Probability of error: Difference between revisions

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{{More citations needed|date=February 2024}}

==Probability of error in hypothesis testing==

In [[statistics]], the term "error" arises in two ways. Firstly, it arises in the context of [[decision making]], where the '''probability of error''' may be considered as being the probability of making a wrong decision and which would have a different value for each type of error. Secondly, it arises in the context of [[statistical modelling]] (for example regression) where the model's predicted value may be in error regarding the observed outcome and where the term '''probability of error''' may refer to the probabilities of various amounts of error occurring.

==Hypothesis testing==

In [[hypothesis testing]] in [[statistics]], two types of ''[[error]]'' are distinguished.

*[[Type I and type II errors|Type I error]]s which consist of rejecting a [[null hypothesis]] that is true; this amounts to a false positive result.

*[[Type I and type II errors|Type II error]]s which consist of failing to rejectingreject a null hypothesis that is false; this amounts to a false negative result.<ref>{{Cite web |title=Type I Error and Type II Error - Experimental Errors in Research |url=https://explorable.com/type-i-error |access-date=2024-02-29 |website=explorable.com}}</ref>

The '''probability of error''' is similarly distinguiseddistinguished.

* For a Type I error, it is shown as &alpha;α (alpha) and is known as the ''size'' of the test and is 1 minus the [[Specificity (tests)|specificity]] of the test. This quantity is sometimes referred to as the confidence of the test, or the level of significance (LOS) of the test.

* For a Type II error, it is shown as &beta;β (beta) and is 1 minus the [[Statistical power|power]] or 1 minus the [[sensitivity (tests)|sensitivity]] of the test.{{Cn|date=May 2024}}

==Statistical and econometric modelling==

ManyThe fitting of many [[statistical model|models]]s in statistics and [[econometrics]] will usually seekseeks to minimise the difference between observed and predicted or theoretical values. This difference is known as an ''error'', though when observed it would be better described as a ''[[Errors and residuals in statistics|residual]]''.

The error is taken to be a [[random variable]] and as such has a [[probability distribution]]. Thus distribution can be used to calculate the probabilities of errors with values within any given range.

== References ==

{{Reflist}}

* https://www.bartleby.com/subject/engineering/electrical-engineering/concepts/probability-of-error

The '''probability of error''' is similarly distinguised.

* For a Type I error, it is shown as &alpha; (alpha) and is known as the ''size'' of the test and is 1 minus the [[specificity]] of the test.

* For a Type II error, it is shown as &beta; (beta) and is 1 minus the [[Statistical power|power]] or 1 minus the [[sensitivity (tests)|sensitivity]] of the test.

{{DEFAULTSORT:Probability Of Error}}

==Probability of error in statisitical modelling and econometrics==

[[Category:Errors and residuals]]

==Probability of error in[[Category:Statistical hypothesis testing==]]

Many [[model]]s in statistics and [[econometrics]] will usually seek to minimise the difference between observed and predicted or theoretical values. This difference is known as an ''error'', though when observed it would be better described as a ''[[Errors and residuals in statistics|residual]]''.

{{statistics-stub}}

The error is taken to be a [[random variable]] and as such has a [[probability distribution]].