Editing P-value (section)

=== Interpretations ===

{{blockquote |text=The error that a practising statistician would consider the more important to avoid (which is a subjective judgment) is called the error of the first kind. The first demand of the mathematical theory is to deduce such test criteria as would ensure that the probability of committing an error of the first kind would equal (or approximately equal, or not exceed) a preassigned number α, such as α = 0.05 or 0.01, etc. This number is called the level of significance. |author=Jerzy Neyman |source="The Emergence of Mathematical Statistics"<ref name="Neyman1976">{{cite book | chapter = The Emergence of Mathematical Statistics: A Historical Sketch with Particular Reference to the United States | title = On the History of Statistics and Probability | page = 161 | year = 1976 | last = Neyman | first = Jerzy | author-link = Jerzy Neyman | place = New York | publisher = Marcel Dekker Inc | editor-last = Owen | editor-first = D.B. | series = Textbooks and Monographs | url = https://openlibrary.org/works/OL18334563W/On_the_history_of_statistics_and_probability?edition=key%3A/books/OL5206547M}}</ref>}}

In a significance test, the null hypothesis <math>H_0</math> is rejected if the ''p''-value is less than or equal to a predefined threshold value [[Alpha|<math>\alpha</math>]], which is referred to as the alpha level or [[statistical significance|significance level]]. <math>\alpha</math> is not derived from the data, but rather is set by the researcher before examining the data. <math>\alpha</math> is commonly set to 0.05, though lower alpha levels are sometimes used. The 0.05 value (equivalent to 1/20 chances) was originally proposed by R. [[Ronald Fisher|Fisher]] in 1925 in his famous book entitled "[[Statistical Methods for Research Workers]]".<ref>{{Citation |last=Fisher |first=R. A. |title=Statistical Methods for Research Workers |date=1992 |work=Breakthroughs in Statistics: Methodology and Distribution |series=Springer Series in Statistics |pages=66–70 |editor-last=Kotz |editor-first=Samuel |url=https://doi.org/10.1007/978-1-4612-4380-9_6 |access-date=2024-07-07 |place=New York, NY |publisher=Springer |language=en |doi=10.1007/978-1-4612-4380-9_6 |isbn=978-1-4612-4380-9 |editor2-last=Johnson |editor2-first=Norman L.}}</ref> 

Different ''p''-values based on independent sets of data can be combined, for instance using [[Fisher's combined probability test]].