Handbook of Psychology, Volume 4: Experimental Psychology

104Foundations of Visual Perception

Variable Criterion

The observers’task is to decide on every trial whether it was

a signal trial or a catch trial. The only evidence they have

isthe stimulus, , which could have been caused by NorSN.

As with high-threshold theory, they could use Bayes’s rule to

calculate the posterior probability of SN,

p(SN
).

Theexpressions
(
SN)and
(
N),explainedinFigure4.8E,

arecalledlikelihoods.(Weusethenotation
()ratherthan

p(),becauseitrepresentadensity,notaprobability.)They

couldalsocalculatetheposterioroddsinfavorofSN,

.

p(SN)



p(N)

(
SN)



(
N)

p(SN
)



p(N
)

(
SN)p(SN)



(
SN)p(SN)
(
N)p(N)

STRICT CRITERION LAX CRITERION

energy

MEDIUM CRITERION

energy

(C) noise

(D) signal

+ noise

energy

d’

(G)ROC CURVES

energy

CATCH TRIALS

noise density

SIGNAL TRIALS

energy

energy energy

energyenergy

noise density signal density

signal + noise

density

noise density

signal + noise

density

noise density

d’

d’

d’

(A)low

energy

(B)energyhigher

l(ε|SN)

l(ε|N)

ε

noisesignal + noise

(E) LIKELIHOOD

(F)ROC CURVE

hit rate

false alarm rate

εcεcεc

Figure 4.8Signal detection theory.

Signal Added to Noise

According to signal detection theory a catch trial is not
merely the occasion for the nonpresentation of a stimulus
(Figures 4.8Aand 4.8B). It is the occasion for the ubiquitous
background noise (be it neural or environmental in origin) to
manifest itself. According to the theory, this background
noisefluctuates from moment to moment. Let us suppose that
this distribution is normal (Egan, 1975, has explored alterna-

tives), with mean (^) Nand standard deviation (^) N(Nstands
forthe noise distribution). On signal trials a signal is added to
the noise. If the energy of the signal is d, its addition will pro-
duce a new fluctuating stimulus, whose distribution is also
normal but whose mean is (^) SN= (^) N+d(SNstands for the
signal+noise distribution). The standard deviations are
identical, (^) SN= (^) N. If we let d
= dN, then d
=^ SN N^ N.