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I'm going to have a hard time even expressing what I'm looking for well. I love statistics and studies and drawing conclusions from them. To do this well one eventually needs to be able to talk about groups of people in statistical averages. For example when reading a study about topic T I may point out that the sample group was created in such a way to get a large number of individuals from group X, studies show that those in group X are more likely to belong in group Y and people in group Y may have a different reaction to topic T then then expected from a truly random sampling of individuals, so we must recognize this study may be slanted slightly by group Y's tendency towards topic T. When talking with other statisticians and the ilk (like on Skeptics board) this is recognized and understood necessary step to understanding and utilizing statistics.

When speaking more with layman (perhaps not the right word, basically people who don't have the same love of statistics and thus not use to need to qualify the limits of a given study) this is harder, because they confuse a statistical average for a statement for a specific individual for the group. If I say group X on average fits into category Y someone may interpret it as a claim that anyone from X will be in category Y, which is clearly false. If category Y is an already charged subject, like socioeconomic status, they may see this a value judgement about group X.

Thus when speaking with laymen I find myself having to constantly qualify every step of an analysis so that they are not misinterpreted. I keep having to repeat that statistical averages over large sample sizes should never be taken to imply that any single individual of a group should be expected to have a specific trait.

I'm looking for a good way of making this distinction clear, that there may be value in speaking of large scale averages across a huge sample size, but that this should never be applied to specific individuals, that it's in fact quite harmful to do so. Something concise I could repeat a few times to reiterate this concept so people don't forget the important distinction. If it could also work in the stress that small correlations should not be taken as absolutes (a 5% chance that someone in group X has trait Y obviously shouldn't be taken as a claim that an individual of X likely has Y; but people seem to leap to that conclusion quickly) that would be great, but perhaps too much to hope to fit in while still being concise.

I'm not looking for a long thesis on how to express the distinction, just help coming up with some consist phrases that can be used, perhaps even something I could explain in a little more detail at start of an analysis but then reiterate as appropriate the short phrase, much like how I use the "correlation is not causation" phrase over and over.

Any convenient phrase or word is good, but as I'm mostly needing to express this idea to statistical 'laymen', and particularly to those who may already be prone to misunderstanding (otherwise this wouldn't be a problem in the first place) I'm looking for a phrase that expresses the concept without being too esoteric, something that is easy to be understood.

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    A teacher of mine used this metaphor to explain the danger and limitations of average: " My feet are burning in the oven and my head is in the freezer , so on average I'm warm" I found that even a 5 years old can understand this concept. You can adapt it to your need.
    – P. O.
    Commented Dec 10, 2015 at 18:11
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    en.wikipedia.org/wiki/Heteroscedasticity
    – Jim
    Commented Dec 10, 2015 at 18:18
  • @P.Obertelli I do love that phrase. Though I fear it is so blatant, so as to be obvious to a 5 year old, as to risk patronizing an adult if used in that exact form. Still, if I find a way to lower the degree of hyperbole in the example just a tad I think it could be a good example for me to use in trying to explain the difference.
    – dsollen
    Commented Dec 10, 2015 at 18:25
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    The teacher who used that uses it for graduate students (macro-economics 101 f0r business students) . It's a classic joke in economy/statistics, if you tell it as a joke, nobody will be offended see listserv.linguistlist.org/pipermail/ads-l/2014-January/… for example of uses since the 60's
    – P. O.
    Commented Dec 10, 2015 at 19:05
  • You're not trying to tar them [all] with the same brush.
    – stevesliva
    Commented Dec 11, 2015 at 6:44

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An idiom for what you are trying to avoid is tarred with the same brush, which American Heritage defines as:

tarred with the same brush -

Considered or described as having the same faults or bad qualities.

Wiktionary adds, "... especially unjustly." And that addition is especially fitting for what you are trying to describe, which is a sort of guilt by association.

The Cambridge Dictionary of American Idioms supports painted with the same brush as an alternative, but on second look at Ngram, tarred is still by far more common even if painted is on the rise.

Metaphorically similar is broad brush.

I'm not sure this is all that fitting because it describes what you're trying not to imply. But it works conversationally: "My research finds-- and I'm not trying to tar everyone with the same brush-- that college students drink too much."

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