Probability of error: Difference between revisions

Revision as of 14:02, 17 December 2009

Revision as of 16:07, 7 October 2010

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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 hypothesisHypothesis 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.

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

==ProbabilitiesStatistical ofand error in statisticaleconometric modelling and econometrics==

The fitting of many [[Mathematicalstatistical 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]]. Thus distribution can be used to calculate the probabilities of errors with values within any given range.

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[[Category:Error]]

[[Category:ExperimentalStatistical designterminology]]

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