Probability of error

<h2 id="hypothesis-testing">Hypothesis testing</h2>
<p>In <a href="/facts/Hypothesis_testing/yv9RPF6U">hypothesis testing</a> in <a href="/facts/Statistics/DNPsKGYU">statistics</a>, two types of <i><a href="/facts/Error/20QgR4EI">error</a></i> are distinguished.
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<ul><li><a href="/facts/Type_I_and_type_II_errors/aazbF3fq">Type I errors</a> which consist of rejecting a <a href="/facts/Null_hypothesis/C8NwSE9J">null hypothesis</a> that is true; this amounts to a false positive result.</li>
<li><a href="/facts/Type_I_and_type_II_errors/aazbF3fq">Type II errors</a> which consist of failing to reject a null hypothesis that is false; this amounts to a false negative result.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a></li></ul>
<p>The probability of error is similarly distinguished. 
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<ul><li>For a Type I error, it is shown as α (alpha) and is known as the <i>size</i> of the test and is 1 minus the <a href="/facts/Specificity_(tests)/pzc9qfdz">specificity</a> of the test. This quantity is sometimes referred to as the confidence of the test, or the level of significance (LOS) of the test.</li>
<li>For a Type II error, it is shown as β (beta) and is 1 minus the <a href="/facts/Statistical_power/5KU54nW1">power</a> or 1 minus the <a href="/facts/Sensitivity_(tests)/pzc9qfdz">sensitivity</a> of the test.</li></ul>
<h2 id="statistical-and-econometric-modelling">Statistical and econometric modelling</h2>
<p>The fitting of many <a href="/facts/Statistical_model/jKkT5ftm">models</a> in statistics and <a href="/facts/Econometrics/7U52gzHt">econometrics</a> usually seeks to minimise the difference between observed and predicted or theoretical values.  This difference is known as an <i>error</i>, though when observed it would be better described as a <i><a href="/facts/Errors_and_residuals_in_statistics/Ef0LgAS4">residual</a></i>.
</p><p>The error is taken to be a <a href="/facts/Random_variable/TwTBXnLT">random variable</a> and as such has a <a href="/facts/Probability_distribution/EpsKKVRu">probability distribution</a>. Thus distribution can be used to calculate the probabilities of errors with values within any given range.
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<ul><li><a href="https://www.bartleby.com/subject/engineering/electrical-engineering/concepts/probability-of-error">https://www.bartleby.com/subject/engineering/electrical-engineering/concepts/probability-of-error</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>"Type I Error and Type II Error - Experimental Errors in Research". explorable.com. Retrieved 2024-02-29. <a href="https://explorable.com/type-i-error" target="_blank">https://explorable.com/type-i-error</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
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Probability of error open-in-new

Probability of error