a ratio scale? It holds all the properties of an interval scale but always has a true minimum. The temperature does not have to be measured in kelvin for there to be a true minimum so why would this answer say that?

Nick Cox
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Lamma
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    It is in ratio scale when in Kelvin, if in Celsius it is only in interval scale. I think you got confused about "true minimum", for a scale to be rational it has to have a meaningful 0, which Kelvin has and Celsius does not. – user2974951 Feb 03 '20 at 11:57
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    The point is about data, not some underlying latent physical scale. It remains true that the ratio of Celsius or Fahrenheit measurements is meaningless, which rules out (e.g.) coefficients of variation being any use. – Nick Cox Feb 03 '20 at 12:23
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    The principle is that the base of the kelvin scale is 0 K, which just happens to be (close to) $-273^\circ$C. Detail: The unit is now kelvin not Kelvin. The general practice when a scientific unit is named after a person is that the unit abbreviation is capitalised but the unit name is not: think watt not Watt, and so forth. (I have to guess that even with international agreements on this principle that it was realised that usages on Fahrenheit and Celsius are beyond a committee's control.) – Nick Cox Feb 03 '20 at 12:24
  • 'But always has a true minimum' - this is not necessarily the case. It's mostly a quirk of the definition, but there exist real systems with negative temperatures on the Kelvin scale (in laser physics, for one). It's just that unintuitively, they are very, very hot. – jkm Feb 03 '20 at 13:18

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