## p-value - Wikipedia, the free encyclopedia

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** /p/-value **

In statistics, the */p/-value* is a function of the observed sample results
(a statistic) that is used for testing a statistical hypothesis. More
specifically, the /p/-value is defined as the probability of obtaining a
result equal to or "more extreme" than what was actually observed, assuming
that the null hypothesis is true.^[1]^[2] Here, "more extreme" is dependent
on the way the hypothesis is tested. Before the test is performed, a
threshold value is chosen, called the significance level of the test,
traditionally 5% or 1% ^[3] and denoted as /Î±/.

If the /p/-value is less than or equal to the chosen significance level
(/Î±/), the test suggests that the observed data are inconsistent with
the null hypothesis, so the null hypothesis must be rejected. However, that
does not prove that the tested hypothesis is true. When the /p/-value is
calculated correctly, this test guarantees that the Type I error rate is at
most /Î±/.

Since /p/-value is used in frequentist inference (and not Bayesian
inference), it does not in itself support reasoning about the probabilities
of hypotheses but is only as a tool for deciding whether to reject the null
hypothesis.

Statistical hypothesis tests making use of /p/-values are commonly used in
many fields of science and social sciences, such as economics,
psychology,^[4]biology, criminal justice and criminology, and
sociology.^[5] Misuse of this tool continues to be the subject of
criticism.^[6]

*Contents*

· 1 Basic concepts
· 2 Definition and interpretation
· 3 Calculation
· 4 Examples

· 4.1 One roll of a pair of dice
· 4.2 Five heads in a row
· 4.3 Sample size dependence
· 4.4 Alternating coin flips
·

Source: en.wikipedia.org/wiki/P-value