0

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.

Mahoni
  • 223
  • 2
    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). – Nick Cox Oct 01 '13 at 15:16
  • 1
    This issue appears in some guise in many dozens of questions here. Some of the more relevant threads are http://stats.stackexchange.com/questions/928/measurement-level-of-percentile-scores and http://stats.stackexchange.com/questions/17029/can-categorical-data-only-take-finitely-or-countably-infinitely-many-values/17074#17074. 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. – whuber Oct 01 '13 at 15:17
  • 1
    @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. – whuber Oct 01 '13 at 15:20
  • 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. – Nick Cox Oct 01 '13 at 15:26
  • @Nick The "definitely" is simply correct, not dogmatic. Stevens had a subtle view of variable typologies, but fundamental to his analysis was the idea of a group acting on the (possible) data. (See Table 1 in his paper.) In the case of interval data the group is the translation group; for ratio data, it is the similarity group (positive rescalings). Because you cannot arbitrarily rescale counts, counts just do not fit into Stevens' ratio category. For Tukey's point of view you don't have to trust me: see the book! – whuber Oct 01 '13 at 15:30
  • That makes your statement much clearer, so thanks. What Stevens was trying to do and what he said is important, if only historically, but I am happy, like I guess most data analysts, to forget the group theory and go with "ratios make sense because zeros are well defined" as the nub of the matter. As I hinted in my first comment, I have no brief to defend NOIR, which is incomplete and misleading as a taxonomy of data, but I think counts can be fitted in without undue stress. – Nick Cox Oct 01 '13 at 15:37
  • Thanks for the discussion in every case, it's insightful for my confusions! – Mahoni Oct 01 '13 at 15:55
  • 2
    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. – jank Oct 01 '13 at 16:57
  • @jank Great reference, really appreciated – Mahoni Oct 01 '13 at 17:27

0 Answers0