Like how much knowledge do you need to parse "bell curve fallacy" versus "incorrect assumption"?

@User1865345 FWIW, many, many questions have appeared confusing a population distribution with a sampling distribution and thereby mis-applying the CLT to the population. We have no tag to help search for such posts, but a quick review of low-voted questions mentioning the CLT ought to turn some up.

I remember a thread pertaining to Stevens' levels of measurement, and there was a comment linking to an external webpage / tutorial / blog post that had a list of examples of data and brief vignettes such that the same data could be interpreted as embodying different levels depending on the question or context.

I would love to see those examples, or other similar examples, for a presentation I am going to give. But I can't find the thread / comment. Does this ring a bell for anyone?

I think this was the main thrust of the paper by Velleman and Wilkinson in American Statistician 1993. An example of my own is inspired by an old paper on brain tumours. The raw, raw data are reports of death by brain tumour. But then they are counted over areas and years and later turned to rates per so many population. A distribution is fitted and the focus is on probability of that outcome or one greater, or some such. The "data" are mapped from one measurement scale to another.

In a nutshell, what are the data? Categories are counted, and lo and behold! nominal scale becomes analysed as ratio scale.

@whuber hm. I agree.

@NickCox wow!

@NickCox I suspect what @gung meant by "the same" data was intended literally: not a compendium, summary, transformation, or whatever: more like Lord's paper on football numbers in which nominal data turn out to carry ordinal information when considered more carefully.

I have seen many examples of such "measurement scale promotion" of such things, such as postal codes (they give geographic information), telephone numbers (ditto, although not so much as in the old days), and even just sequences in which data were collected (ordinal data can turn out to be usefully analyzed as interval data when the sequence was not randomized).

@NickCox, @whuber, yes, I am thinking of a comment with a link that led to a discussion of this and there would be an example of a variable (such as zip codes, although that wasn't it, I don't think) that could be ordinal from one perspective but interval from another perspective. Something more like Lord's "football numbers". FTR, I am aware of Velleman & Wilkinson; this was someone's webpage, not a published paper.