Statistics

=====Null hypothesis and alternative hypothesis=====
Interpretation of statistical information can often involve the development of a [[null hypothesis]] which is usually (but not necessarily) that no relationship exists among variables or that no change occurred over time.<ref>{{cite book | last = Everitt | first = Brian | title = The Cambridge Dictionary of Statistics | publisher = Cambridge University Press | location = Cambridge, UK New York | year = 1998 | isbn = 0521593468 | url = https://archive.org/details/cambridgediction00ever_0 }}</ref><ref>{{cite web |url=http://www.yourstatsguru.com/epar/rp-reviewed/cohen1994/ |title=Cohen (1994) The Earth Is Round (p < .05) |publisher=YourStatsGuru.com |access-date=2015-07-20 |archive-date=2015-09-05 |archive-url=https://web.archive.org/web/20150905081658/http://www.yourstatsguru.com/epar/rp-reviewed/cohen1994/ |url-status=live }}</ref>

The best illustration for a novice is the predicament encountered by a criminal trial. The null hypothesis, H<sub>0</sub>, asserts that the defendant is innocent, whereas the alternative hypothesis, H<sub>1</sub>, asserts that the defendant is guilty. The indictment comes because of suspicion of the guilt. The H<sub>0</sub> (status quo) stands in opposition to H<sub>1</sub> and is maintained unless H<sub>1</sub> is supported by evidence "beyond a reasonable doubt". However, "failure to reject H<sub>0</sub>" in this case does not imply innocence, but merely that the evidence was insufficient to convict. So the jury does not necessarily ''accept'' H<sub>0</sub> but ''fails to reject'' H<sub>0</sub>. While one can not "prove" a null hypothesis, one can test how close it is to being true with a [[Statistical power|power test]], which tests for [[type II error]]s.

What [[statisticians]] call an [[alternative hypothesis]] is simply a hypothesis that contradicts the null hypothesis.