Editing Null hypothesis (section)

==Technical description==
The null hypothesis is a default hypothesis that a quantity to be measured is zero (null). Typically, the quantity to be measured is the difference between two situations. For instance, trying to determine if there is a positive proof that an effect has occurred or that samples derive from different batches.<ref>{{cite book | last = Everitt | first = Brian | title = The Cambridge Dictionary of Statistics | publisher = Cambridge University Press | location = Cambridge and New York | year = 1998 | isbn = 978-0521593465 | url-access = registration | url = https://archive.org/details/cambridgediction00ever_0 }}</ref><ref name=":0">{{Cite web|url=https://www.investopedia.com/terms/n/null_hypothesis.asp|title=Null Hypothesis Definition|last=Hayes|first=Adam|website=Investopedia|language=en|access-date=10 December 2019}}</ref>

The null hypothesis is generally assumed to remain possibly true. Multiple analyses can be performed to show how the hypothesis should either be rejected or excluded e.g. having a high confidence level, thus demonstrating a statistically significant difference. This is demonstrated by showing that zero is outside of the specified confidence interval of the measurement on either side, typically within the [[real number]]s.<ref name=":0" /> Failure to exclude the null hypothesis (with any confidence) does not logically confirm or support the (unprovable) null hypothesis. (When it is proven that something is e.g. bigger than ''x'', it does not necessarily imply it is plausible that it is smaller or equal than ''x''; it may instead be a poor quality measurement with low accuracy. Confirming the null hypothesis two-sided would amount to positively proving it is bigger or equal than 0 ''and'' to positively proving it is smaller or equal than 0; this is something for which infinite accuracy is needed as well as exactly zero effect, neither of which normally are realistic. Also measurements will never indicate a non-zero probability of exactly zero difference.) So failure of an exclusion of a null hypothesis amounts to a "don't know" at the specified confidence level; it does not immediately imply null somehow, as the data may already show a (less strong) indication for a non-null. The used confidence level does absolutely certainly not correspond to the likelihood of null at failing to exclude; in fact in this case a high used confidence level ''expands'' the still plausible range.

A non-null hypothesis can have the following meanings, depending on the author a) a value other than zero is used, b) some margin other than zero is used and c) the [[alternative hypothesis|"alternative" hypothesis]].<ref>{{Cite journal|last=Zhao|first=Guolong|date=18 April 2015|title=A Test of Non Null Hypothesis for Linear Trends in Proportions|url=https://doi.org/10.1080/03610926.2013.776687|journal=Communications in Statistics – Theory and Methods|volume=44|issue=8|pages=1621–1639|doi=10.1080/03610926.2013.776687|s2cid=120030713 |issn=0361-0926|url-access=subscription}}</ref><ref>{{Cite web|title=OECD Glossary of Statistical Terms – Non-null hypothesis Definition|url=https://stats.oecd.org/glossary/detail.asp?ID=3737|access-date=5 December 2020|website=stats.oecd.org}}</ref>

Testing (excluding or failing to exclude) the null [[hypothesis]] provides evidence that there are (or are not) statistically sufficient grounds to believe there ''is'' a relationship between two phenomena (e.g., that a potential treatment has a non-zero effect, either way). Testing the null hypothesis is a central task in [[statistical hypothesis testing]] in the modern practice of science. There are precise criteria for excluding or not excluding a null hypothesis at a certain confidence level. The confidence level should indicate the likelihood that much more and better data would still be able to exclude the null hypothesis on the same side.<ref name=":0" />

The concept of a null hypothesis is used differently in two approaches to statistical inference. In the significance testing approach of [[Ronald Fisher]], a null hypothesis is rejected if the observed data are [[Statistical significance|significantly]] unlikely to have occurred if the null hypothesis were true. In this case, the null hypothesis is rejected and an [[alternative hypothesis]] is accepted in its place. If the data are consistent with the null hypothesis statistically possibly true, then the null hypothesis is not rejected. In neither case is the null hypothesis or its alternative proven; with better or more data, the null may still be rejected. This is analogous to the legal principle of [[presumption of innocence]], in which a suspect or defendant is assumed to be innocent (null is not rejected) until proven guilty (null is rejected) beyond a reasonable doubt (to a statistically significant degree).<ref name=":0" />

In the hypothesis testing approach of [[Jerzy Neyman]] and [[Egon Pearson]], a null hypothesis is contrasted with an [[alternative hypothesis]], and the two hypotheses are distinguished on the basis of data, with certain error rates. It is used in formulating answers in research.

Statistical inference can be done without a null hypothesis, by specifying a [[statistical model]] corresponding to each candidate hypothesis, and by using [[model selection]] techniques to choose the most appropriate model.<ref>{{Citation |last1=Burnham |first1=K. P. |last2=Anderson |first2=D. R. |year=2002 |title=Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach |edition=2nd |publisher=Springer-Verlag |isbn=978-0-387-95364-9 |url-access=registration |url=https://archive.org/details/modelselectionmu0000burn }}.</ref> (The most common selection techniques are based on either [[Akaike information criterion]] or [[Bayes factor]]).