Is the variable at ratio or interval level if it can take any value between 1 and 100 but not 0? I cannot determine using the definitions of ratio and interval variables.

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    $\begingroup$ If there is no true zero, it is safe to call it an interval variable. $\endgroup$ – Thomas Bilach Oct 25 at 21:56

This doesn't depend on the possible values but on interpretation and what is measured. If it's counts of something, it's ratio, as if one value is twice as high as another, it really means "twice as much" in a properly interpretable way (actually proper counts are absolute scales, which means that they fulfill the conditions for all lower scale types).

Many sources say that a "ratio scale" requires an "absolute zero point". Note that according to the "definition" that I have given, the zero has a special role, because one can't divide by zero. In fact "interpretable ratios" imply (at least in all practical situations, if not strictly mathematically) that the measurements to be compared all have the same sign (normally they are all positive). Zero is then a borderline value that is treated differently from all the other values, as it is not involved in any meaningful ratios. Usually there is a specific interpretation for this, with zero meaning the absence of anything to be measured (zero counts, zero length, zero weight etc.).

On the other hand, if it is for example a rating scale without properly defined meaning of the numerical values (like for example used by a film critic to rate films), it is not even interval (which requires differences to be properly interpreted, meaning that in a well defined sense the difference between 94 and 96 has to be the same as between 12 and 14, say) but only ordinal (all we can say is 96 is better than 94 and 14 better than 12, but there is no quantitative meaning to "how much better").

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  • $\begingroup$ thank you for the response. I understand the type is related to the interpretation and usage of the variable. Let's assume the values are equally spaced so that, for example, the difference between 1 and 2 is the same as between 98 and 99. According to your response, it is a ratio variable? I agree it is more likely a ratio variable than an interval variable. But I am concerned of interpretation of 0 in this case. Could you please clarify? Thanks. $\endgroup$ – xyx Oct 26 at 2:12
  • $\begingroup$ What you describe is the definition of an interval scale, meaning that the same "intervals" (differences) have the same meaning. The ratio scale on top of that requires that ratios ("50 is related to 25 in the same manner as 20 to 10") are meaningful. With counts, for example, a ratio of 2 always means "taking twice the lower number and putting them together gives the higher one". $\endgroup$ – Lewian Oct 26 at 10:37
  • $\begingroup$ What might be called judgment scores -- where a personal judgement is what lies behind a score -- are indeed ordinal insofar as there are no grounds for supposing that e.g. 96 $-$ 94 $=$ 6 $-$ 4. But these are often averaged nevertheless, and indeed in many academic systems they are given in full knowledge of their being averaged. Otherwise put, the pragmatic view is that they are as good as interval scales as you can get. (And marks or grades are often mixed with those from a marking scheme, a correct answer on Question 1 getting 10% of the total and so forth.) $\endgroup$ – Nick Cox Oct 26 at 14:22
  • $\begingroup$ Note that even ranks -- supposedly the quintessential ordinal scale -- are often averaged, e.g. Spearman correlation treats ranks exactly as if they were interval scale. Some purists say that this is precisely what you shouldn't do. More discussion at stats.stackexchange.com/questions/67551/… $\endgroup$ – Nick Cox Oct 26 at 14:26
  • $\begingroup$ Other way round, something like Fahrenheit or Celsius temperature is often held up to those outside physical science as an exemplary interval scale but the history of temperature measurement over some centuries is a messy mixture of approximations, some practical and some theory-guided. $\endgroup$ – Nick Cox Oct 26 at 14:30

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