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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. "
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.
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.
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 — Preceding unsigned comment added by 220.127.116.11 (talk)
Alleged distinction between "scientific" and "statistical" hypotheses
The following passage is unsourced and unclear, and seems to only add confusion:
"It should be emphasised that a statistical hypothesis is conceptually different from a scientific hypothesis. Therefore, in order to apply the null hypothesis test, the scientific hypothesis should first be converted into a suitable statistical hypothesis. For instance, in a clinical trial, the claim may be that there is a difference between two study groups, whereas its counter-claim would be that there is no such difference. Here, the "no difference between two groups" is a scientific claim, and as such a scientific null hypothesis."
That appears to make no sense. Why is "no difference between groups" not a "statistical" hypothesis? It is in fact the null hypothesis in NHST. Note that after saying that the distinction between "scientific" and "statistical" should be emphasized, that distinction hasn't even been defined. If there is a meaningful difference between the two, it is not explained by the example. If the editor feels strongly about including this passage, the editor should find a reputable, authoritative source on the topic and paraphrase its explanation. — Preceding unsigned comment added by 2605:E000:8443:8D00:A1A2:26F6:EDF3:743A (talk) 21:54, 4 June 2017 (UTC)
- The distinction is implied in the definition of the statistical hypothesis, which is given at the beginning of the paragraph. Statistical hypothesis refers to a distribution from which the data is drawn from. E.g. standard normal distribution, Cauchy distribution, chi-squared distribution. "No difference between two groups," "Earth is flat", "Earth revolves around the sun" are general statements, not a distribution. I guess the failure to recognise this distinction this is one of the reason why people misuse NHST. As such I am reverting the passage back. If you feel like you can improve the overall statements, then please feel free to make change. Also, as a general courtesy to other editors, please refrain from outright deleting the passages without reaching a consensus (or giving some warning) in the talk page. Manoguru (talk) 06:26, 5 June 2017 (UTC)
Manoguru still hasn't provided a source for the contended distinction, so I am removing it in accordance with wiki policy. A single user believing something is true, without proper citations, is not sufficient for inclusion. The burden of consensus and "general courtesy" is on Manoguru in this case. Moreover, Manoguru's explanation for the supposed distinction between "scientific hypothesis" and "statistical hypothesis" appears contradictory. "No difference between two groups" is a null hypothesis in what the article calls "statistical hypothesis testing," yet Manoguru claims "no difference between groups" is only a "scientific hypothesis," not a "statistical hypothesis." Manoguru also claims that statistical hypotheses are about what shape (normal, chi square, etc.) the distribution of the data has. That seems to be a very unconventional definition of "statistical hypothesis." Although p-values can be used in tests of, say, departure from normality, p-values are more often used for tests of mean differences or associations. Indeed, the shape of the distribution is not typically what is being tested in NHST; rather, a particular distribution is more often an assumption required for the validity of the test. 18.104.22.168 (talk) 17:09, 5 June 2017 (UTC)
Distribution of a test statistic?
In the Calculation section, end of first paragraph:
"As such, the test statistic follows a distribution determined by the function used to define that test statistic and the distribution of the input observational data."
I am only an arm-chair math fan, but if I use my think box real hard, I can usually grok the message. Here, I was confused. Are we talking a 'probability' distribution? If so, how does this statement follow from what precedes it? I'm trying to make a picture of it in my mind, and it is going all M.C. Escher on me. OmneBonum (talk) 07:37, 8 July 2017 (UTC)