This question is specifically aimed toward the practice of statistics and data science and toward statistics educators (particularly introductory level statistics).

In brief, ¿when do we really need to distinguish between interval and ratio measurement levels? More specifically, ¿have you ever encountered a situation where the analysis technique or statistical protocol used changed because you were using interval level data instead of ratio level data? (This is an extension of a recent conversation between colleagues.)

I personally have moved away from Stevens' 4-level typology to my own categorization:

  1. dichotomous
  2. categorical
  3. ordinal
  4. scalar

In my teaching (from introductory level statistics to graduate level applied statistics), this has served me & my students very well. By reflecting on the type of variable on this new typology, students can make decisions about which analysis strategy to employ.

So, my question here is to see if the interval/ratio distinction has been useful to others...and more importantly, if so, is this something that is worth sharing with our introductory level statistics/data-science students.

(I recognize there may be some subjectivity to people's responses, but I am hoping there also will be some concrete examples people might be able to share.)

  • 2
    $\begingroup$ The coefficient of variation SD / mean requires ratio level measurement to make sense. More generally, if a zero is arbitrary that usually means negative values are possible and if negative values are possible quite a few operations don't make statistical sense (e.g. taking logarithms). $\endgroup$
    – Nick Cox
    Jan 16, 2022 at 17:05
  • 2
    $\begingroup$ I agree that the four level scheme proposed by Stevens has been oversold. See e.g. tandfonline.com/doi/abs/10.1080/00031305.1993.10475938 The important thing is not how data are recorded but what you do with them. The original recorded form may be categorical but the analysis may be in terms of counts, proportions, odds ratios, whatever. $\endgroup$
    – Nick Cox
    Jan 16, 2022 at 17:10
  • $\begingroup$ Well, you'd usually want inference on interval-level data to be location-equivariant. $\endgroup$ Jan 16, 2022 at 18:14
  • $\begingroup$ The coef of var is indeed a concept that is introduced in some intro stats courses, but I've always been uncertain how much of that is useful information (e.g., I've not seen an authentic analysis at the intro level)...personally, I've not used for for anything below the level of generalized linear modeling; as for location-equivalence, I think most would agree this is a topic beyond the scope of an intro stats course (but still good to note) $\endgroup$
    – Gregg H
    Jan 16, 2022 at 19:46
  • 1
    $\begingroup$ Wilkinson and others have strongly argued that "mak[ing] decisions about which analysis strategy to employ" based on assessments of data type leads to "bad data analysis and bad science." However, I have no doubt it can help college freshmen pass examinations. Therein is the dilemma of the conscientious instructor: teach good statistics or teach exam-passing skills? (The two need not be mutually exclusive, but it is likely less would be "covered" in the former case.) $\endgroup$
    – whuber
    Jan 17, 2022 at 15:53


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