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My colleague took exception to this sentence in a genetics paper we are drafting together:

"For each genetic locus in which we identified significantly associated variants, ..."

He feels that "significantly associated" is an abuse of terminology, an (incorrect) shorthand for something like "achieving p-values below our specified level of significance". I would argue that while it may be a shorthand, it is accepted and well-understood. See for example the abstract of this genetics paper.

Note that our sentence comes in the discussion section of the paper, after we have presented our results (the variants being referred to) and specified the significance level we have used to account for multiple testing.

Who is correct? Is there an accepted authority on such matters?

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    $\begingroup$ Regarding an accepted authority: I'd say that CrossValidated comes close... $\endgroup$
    – Stephan Kolassa
    Commented May 30, 2017 at 13:41
  • $\begingroup$ English, Ah, what a slippery fellow! The test of correctness is whether reasonably knowledgeable readers understand clearly. Try it out on a few people on your hallway at the lab. $\endgroup$
    – David Smith
    Commented May 30, 2017 at 20:56

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From what I see, people talk about "significant main effects", "significant interactions", "significant differences", "significant correlations" and - yes - "significant associations" all the time, instead of "main effects whose parameter estimates, in $t$ tests, achieved p-values below our specified level of significance" and so forth.

Some shorthand is commonly accepted, and "significantly associated", in my opinion, does not even reach the kind of "shorthand" that could cause confusion.

I'd say: go ahead and use the short version.

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    $\begingroup$ +1 but I think it's always better to write "statistically significant" instead of "significant". $\endgroup$
    – amoeba
    Commented May 30, 2017 at 13:10
  • $\begingroup$ @amoeba Even when it becomes "statistically significantly associated" instead of "significantly associated"? I agree it's technically more correct but it's also more of a mouthful and hence more offputting in terms of sentence flow (which is always a consideration for me as I feel it's really important for comprehension) $\endgroup$
    – Nick
    Commented May 30, 2017 at 13:21
  • $\begingroup$ @Nick I agree that "statistically significantly" is a bit of a mouthful (unlike "statistically significant"). Not sure what to suggest then, perhaps "significantly" alone is okay, at least nothing else comes to my mind right now. $\endgroup$
    – amoeba
    Commented May 30, 2017 at 13:26
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    $\begingroup$ (+1) @amoeba Because the phrase "statistically significant," in the sense intended here, is redundant, I have long found it better to establish a clear and consistent terminology at the outset. A convenient one is to tell your readers that "significant" means that a p-value is less than such-and-such a threshold (such as 5%) and that important means the effect is large enough to be worthy of attention. $\endgroup$
    – whuber ♦
    Commented May 30, 2017 at 13:39

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