# What is the difference between our hypothesis-testing, statistical-significance, and p-value tags? Do they need to stay separate?

Two very popular tags are (3.4k questions) and (2.4k questions).

These two concepts are very much related, and whenever I happen to edit a question that has one of these tags I almost always feel that I should add another one too. Looking now at the top-voted questions in both tags, I don't see much of a difference in topics. However, I am not actively following any of these tags and so can easily miss some nuances. Hence my question:

• Should we maybe make them synonyms? If so, what is a better master tag?

• Or should we maintain some difference in usage between these tags? If so, what should this difference be? Can we hope to enforce this difference, given 6k existing questions?

There is also a very related tag (950 questions), but I feel that it should stay separate. There are enough questions asking specifically about $p$-values, their meaning, and properties. Update following @gung's comment: Actually, [p-value] is used mostly interchangeably with the former two tags, so perhaps we should think of combining all three tags together.

• To me, [p-value] & [statistical-significance] are closer to synonyms. I think of [hypothesis-testing] as indicating the question is about the underlying logic of HT. But I agree that they overlap a lot & especially in people's usage of them on CV. – gung - Reinstate Monica Mar 10 '16 at 19:35
• @gung, I am all in favour of having a tag that is about the logic/principles/controversies behind HT/p-values, but I am afraid none of these tags is currently doing this job. With 3.4k questions, [hypothesis-testing] certainly includes hundreds/thousands of questions about particular tests on particular datasets. Given the sheer amount of questions, I think realistically there is no chance of sorting this all out in any meaningful way, hence we might (?) be better off giving up and merging all three tags. Re [p-value] you have a point, I will edit. – amoeba Mar 10 '16 at 20:17
• I'm not taking a strong stance here. The above is just my opinion. To really figure this out would take a good deal of work. For my part, I would be OK with either merging or leaving separate, as the community prefers. – gung - Reinstate Monica Mar 10 '16 at 20:39
• I think [hypothesis testing] is a much broader domain than [p-value], incorporating the articulation of null and alternative hypotheses, selecting a distributional model of the parameter being hypothesized about, constructing a test statistic given that model, finding the p-value for that statistic and interpreting it, making a rejection decision based on the p-vlaue, drawing a substantive conclusion following the decision to reject or not. Merging [p-value] with [statistical-significance] ostensibly makes sense. – Alexis Mar 15 '16 at 22:09
• Thanks, @Alexis. This makes sense and also agrees with what gung wrote. – amoeba Mar 15 '16 at 22:33
• (this is mere opinion here) but I tend to somewhat agree with gung and Alexis in that I see [hypothesis-testing] as clearly distinct, and the other two as substantially closer, but nevertheless I see statistical significance and p-values as still distinct concepts. One can ask questions about p-values without having a significance level (so significance doesn't really enter into it) and one can ask about significance without ever having heard of a p-value (using only a pure critical value approach). We might need to identify whether they're effectively synonyms here in practice. – Glen_b Apr 3 '16 at 1:30
• To expand on my previous comment ... If I wanted to ask a question about why p-values are uniform under the null, I'd want a "p-value" tag on my post (and wouldn't see statistical-significance as much of a substitute), but if I had a question about how to find a critical value in a chi-square test, I might find the mapping of statistical-significance to p-value to be baffling to say the least. On the other hand if they're nearly always not distinct, perhaps there's an argument for combining them. If we were to merge them, which would merge into which? – Glen_b Apr 3 '16 at 1:34
• @Glen_b Thanks for joining the discussion. To tell the truth, I was sort of convinced here that it's better not to do anything about these tags. It seems to be one of the cases of largely intersecting but nevertheless separate tags. I would accept such an answer if somebody posted it. – amoeba Apr 6 '16 at 21:53