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Some measures seem to be of a different type to others, depending on what kind of statements are meaningful. Different scale types try to capture that difference.

Known interval scale types are:

  1. Nominal
  2. Ordinal
  3. Interval
  4. Ratio

The great thing is, that each scale type builds on the previous one, adding additional properties. I came across a fifth scale type, which comes after the ratio scale type.

The problem is, I only found it in the book Software Metrics: A Rigorous & Practical Approach. also explained on these slides.

Absolute scale measurement is just counting

  • The attribute must always be of the form of ‘number of occurrences of x in the entity’
  • number of failures observed during integration testing
  • number of students in this class
  • Only one possible measurement mapping (the actual count)
  • All arithmetic is meaningful

A previous definition was, that the absolute scale was simply on a fixed range of values, but the more I seek for it I come across this more simple definition: it's limited to counting.

Any thoughts on this? I feel a bit insecure here.

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    $\begingroup$ The NOIR system is more problematic than most accounts allow, but it seems to me that counts don't need much special treatment. They are ratio scale, as zeros are well defined. They can't be negative, but neither can many ratio scale variables (e.g. height, weight, temperature in Kelvin). $\endgroup$
    – Nick Cox
    Oct 1, 2013 at 15:16
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    $\begingroup$ This issue appears in some guise in many dozens of questions here. Some of the more relevant threads are stats.stackexchange.com/questions/928/… and stats.stackexchange.com/questions/17029/…. I summarized one of my answers as I am suggesting that the question itself is too limiting and that one should be open to possibilities that go beyond those suggested by the classical taxonomy of variables. That applies here, too. $\endgroup$
    – whuber
    Oct 1, 2013 at 15:17
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    $\begingroup$ @Nick Counts do deserve special treatment for many reasons. That is why, for instance, Tukey explicitly devoted the last quarter of EDA to analysis of count data. They definitely are not ratio variables, at least not according to Stevens' original definitions. $\endgroup$
    – whuber
    Oct 1, 2013 at 15:20
  • $\begingroup$ I find that "definitely" a little dogmatic. What do you think they are according to Stevens? I don't think the Stevens taxonomy implies that any of its categories is homogeneous, e.g. ordinal includes "poor, better, best" and ranks, but ranks are just counts in another guise (e.g. number higher or lower PLUS 1). So, saying that counts are ratio scale does not commit me (or Tukey's shade) to saying that counts behave like all other ratio variables. In short, my point is counts can be seen as R within NOIR, but that doesn't circumscribe how they should be analysed. $\endgroup$
    – Nick Cox
    Oct 1, 2013 at 15:26
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    $\begingroup$ there is an interesting discussion of Stevens's proposal in: Velleman, P. F., & Wilkinson, L. (1993). Nominal, ordinal, interval, and ratio typologies are misleading. The American Statistician, 47(1), 65-72. Counting data are just one example of scales that do not fit precisely into the NOIR-system. $\endgroup$
    – jank
    Oct 1, 2013 at 16:57

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