Editing Statistical inference (section)

=== Frequentist inference ===
{{Main|Frequentist inference}}

This paradigm calibrates the plausibility of propositions by considering (notional) repeated sampling of a population distribution to produce datasets similar to the one at hand. By considering the dataset's characteristics under repeated sampling, the frequentist properties of a statistical proposition can be quantified—although in practice this quantification may be challenging.

==== Examples of frequentist inference ====
* [[p-value|''p''-value]]
* [[Confidence interval]]
* [[Null hypothesis]] significance testing

==== Frequentist inference, objectivity, and decision theory ====
One interpretation of [[frequentist inference]] (or classical inference) is that it is applicable only in terms of [[frequency probability]]; that is, in terms of repeated sampling from a population. However, the approach of Neyman<ref>{{cite journal | last = Neyman | first = J. | author-link = Jerzy Neyman | year = 1937 | title = Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability | jstor = 91337 | journal = Philosophical Transactions of the Royal Society of London A | volume = 236 | issue = 767| pages = 333–380 | doi=10.1098/rsta.1937.0005 | bibcode = 1937RSPTA.236..333N | doi-access = free }}</ref> develops these procedures in terms of pre-experiment probabilities. That is, before undertaking an experiment, one decides on a rule for coming to a conclusion such that the probability of being correct is controlled in a suitable way: such a probability need not have a frequentist or repeated sampling interpretation. In contrast, Bayesian inference works in terms of conditional probabilities (i.e. probabilities conditional on the observed data), compared to the marginal (but conditioned on unknown parameters) probabilities used in the frequentist approach.

The frequentist procedures of significance testing and confidence intervals can be constructed without regard to [[utility function]]s. However, some elements of frequentist statistics, such as [[statistical decision theory]], do incorporate [[utility function]]s.{{Citation needed|date=April 2012}} In particular, frequentist developments of optimal inference (such as [[minimum-variance unbiased estimator]]s, or [[uniformly most powerful test]]ing) make use of [[loss function]]s, which play the role of (negative) utility functions. Loss functions need not be explicitly stated for statistical theorists to prove that a statistical procedure has an optimality property.<ref>Preface to Pfanzagl.</ref> However, loss-functions are often useful for stating optimality properties: for example, median-unbiased estimators are optimal under [[absolute value]] loss functions, in that they minimize expected loss, and [[least squares]] estimators are optimal under squared error loss functions, in that they minimize expected loss.

While statisticians using frequentist inference must choose for themselves the parameters of interest, and the [[estimators]]/[[Test statistic#Common test statistics|test statistic]] to be used, the absence of obviously explicit utilities and prior distributions has helped frequentist procedures to become widely viewed as 'objective'.<ref>{{Cite journal|last=Little|first=Roderick J.|date=2006|title=Calibrated Bayes: A Bayes/Frequentist Roadmap|journal=The American Statistician|volume=60|issue=3|pages=213–223|issn=0003-1305|jstor=27643780|doi=10.1198/000313006X117837|s2cid=53505632}}</ref>