(a) The Signal Detection Theory (1) framework for the
dual-criterion experiment. Gaussian functions describe the probability
density, P(z), of the internal response distributions
(in standard z-scores; abscissa) for the noise [N:
PN(z)] alone (dashed curve)
and for the signal + noise [S:
PS(z)]. Thin vertical lines
show their means with sensitivity (d′ = zHit −
zFA, with zHit and zFA the z scores for the observed
correct target detection and false alarm rates) being the distance
between these means (d′ = 1 in this case) measured in
units of the noise standard deviation, σN, and assuming
that N and S are normally distributed
with σ = σN = σS. We define an
“absolute” criterion as cA =
−zFA. Defined in this way, criteria are independent of the univariance
assumption (i.e., σS = σN), because
they depend on the N distribution only. The
corresponding values of the likelihood ratio criterion, β =
Ps(z =
cA)/PN(z
= cA), characterize observers' response
bias independently of d′. Error rate is minimized when
β =
PN/PS,
(with PN and PS
the a priori N and S
probabilities) but experimental results show that observers adopt a
more conservative behavior with βs closer to one (1). The vertical
dashed and continuous heavy lines show optimal criteria for
PS = 0.5 and
PS = 0.25, respectively. The shaded
area denotes the False Alarm (FA) rate for the latter case.
(b) One trial sequence as detailed in the text.
(c) The 12 experimental conditions as characterized by
the combination of two distinct stimuli of contrast
C1 and C2 and of
four stimulus probabilities.