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#

P-value analysis of the `statistical significance' of the data

P-value is the term preferred in modern statistics to
describe what physicists call, in simple words, ``probability of the tail(s),'' or
``probability to observe the events actually observed,
or rarer ones, *given* a null hypothesis''
(note `given': the probability
of whatever *has been* observed, without the specification of a
particular condition, is always unity).
In the frequentistic approach,
the null hypothesis is rejected with a significance level if
the p-value gets below , where is typically chosen to be
or . Besides the recognized misinterpretation of the p-value result
(see e.g. [2]), there are often disputes about how this
reasoning should be applied, because it is easy to show that
there is much arbitrariness in the kind of test to be performed
(it is well known that practitioner often seeks for the test that tells
what they like, moving for -test, to run-test and to
other tests with fancy names, if the previously tried tests
were ``not sensitive to the effect'') and
in the data to include in the test,
as it is sketched in the following subsections.

**Subsections**

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Giulio D'Agostini
2005-01-09