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== Null hypothesis vs. "our hypothesis" ==
== Misleading examples ==


I am referring to the sentence:
The examples given are rather misleading. For example in the section about the rolling of two dice the articles says.
"In this case, a single roll provides a very weak basis (that is, insufficient data) to draw a meaningful conclusion about the dice. "


<code>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.
However it makes no attempt to explain why this is so - and a slight alteration of the conditions of the experiment renders this statement false.
</code>


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.
Consider a hustler/gambler who has two sets of apparently identical dice - one of which is loaded and the other fair. If he forgets which is which - and then rolls one set and gets two sixes immediately then it is quite clear that he has identified the loaded set.


This is especially confusing in the beginning when the reader does not know what is going to be tested.
The example relies upon the underlying assumption that dice are almost always fair - and therefore it would take more than a single roll to convince you that they are not. However this assumption is never clarified - which might mislead people into supposing that a 0.05 p value would never be sufficient to establish statistical significance. Richard Cant <small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/152.71.70.77|152.71.70.77]] ([[User talk:152.71.70.77|talk]]) </small><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->


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? [[User:Alexander Shekhovtsov|Alexander Shekhovtsov]] ([[User talk:Alexander Shekhovtsov|talk]]) 12:38, 14 June 2023 (UTC)
That cheating gambler would be wrong in his conclusion 1 out of 36 times though [[User:Yinwang888|Yinwang888]] ([[User talk:Yinwang888|talk]]) 16:31, 24 November 2021 (UTC)


== p-value, P-value, p value, P value? ==
== Recent edits ==
It is rather traditional that values of 5% and 1% are chosen as significance level. In fact the value of p itself is an indication of the strenght of the observed result. Whether or not the null hypothesis may be rejected is also a matter of 'taste'. But anyway does a small p-value suggest that the observed data is sufficiently inconsistent with the null hypothesis.[[User:Madyno|Madyno]] ([[User talk:Madyno|talk]]) 09:47, 8 December 2021 (UTC)


What is the best way to use here? I have seen all of these. [[Special:Contributions/130.226.41.15|130.226.41.15]] ([[User talk:130.226.41.15|talk]]) 11:54, 16 June 2023 (UTC)
The .05 level is by far the most conventional level. The .01 level is sometimes used but much more rarely. But in any case, the "Usage" section was mainly just a repetition of what had already been said in the "Basics Concepts" section and the "Definition and Interpretation" section, so I've trimmed it down considerably. A section that's just restating what's already been said doesn't need to give so much detail (if it needs to exist at all). [[Special:Contributions/23.242.195.76|23.242.195.76]] ([[User talk:23.242.195.76|talk]]) 02:28, 15 December 2021 (UTC)


:This is addressed at [[P-value#cite_note-2]].
== Does the hyphenization indeed vary? ==
:However, all three examples are from the USA. There should be more balance, preferably with an international source (ISO standard, or IMS, or IMU, or ISI?), or at least from some other countries/regions.
:''Cf.'' [https://doi.org/10.2307/2681417 Recommended Standards for Statistical Symbols and Notation. COPSS Committee on Symbols and Notation] from 1965.
:Personally I prefer lowercase ("''p''-value" or "''p'' value"), which I believe is more common, except when ''p'' has already been assigned to another variable. Italics should always be used for the "''p''"!
:—DIV ([[Special:Contributions/1.145.104.186|1.145.104.186]] ([[User talk:1.145.104.186|talk]]) 01:50, 14 August 2024 (UTC))


== Unnecessary hedging: "Usually, T is a test statistic." ==
"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. [[User:Victorvscn|~victorsouza]] ([[User talk:Victorvscn|talk]]) 16:57, 17 March 2022 (UTC)

As a reader, if I read "usually" that suggests an exception. 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." [[User:DavidCJames|DavidCJames]] ([[User talk:DavidCJames|talk]]) 22:09, 29 June 2024 (UTC)

:[[WP:BOLD|Be bold]]. —DIV ([[Special:Contributions/1.145.104.186|1.145.104.186]] ([[User talk:1.145.104.186|talk]]) 01:54, 14 August 2024 (UTC))

Latest revision as of 01:54, 14 August 2024

Null hypothesis vs. "our hypothesis"

[edit]

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?

[edit]

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]

This is addressed at P-value#cite_note-2.
However, all three examples are from the USA. There should be more balance, preferably with an international source (ISO standard, or IMS, or IMU, or ISI?), or at least from some other countries/regions.
Cf. Recommended Standards for Statistical Symbols and Notation. COPSS Committee on Symbols and Notation from 1965.
Personally I prefer lowercase ("p-value" or "p value"), which I believe is more common, except when p has already been assigned to another variable. Italics should always be used for the "p"!
—DIV (1.145.104.186 (talk) 01:50, 14 August 2024 (UTC))[reply]

Unnecessary hedging: "Usually, T is a test statistic."

[edit]

As a reader, if I read "usually" that suggests an exception. 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]

Be bold. —DIV (1.145.104.186 (talk) 01:54, 14 August 2024 (UTC))[reply]
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