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To conclude this section, let us summarize the reasons for
not to use procedures based on p-values.
- The interpretation of p-values is misleading, because they do
not provide probabilities of hypotheses,
though they sound and are commonly interpreted as such.
- Methods based on p-values pretend to provide answers only based
on the statistical properties of the null hypothesis, without
taking into account if other hypotheses are conceivable, and how the
alternative hypotheses describe the data. For example,
these methods do not take into account the fact that
a supposed signal appears at a given place rather than elsewhere,
which bins could be affected by a physical model
and how reasonable a model is.
- These methods provide only binary answers, accepted/rejected.
As a consequence they are not efficient enough to analyze
rare phenomena, which can only be discovered by
a proper combination of (even very) small pieces of evidence.