Editing Receiver operating characteristic (section)

==Basic concept==
{{See also|Type I and type II errors|Sensitivity and specificity}}
A classification model ([[Classifier (mathematics)|classifier]] or [[medical diagnosis|diagnosis]]<ref name="Sushkova">{{cite journal |last1=Sushkova |first1=Olga |last2=Morozov |first2=Alexei |last3=Gabova |first3=Alexandra |last4=Karabanov |first4=Alexei |last5=Illarioshkin |first5 =Sergey |journal=Sensors |number=14 |pages=4700 |title=A Statistical Method for Exploratory Data Analysis Based on 2D and 3D Area under Curve Diagrams: Parkinson's Disease Investigation |volume=21 |year=2021 |pmid=34300440 |doi=10.3390/s21144700| pmc=8309570 |bibcode=2021Senso..21.4700S |doi-access=free }}</ref>) is a [[Mapping (mathematics)|mapping]] of instances between certain classes/groups. Because the classifier or diagnosis result can be an arbitrary [[Real number|real value]] (continuous output), the classifier boundary between classes must be determined by a threshold value (for instance, to determine whether a person has [[hypertension]] based on a [[blood pressure]] measure). Or it can be a [[Countable set|discrete]] class label, indicating one of the classes.

Consider a two-class prediction problem ([[binary classification]]), in which the outcomes are labeled either as positive (''p'') or negative (''n''). There are four possible outcomes from a binary classifier. If the outcome from a prediction is ''p'' and the actual value is also ''p'', then it is called a ''true positive'' (TP); however if the actual value is ''n'' then it is said to be a ''false positive'' (FP). Conversely, a ''true negative'' (TN) has occurred when both the prediction outcome and the actual value are ''n'', and a ''false negative'' (FN) is when the prediction outcome is ''n'' while the actual value is ''p''.

To get an appropriate example in a real-world problem, consider a diagnostic test that seeks to determine whether a person has a certain disease. A false positive in this case occurs when the person tests positive, but does not actually have the disease. A false negative, on the other hand, occurs when the person tests negative, suggesting they are healthy, when they actually do have the disease.

Consider an experiment from '''P''' positive instances and '''N''' negative instances for some condition. The four outcomes can be formulated in a 2×2 ''[[contingency table]]'' or ''[[confusion matrix]]'', as follows:

{{diagnostic testing diagram}}
<!-- 
{| align=center
|-
! colspan=2 | &nbsp;
! colspan=2 align=center | actual value
|-
! colspan=2 | &nbsp; !! ''p'' !! ''n'' !! style="padding-left:1em;" | total
|-
! rowspan=2 valign=middle | prediction<br 
/>outcome
! valign=middle style="padding-right:1em;" | ''p'''
| style="border:thin solid; padding:1em;" | True<br />Positive
| style="border:thin solid; padding:1em;" | False<br />Positive
| style="padding-left:1em;" | P'
|-
! valign=middle style="padding-right:1em;" | ''n'''
| style="border:thin solid; padding:1em;" | False<br />Negative
| style="border:thin solid; padding:1em;" | True<br />Negative
| style="padding-left:1em;" | N'
|-
! colspan=2 align=right style="padding-right:1em;" | total
| align=center| P || align=center | N
|}.
-->