Psychophysical Methods 103differed in color (Figure 4.6A), shape (Figure 4.6B), or both
(Figure 4.6C); they were called Different. In the test chamber
two food hoppers were available; one of them delivered food
when the texture was Same, the other when the texture was
Different. Choosing the Different hopper can be taken to be
analogous to a “Yes” response, and choosing the Same hopper
analogous to a “No” response. To produce ROC curves, Cook
and Wixted (1997) manipulated the prior probabilities of
Same and Different patterns. The ROC curves were nonlinear,
as Figure 4.7 shows.
Signal Detection Theory
Nonlinear ROC curves require a different approach to the
problem of detection, called signal detection theory,summa-
rized in Figure 4.8. The key innovation of signal detection
theory is to assume that (a) all detection involves the detec-
tion of a signal added to background noise and (b) there is no
observer threshold (as we will see, this does not mean that
there is no energy threshold).
(A) Color display (B) Shape display(C) Redundant display (D) Same display
Figure 4.6 Illustrative examples of the many color, shape, and redundant Different and Same displays used in
the experiments of Cook and Wixted (1997), after their Figure 4.3 and figures available at http://www.pigeon.
psy.tufts.edu/jep/sdmodel/htm (accessed January 2, 2002). See insert for color version of this figure.p(hit)1.00.80.60.40.20.0
0.0 0.2 0.4 0.6 0.8 1.0
p(false alarm)
Figure 4.7 The ROC curve of shape discrimination for Ellen, one of the pi-
geons in the Cook and Wixted (1997) experiments. Circle: equal prior prob-
abilities for Same and Different textures. Squares: prior probability favored
Different. Triangles: prior probability favored Same. Redrawn from authors’
Figure 5.