Editing Detection theory (section)

==Psychology==
Signal detection theory (SDT) is used when psychologists want to measure the way we make decisions under conditions of uncertainty, such as how we would perceive distances in foggy conditions or during [[eyewitness identification]].<ref>{{Cite journal | doi=10.1177/2372732215602267|title = Eyewitness Identification and the Accuracy of the Criminal Justice System| journal=Policy Insights from the Behavioral and Brain Sciences| volume=2| pages=175–186|year = 2015|last1 = Clark|first1 = Steven E.| last2=Benjamin| first2=Aaron S.| last3=Wixted| first3=John T.| last4=Mickes| first4=Laura| last5=Gronlund| first5=Scott D.| hdl=11244/49353| s2cid=18529957 | hdl-access=free}}</ref><ref>{{Cite journal | url=https://digitalcommons.fiu.edu/dissertations/AAI3169457/ | title=A theoretical analysis of eyewitness identification: Dual -process theory, signal detection theory and eyewitness confidence| journal=ProQuest Etd Collection for Fiu| pages=1–98| date=January 2005| last1=Haw| first1=Ryann Michelle}}</ref> SDT assumes that the decision maker is not a passive receiver of information, but an active decision-maker who makes difficult perceptual judgments under conditions of uncertainty. In foggy circumstances, we are forced to decide how far away from us an object is, based solely upon visual stimulus which is impaired by the fog. Since the brightness of the object, such as a traffic light, is used by the brain to discriminate the distance of an object, and the fog reduces the brightness of objects, we perceive the object to be much farther away than it actually is (see also [[decision theory]]). According to SDT, during eyewitness identifications, witnesses base their decision as to whether a suspect is the culprit or not based on their perceived level of familiarity with the suspect.

To apply signal detection theory to a data set where stimuli were either present or absent, and the observer categorized each trial as having the stimulus present or absent, the trials are sorted into one of four categories:

:{| class="wikitable"
|-
!
! Respond "Absent"
! Respond "Present"
|-
! Stimulus Present
| [[Type 1 error#Type I and type II errors|Miss]]
| Hit
|-
! Stimulus Absent
| Correct Rejection
| [[Type 1 error#Type I and type II errors|False Alarm]]
|}

Based on the proportions of these types of trials, numerical estimates of sensitivity can be obtained with statistics like the [[sensitivity index|sensitivity index ''d''']] and A',<ref name="Stanislaw 1999 137–49">{{cite journal |last1=Stanislaw |first1=Harold |last2=Todorov |first2=Natasha |title=Calculation of signal detection theory measures |journal=Behavior Research Methods, Instruments, & Computers |date=March 1999 |volume=31 |issue=1 |pages=137–149 |doi=10.3758/BF03207704 |pmid=10495845 |doi-access=free }}</ref>  and response bias can be estimated with statistics like c and β.<ref name="Stanislaw 1999 137–49"/> β is the measure of response bias.<ref>{{Cite web |title=Signal Detection Theory |url=https://elvers.us/perception/sdtGraphic/ |access-date=2023-07-14 |website=elvers.us}}</ref>

Signal detection theory can also be applied to memory experiments, where items are presented on a study list for later testing. A test list is created by combining these 'old' items with novel, 'new' items that did not appear on the study list. On each test trial the subject will respond 'yes, this was on the study list' or 'no, this was not on the study list'. Items presented on the study list are called Targets, and new items are called Distractors. Saying 'Yes' to a target constitutes a Hit, while saying 'Yes' to a distractor constitutes a False Alarm.

:{| class="wikitable"
|-
!
! Respond "No"
! Respond "Yes"
|-
! Target
| [[Type 1 error#Type I and type II errors|Miss]]
| Hit
|-
! Distractor
| Correct Rejection
| [[Type 1 error#Type I and type II errors|False Alarm]]
|}