Editing Frequentist probability (section)

== Scope ==
The frequentist interpretation is a philosophical approach to the definition and use of probabilities; it is one of several such approaches. It does not claim to capture all connotations of the concept 'probable' in colloquial speech of natural languages.

As an interpretation, it is not in conflict with the mathematical axiomatization of probability theory; rather, it provides guidance for how to apply mathematical probability theory to real-world situations. It offers distinct guidance in the construction and design of practical experiments, especially when contrasted with the [[Bayesian probability|Bayesian interpretation]]. As to whether this guidance is useful, or is apt to mis-interpretation, has been a source of controversy. Particularly when the frequency interpretation of probability is mistakenly assumed to be the only possible basis for [[frequentist inference]]. So, for example, a list of mis-interpretations of the meaning of [[p-values]] accompanies the article on {{mvar|p}}-values; controversies are detailed in the article on [[Statistical hypothesis testing#Controversy|statistical hypothesis testing]]. The [[Jeffreys–Lindley paradox]] shows how different interpretations, applied to the same data set, can lead to different conclusions about the 'statistical significance' of a result.{{citation needed|date=April 2012}}

As [[William Feller|Feller]] notes:{{efn|
Feller's comment is a criticism of [[Pierre-Simon Laplace]]'s solution to the "tomorrow's sunrise" problem that used an alternative probability interpretation.
:
Despite [[Pierre-Simon Laplace|Laplace]]'s explicit and immediate disclaimer ''in the source'', based on Laplace's personal expertise in both astronomy and probability, two centuries of nattering criticism have followed.
}}
{{Blockquote|
There is no place in our system for speculations concerning the probability that the [[sunrise problem|sun will rise tomorrow]]. Before speaking of it we should have to agree on an (idealized) model which would presumably run along the lines ''"out of infinitely many worlds one is selected at random&nbsp;..."'' Little imagination is required to construct such a model, but it appears both uninteresting and meaningless.<ref name=Feller-1957>
{{cite book
 |first = W. |last = Feller  |author-link = William Feller
 |year = 1957
 |title = An Introduction to Probability Theory and Its Applications
 |volume = 1  |page = 4
}}
</ref>
}}