Fundamental Issues, Models, and Theories 297the stage that performs mental rotation is typically character-
ized as continuous, in the sense that the mentally rotated ob-
ject passes through a continuum of intermediate states from its
initial orientation to the final orientation (Cooper & Shepard,
1973). A completely discrete transformation would be to gen-
erate the final orientation in a single step. For transmission, a
model is discrete if the processing of successive stages cannot
have temporal overlap; that is, the next stage in the sequence
must wait until processing of the immediately preceding
stage is completed. The discrete stage model underlying
Sternberg’s (1969) additive factors method postulates discrete
representation and transmission. McClelland’s (1979) cas-
cade model, on the other hand, postulates continuous repre-
sentation and transmission, as well as transformation.
A variety of models exist that are intermediate to these
two extremes. One such model is Miller’s (1982, 1988) asyn-
chronous discrete coding model. This model assumes that
most stimuli are composed of features, and these features are
identified separately. The processing is discrete in that each
feature must be identified before output about it can be
passed to the response-selection stage. However, the identity
of one feature may be passed to response selection while
stimulus identification processes are still operating on other
features.
Speed-Accuracy Trade-Off
The subtractive and additive factors methods are usually
based solely on RT data. However, RT in any specific task sit-
uation is related to the number of errors that one is willing to
make. A person can respond rapidly and make many errors or
slowly and make few errors. This relation is called the speed-
accuracy trade-off, and the function plotting speed versus
accuracy is known as the speed-accuracy operating charac-
teristic. For RT research, two aspects are crucial. First, if
slower RT is accompanied by lower error rate, then the RT
difference cannot be attributed unambiguously to differences
in processing efficiency. Second, under conditions in which
accuracy is relatively high, as in most choice-reaction stud-
ies, a small difference in error rate can translate into a large
difference in RT.
Because of this close relation between speed and accuracy,
some researchers have advocated conducting experiments in
which the speed-accuracy criterion is varied between blocks
of trials (Dosher, 1979; Pachella, 1974). There are numerous
ways to vary the speed-accuracy criterion: payoffs, instruc-
tions, deadlines, time bands (responding within a certain time
interval), and response signals (responding when the re-
sponse signal is presented; see Wickelgren, 1977, for details).
When a speed-accuracy function is obtained, information is
provided about the intercept (time at which accuracy ex-
ceeds chance), asymptote (the maximal accuracy), and rate
of ascension from the intercept to the asymptote, each of
which may reflect different processes. Thus, a speed-
accuracy study has the potential to be more informative than
one based solely on RT. However, speed-accuracy studies
require 5–10 times more data than RT studies and, in many
circumstances, do not provide better insight into the phenom-
enon of interest.
In addition to looking at the macro trade-off produced
by varying speed-accuracy emphasis across trial blocks, it
is also possible to examine the micro trade-off between speed
and accuracy of responding within a particular speed-
accuracy emphasis block of the macro function. Models of
the macro speed-accuracy trade-off can be differentiated on
their predictions regarding the micro trade-off (Pachella,
1974). Osman et al. (2000) presented strong empirical evi-
dence that the macro and micro functions are independent. In
their experiment, which used psychophysiological measures
as well as behavioral measures, the effect of the macro trade-
off manipulation on RT was independent of that of the micro
trade-off, with the micro trade-off affecting the part of the RT
interval prior to the lateralized readiness potential (an indica-
tor of readiness to make a left or right response, described
later) and the macro trade-off affecting the part of the RT in-
terval after the lateralized readiness potential.
The best models currently for characterizing both RT and
accuracy data are sequential sampling models, which assume
that information gradually accumulates until a response crite-
rion is reached (Van Zandt, Colonius, & Proctor, 2000). In
random walk models, a single counter records evidence as
being toward one response criterion and away from another,
or vice versa. In race models, separate counters accumulate
evidence for each response alternative until the winner
reaches criterion. Sequential sampling models explain the
speed-accuracy trade-off by assuming that the response crite-
ria are placed further from or closer to the starting point of
the accumulation process. They explain biases toward one
response over another in terms of asymmetric settings of the
response criteria for the respective alternatives. Although
continuous models of this general type describe the relation
between speed and accuracy well, discrete models that allow
pure guesses on a certain percentage of trials can also explain
this relation.Psychophysiological MeasuresIn recent years, there has been increasing use of psychophys-
iological measures to supplement RT data (Rugg & Coles,
1995). One of the most popular methods is to record