Editing Accuracy and precision (section)

==In classification==
===In binary classification===
{{Main|Evaluation of binary classifiers#Single metrics}}
''Accuracy'' is also used as a statistical measure of how well a [[binary classification]] test correctly identifies or excludes a condition. That is, the accuracy is the proportion of correct predictions (both [[true positive]]s and [[true negative]]s) among the total number of cases examined.<ref>{{cite journal| url= http://www.umich.edu/~ners580/ners-bioe_481/lectures/pdfs/1978-10-semNucMed_Metz-basicROC.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.umich.edu/~ners580/ners-bioe_481/lectures/pdfs/1978-10-semNucMed_Metz-basicROC.pdf |archive-date=2022-10-09 |url-status=live |last= Metz |first= CE |title= Basic principles of ROC analysis |journal= Semin Nucl Med.| date= October 1978 |volume= 8| number=4 |pages=283–98|doi= 10.1016/s0001-2998(78)80014-2 |pmid= 112681 }}</ref> As such, it compares estimates of [[pre- and post-test probability]]. To make the context clear by the semantics, it is often referred to as the "Rand accuracy" or "[[Rand index]]".<ref>{{cite web |url=http://www.alta.asn.au/events/altss_w2003_proc/altss/courses/powers/ALTSS2003-Val+Eval-L3.pdf |title=Archived copy |access-date=2015-08-09 |url-status=dead |archive-url=https://web.archive.org/web/20150311073014/http://alta.asn.au/events/altss_w2003_proc/altss/courses/powers/ALTSS2003-Val+Eval-L3.pdf |archive-date=2015-03-11 }}</ref><ref>{{cite arXiv |eprint=1503.06410|title=What the F-measure doesn't measure|last1=Powers|first1=David M. W.|class=cs.IR|year=2015}}</ref><ref>{{cite web|url=http://www.anthology.aclweb.org/E/E12/E12-1035.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.anthology.aclweb.org/E/E12/E12-1035.pdf |archive-date=2022-10-09 |url-status=live|title=The Problem with Kappa|author=David M W Powers|website=Anthology.aclweb.org|access-date=11 December 2017}}</ref> It is a parameter of the test.
The formula for quantifying binary accuracy is:
<math display="block">\text{Accuracy}=\frac{TP+TN}{TP+TN+FP+FN}</math>
where {{math|1=TP = True positive}}; {{math|1=FP = False positive}}; {{math|1=TN = True negative}}; {{math|1=FN = False negative}}

In this context, the concepts of trueness and precision as defined by ISO 5725-1 are not applicable. One reason is that there is not a single “true value” of a quantity, but rather two possible true values for every case, while accuracy is an average across all cases and therefore takes into account both values. However, the term ''[[Precision and recall|precision]]'' is used in this context to mean a different metric originating from the field of information retrieval ([[#In information systems|see below]]).

===In multiclass classification===
When computing accuracy in multiclass classification, accuracy is simply the fraction of correct classifications:<ref name="op24">{{cite journal|last=Opitz|first=Juri|title=A Closer Look at Classification Evaluation Metrics and a Critical Reflection of Common Evaluation Practice|journal=Transactions of the Association for Computational Linguistics|date=2024|volume=12|pages=820–836|doi=10.1162/tacl_a_00675|url=https://doi.org/10.1162/tacl_a_00675|arxiv=2404.16958}}</ref><ref>{{cite web |title=3.3. Metrics and scoring: quantifying the quality of predictions |url=https://scikit-learn.org/stable/modules/model_evaluation.html#accuracy-score |website=scikit-learn |access-date=17 May 2022 |language=en}}</ref>
<math display="block">\text{Accuracy}=\frac{\text{correct classifications}}{\text{all classifications}}</math>
This is usually expressed as a percentage. For example, if a classifier makes ten predictions and nine of them are correct, the accuracy is 90%.

Accuracy is sometimes also viewed as a ''micro metric'', to underline that it tends to be greatly affected by the particular class prevalence in a dataset and the classifier's biases.<ref name="op24"/>

Furthermore, it is also called top-1 accuracy to distinguish it from top-5 accuracy, common in [[convolutional neural network]] evaluation.  To evaluate top-5 accuracy, the classifier must provide relative likelihoods for each class.  When these are sorted, a classification is considered correct if the correct classification falls anywhere within the top 5 predictions made by the network.  Top-5 accuracy was popularized by the [[ImageNet]] challenge. It is usually higher than top-1 accuracy, as any correct predictions in the 2nd through 5th positions will not improve the top-1 score, but do improve the top-5 score.