Talk:P-value

Source cited for definition of P-value

For an article about p-values, it is odd that the definition is taken from a journal paper that disparages the p-value: I would not expect a fair/balanced definition from such a source. If the definition was not taken from the cited paper, then the citation is wrong and is probably due to somebody's personal agenda.

Edited the lead of the article

I just shortened the lead of the article, as well as clarified how p-value fits with hypothesis testing.

I removed the following sentences, and am leaving them here if someone thinks they can be incorporated in other parts of the article (I think they don't, but feel free to try):

An informal interpretation of a p-value, based on a significance level of about 10%, might be:

* $p\leq 0.01$ : very strong presumption against null hypothesis

* $0.01<p\leq 0.05$ : strong presumption against null hypothesis

* $0.05<p\leq 0.1$: low presumption against null hypothesis

* $p>0.1$: no presumption against the null hypothesis

The p-value is a key concept in the approach of Ronald Fisher, where he uses it to measure the weight of the data against a specified hypothesis, and as a guideline to ignore data that does not reach a specified significance level. Fisher's approach does not involve any alternative hypothesis, which is instead a feature of the Neyman–Pearson approach.

The p-value should not be confused with the significance level α in the Neyman–Pearson approach or the Type I error rate [false positive rate].

Fundamentally, the p-value does not in itself support reasoning about the probabilities of hypotheses, nor choosing between different hypotheses – it is simply a measure of how likely the data (or a more "extreme" version of it) were to have occurred, assuming the null hypothesis is true.

Tal Galili (talk) 09:25, 3 January 2015 (UTC)

The problem here is two-fold: (i) You've moved the correct definition *out* of the lead, to the next paragraph, and instead (ii) left in an unintuitive definition that essentially relies on a Neyman-Pearson framework. If someone is operating from a more Fisherian paradigm, the lead paragraph is next to useless to them, while the "as or more extreme" part, while somewhat clumsily worded in the article, would be more intuitive and correct for both.

Glenbarnett (talk) 00:58, 23 March 2015 (UTC)

actual observations versus test statistic

The article states: "Usually, instead of the actual observations, X is instead a test statistic." It would be fair to explain why (what I can't because I do know). Thanks Cuvwb (talk) 17:18, 7 February 2015 (UTC)

formatting problem

This is the opening of #Definition and interpretation:

The p-value is defined as the probability, under the assumption of hypothesis $H$, of obtaining a result equal to or more extreme than what was actually observed. Depending on how we look at it, the "more extreme than what was actually observed" can either mean $\{X\geq x\}$ (right tail event) or $\{X\leq x\}$ (left tail event) or the "smaller" of $\{X\leq x\}$ and $\{X\geq x\}$ (double tailed event).

The problem is the H in the first line is cut off at the bottom, missing a row or two of pixels and its serifs, both in the article and in reproduced here. I have 'MathML' set for math rendering in my preferences, the recommended setting for modern browsers which mine is (up to date Mac OS and Safari).--JohnBlackburne^words_deeds 21:07, 12 March 2015 (UTC)

Lead paragraph

The lead paragraph is unintelligible.drh (talk) 17:40, 13 April 2015 (UTC)