Talk:P-value

Does the hyphenization indeed vary?

"As far as I'm aware, APA guidelines say you have to italicize every statistic, period. Saying "p value" is no different than saying "DP value". I mean, it's not a symptom of dropping the hyphen, but merely a situation where the topic was the value of p, rather than the p-value. Whether that makes sense, i.e., that there really exists a difference between these situations which justifies the different styling, I do not know. But I'm under the impression that that's how people use it. It's the rationalization that I have been able to do, since I have seen many articles formatted under APA style that use "p-value" at some point. ~victorsouza (talk) 16:57, 17 March 2022 (UTC)

In short, yes, hyphenization does indeed vary. I've seen "p value" with and without a hyphen in APA journals. In AMA journals (such as JAMA), I've typically seen "p value" or "P value" unhyphenated. But in American Statistical Association sources, I nearly always see "p-value" hyphenated. Regarding your claim that "APA guidelines say you have to italicize every statistic, period," there's no such guideline. In fact, the official APA style blog (https://blog.apastyle.org/apastyle/hyphenation/) explicitly recommends "t test" not be hyphenated unless used as an adjective (e.g., "t-test results"). 172.91.120.102 (talk) 05:01, 25 April 2022 (UTC)

continuous variables

Note that in the statistics of continuous variables, the probability that a variable will have any specific value is zero. (Unless it comes from a delta function.) In a statistical sense < and <= are the same. In numerical approximations, one might have to be more careful, but then that comes from the process of doing the approximation, not from the statistics itself. Gah4 (talk) 20:56, 25 April 2022 (UTC)

True. And in nearly all real-word circumstances, saying something like p ≤ .05 is indeed equivalent to saying something like p < .05. But not all variables are continuous. For some situations involving count data, you can end up with p-values that are rational numbers, and in theory the p-value could even be exactly .05. So I see the purpose of the "less than or equal to" language for the sake of more universal technical correctness, even if only to accommodate unlikely theoretical cases. 172.91.120.102 (talk) 06:06, 26 April 2022 (UTC)

Hmm, OK. In most problems that I know, either the p variable is continuous, or close enough to continuous that assuming it is, is close enough. In the cases were it isn't, I am not so sure it makes sense either way. That is, if you have a problem where the difference between < and <= seems important, there is probably something else to worry about more. Gah4 (talk) 05:04, 27 April 2022 (UTC)

I agree that there is likely no practical example where there is a consequential distinction between p < .05 and p ≤ .05. Even when the p-value is from a discrete distribution and is a rational number, I don't think it's plausible for it to be exactly .05 except in a highly contrived theoretical scenario. That said, I don't really see a drawback to using the ≤ symbol rather than the < symbol if that placates some theoretical quibble. 134.69.229.134 (talk) 19:24, 27 April 2022 (UTC)

Errors in the article

The article says the p-value is the 'Probability of obtaining a real-valued test statistic at least as extreme as the one actually obtained'. That's only true under the assumption that the null hypothesis actually holds. This is key point!

https://amstat.tandfonline.com/doi/pdf/10.1080/00031305.2016.1154108?needAccess=true is a good source on all this.. Sciencecritical (talk) 23:44, 28 September 2022 (UTC)

First paragraph after "p-value as the statistic for performing significance tests" confuses significance tests with hypotheses tests. The p-value is a result of a significance test, not a statistic for performing statistical tests.

A good reference clarifying the differences between significance tests and hypothesis tests: Biau DJ, Jolles BM, Porcher R. P value and the theory of hypothesis testing: an explanation for new researchers. Clin Orthop Relat Res. 2010 Mar;468(3):885-92. doi: 10.1007/s11999-009-1164-4. PMID: 19921345; PMCID: PMC2816758. — Preceding unsigned comment added by 217.215.254.120 (talk) 06:15, 3 May 2023 (UTC)