Talk:P-value

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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)[reply]

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)[reply]

Null hypothesis vs. "our hypothesis"

I am referring to the sentence:

As our statistical hypothesis will, by definition, state some property of the distribution, the null hypothesis is the default hypothesis under which that property does not exist.

In subsequent examples, the Null hypothesis is always stated explicitly, e.g. as "data comes from the standard normal distribution", "the coin is fair", etc. There is no example when a property of the distribution is stated and the null hypothesis would be defined as non-existence or a logical negation of the property. Furthermore, "data comes not from N(0,1)" makes little sense as "our statistical hypothesis" because it is too unspecific.

This is especially confusing in the beginning when the reader does not know what is going to be tested.

Would it be better to stick with the Null hypothesis only, state that the test can reject it or not reject it and leave the logic implications to the reader? Or perhaps add a clear example where we can infer acceptance of "our hypothesis" based on rejection of the null hypothesis? Alexander Shekhovtsov (talk) 12:38, 14 June 2023 (UTC)[reply]

p-value, P-value, p value, P value?

What is the best way to use here? I have seen all of these. 130.226.41.15 (talk) 11:54, 16 June 2023 (UTC)[reply]

"Usually, T is a test statistic."

As a reader, if I read "usually" that leaves open the door for counter example. But there is no counter example. A p-value is ALWAYS derived from a a test statistic. Therefore, Wikipedia should drop "usually" in this sentence.

I propose the sentence say "As stated above, T is a test statistic." This matches a sentence earlier in the article, this sentence is present: "The p-value is a function of the chosen test statistic and is therefore a random variable." DavidCJames (talk) 22:09, 29 June 2024 (UTC)[reply]