The current tag except (and description) of reads

Hypothesis testing assesses whether data are inconsistent with a given hypothesis rather than being an effect of random fluctuations.

It seems to me this is a false dichotomy, as data can often be considered outcomes of a random data generating process regardless of whether $H_0$ holds or not. I wonder if we could get a better excerpt (and description).

I do not feel competent enough to write a really good excerpt myself, but we do have highly competent users around; maybe they will find my concern valid and will chip in.

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    $\begingroup$ I think this is a result of our preference to have short excerpts. W/ a little elaboration, it'll be fine. $\endgroup$ Sep 1 at 11:24
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    $\begingroup$ Maybe I'm overthinking it, but the right definition depends on whether you want the tag to encompass all forms of hypothesis testing, including Bayesian alternatives (e.g. BEST), or whether it should strictly be about null-hypothesis significance testing. $\endgroup$ Sep 2 at 6:16
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    $\begingroup$ @FransRodenburg, my first concern is to remove whatever is misleading or incorrect. After that I think hypothesis-testing should cover hypothesis testing in general (including Bayesian), not only specific instances (frequentist). $\endgroup$ Sep 2 at 6:28

In the spirit of keeping the description short, here are some suggestions for removing the imprecise language of "random fluctuations":

  • Hypothesis testing provides an empirical answer to a yes or no question. (See comments.)
  • Hypothesis testing assesses whether data provides sufficient evidence to favor one hypothesis over another.

Or a slightly longer one for NHST specifically:

  • A frequentist statistical tests assesses how likely it is that the data were generated under the null-hypothesis (a statement of no difference, or no effect), and then decides whether or not to reject it.
  • $\begingroup$ I prefer your second definition to your first, which seems to encompass all binary decisions in decision theory (and much else besides) $\endgroup$
    – Glen_b
    Sep 7 at 5:33
  • $\begingroup$ @Glen_b I tried to write something as short as possible, but I agree it is too broad like that, so I've crossed it out. $\endgroup$ Sep 7 at 15:49

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