Task 2 Signal detection theory Flashcards
Signal and noise distributions
signal: stimulus presented to a subject (e.g., tone)
noise: all other stimuli in the environment –> can sometimes be mistaken for a stimulus
False alarm, Correct rejection, Hit, Miss
False alarm: subject says yes on a noise trial
Hit: subject says yes on signal trial
Miss: subject says no when signal is present
Correct rejection: subject says no when noise is present
FA, H, M, CR
false alarm: subject says yes on noise trial
hit: subject says yes on signal trial
miss: subject says no on signal trial
correct rejection: subject says no on noise trial
Probability distribution of signal detection trial
- left curve: P of perceptual effect caused by noise (N)
- right curve: P of perceptual effect caused by signal-plus-noise (S+N)
perceptual effect: subject’s experience on each trial
discriminatory index d’
the subject’s sensitivity to a stimulus is indicated by the distance d’
calculated by separation divided by spread
Signal detection theory
used in decision making processes where there is uncertainty (close to threshold)
- the decision of the subject depends on the location of the subject’s criterion
subject criterion: rule followed by subject (“ if the perceptual effect is greater than the criterion the signal is (not) present”)
Effect of shifting criterion
liberal criterion:
a) Noise: most of distribution falls to the right of the criterion –> high probability of false alarm
b) Signal: entire distribution falls to the right of the distribution –> high P of hit
neural criterion:
a) noise: small part of the distribution falls to the right of the criterion –> small P of false alarm
b) Signal: most of distribution falls to right of criterion –> high P of hit
conservative criterion:
a) noise: almost none of the curve to the right of the criterion –> low P of false alarm
b) signal: only small proportion right of criterion –> low P of hit
Effect of signal strength
signal strength affects the probability density functions:
- streonger signal: shifts S+N curve to the right further away from the N curve
Payoffs
- adding cost/benefit to possible outcomes causes changes to the motivation towards choosing a liberal/conservative criterion
Beta
- ratio of neural activity produced by signal and noise at Xc –> ratio of both curves
β= P(X|S) / P(X|NS)
Effect of shifting criterion on beta
a) if Xc is shifted to right (conservative): β > 1 –> fewer yes = fewer hits and fewer false alarms
b) if Xc is shifted to left (liberal): β < 1 –> more yes = more hits and more false alarms
c) if β = 1: P(H) = P (CR) = P(M) = P (FA) –> neural criterion
Optimal beta
best that can be expected for signal strength and a given level of sensitivity
Influence of signal probability
- if P=.5: βopt = 1
- if P< .5: βopt <1 –> liberal adjustment
- if P> .5: βopt > 1 –> conservative adjustment
Influence of payoffs on beta
v: value of desirable event
c: cost of undesirable event
- increase in denominator: decrease in opt. beta = liberal responding
- increase in numerator: increase in opt. beta = conservative responding
Sluggish beta
sluggish beta: humans do not adjust beta in response to probability as much as they should for optimal outcomes
- less conservative than they should if opt. beta is high
- less liberal than they should be if opt. beta is low
ROC curve
receiver operating characteristic curve:
- plots & of hits vs. that of false alarms –> describes full range of subject’s options in one curve
- can tell us whether two subjects are equally sensitive to a tone –> shape of the curve indicates the subject’s sensitivity
- portrays equivalence of sensitivity across changing levels of bias:
each signal detection condition generates one point on the curve –> if signal strength and sensitivity remain constant, the changing β produces a curved set of points - lower left: conservative
- upper right: liberal
