Probability of error: Difference between revisions

Revision as of 21:52, 5 July 2009

Revision as of 14:02, 17 December 2009

Line 1:

{{Unreferenced|date=December 2009}}

{{Orphan|date=December 2009}}

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.

==Probabilities of error in 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.

Line 8 ⟶ 10:

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

* For a Type I error, it is shown as αα (alpha) and is known as the ''size'' of the test and is 1 minus the [[Specificity (tests) | specificity]] of the test. It should also be noted that α (alpha) 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 ββ (beta) and is 1 minus the [[Statistical power|power]] or 1 minus the [[sensitivity (tests)|sensitivity]] of the test.

==Probabilities of error in statistical modelling and econometrics==

The fitting of many [[Mathematical model|models]] in statistics and [[econometrics]] usually seeks 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]].

{{DEFAULTSORT:Probability Of Error}}

[[Category:Error]]

[[Category:Experimental design]]

[[Category:Articles lacking sources (Erik9bot)]]

[[de:Irrtumswahrscheinlichkeit]]