Acta Psychologica 102 (1999) 43±75
Donders's assumption of pure insertion: an evaluation on
the basis of response dynamics
Rolf Ulrich
a
a,*
, Stefan Mattes a, Je€ Miller
b
University of T
ubingen, Phychological Institute, Friedrichstr. 21, 72072 T
ubingen, Germany
b
University of Otago, Dunedin, New Zealand
Received 13 August 1998; received in revised form 26 November 1998; accepted 5 February 1999
Abstract
In order to assess DondersÕs assumption of pure insertion for the response execution stage,
we measured the magnitude and time course of response force in the three classical reaction
time (RT) tasks: simple RT, go/nogo and choice RT. Response force was virtually identical for
the simple and choice RT tasks (Experiments 1 and 2). However, the go/nogo task yielded
more forceful responses than both the simple RT (Experiment 3) and choice RT (Experiments
4 and 5) tasks. These results support DondersÕs original assumption that the response execution process operates identically in the simple and choice RT tasks. More response activation seems to be generated in the go/nogo task, however, consistent with a motor readiness
model. Ó 1999 Elsevier Science B.V. All rights reserved.
Keywords: Reaction time; Response force; Subtraction method; Stage models; Pure insertion
1. Introduction
In¯uenced by Helmholtz's (1850) technique for assessing nerve conduction velocity,
Donders (1868) introduced the so-called subtraction method to infer the speed of
higher mental processes from reaction time (RT). Donders devised three basic tasks to
measure the durations of cognitive processes: the A-task (or simple RT), the B-task (or
choice RT) and the C-task (or go/nogo task). He argued that the go/nogo task is
identical to the simple RT task except that it requires the additional process of stimulus
*
Corresponding author. Fax: +49-7071-292410; e-mail: [email protected]
0001-6918/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved.
PII: S 0 0 0 1 - 6 9 1 8 ( 9 9 ) 0 0 0 1 9 - 0
44
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
discrimination. Similarly, the go/nogo and the choice RT tasks are identical, except
that the latter includes the additional process of response selection. Thus, subtracting
mean RT of the simple RT task from the go/nogo task yields an estimate of the duration of stimulus discrimination, whereas subtracting RT for the go/nogo task from
that of the choice task yields an estimate of the duration of response selection.
DondersÕs method is based on three assumptions. First, it is assumed that in these
tasks the mental processes of stimulus detection, stimulus identi®cation, response
selection and response execution are arranged sequentially in the sense that the
output of one serves as the input to the next. Second, it is assumed that only one
process can be active at each moment in time between stimulus input and response
output. Thus, each process or processing stage is assumed to be functionally distinct
(Sternberg, 1998a) and to consume a certain duration, denoted as the stage duration.
According to this serial processing model, RT is equal to the sum of all the stage
durations (the serial processing assumption). 1 Third, it is assumed that a mental
process can be added or omitted without a€ecting the duration of the other processes,
the so-called assumption of pure insertion (cf. Sternberg, 1969). Especially the ®rst
(cf. Eriksen & Schultz, 1979; McClelland, 1979) and the second assumption have been
supported and tentatively accepted by many researchers (cf. Meyer, Osman, Irwin &
Yantis, 1988; Miller, 1988; Roberts & Sternberg, 1992), whereas the third assumption
has been severely criticized (Boring, 1929; Massaro, 1989; Pachella, 1974).
Using these three assumptions, Donders estimated the durations of various processes by subtracting the RT for one task from the RT for another more complex task;
that is, the more complex task was assumed to require an extra mental process compared to the less complex task. He reasoned that the di€erence in RT between the tasks
provides an estimate of the duration of this extra process. A drawback of this method
is that the estimation procedure involves three unknowns (the durations of stimulus
identi®cation, response selection and the residual processes like stimulus detection and
motor processing) and three independent functions relating mean RT to mean stage
durations for each task. Thus, from a mathematical point of view this system of
equations is completely determined and therefore untestable. Consequently, Donders'
estimation procedure provides no internal checks on the validity of its assumptions. 2
1
One should note that the serial processing assumption does not necessarily imply the assumption of
pure bottom-up processing. Within this serial stage model there is always the possibility that earlier stages
can be preset or prepared by later ones (cf. Sanders, 1997, ch. 4). Thus, stage models may accommodate
top-down processes as well as bottom-up processes.
2
This system would be testable if enough conditions could be used. To see this, suppose that there are
three stages with mean processing times a, b and c. If it would be possible to ®nd four suitable tasks, one
with all three stages, and three each omitting a di€erent stage, the model would predict the following four
mean RTs
RT1 ˆ a ‡ b ‡ c;
RT2 ˆ a ‡ b;
RT3 ˆ a
‡ c;
RT4 ˆ
b ‡ c:
Thus, there are four independent equations with three unknowns and so the model would be testable. In
practice, however, the required tasks are dicult to ®nd. We are aware of only one study (Taylor, 1966)
which utilized this approach, and this work is reviewed below.
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
45
K
ulpe (1893) noted that various laboratories reported inconsistent duration estimates, which often di€ered substantially from each other. K
ulpe suggested that this
inconsistency was most likely caused by violations of the assumption of pure inulpe argued that changing from a
sertion. 3 Relying on introspective reports, K
simpler to a more complex task may not only insert an extra processing stage but
also a€ect other stages, both qualitatively and quantitatively (see also Ach, 1905;
Watt, 1905). Additional discussion of these historical concerns can be found in, for
instance, Luce (1986, pp. 212±215), Welford (1980) and Woodworth (1938).
Although early RT researchers criticized the subtraction method, we doubt that
these criticisms are empirically strong enough to rule out any possibility of applying
this method. The subtraction method would clearly be a very powerful tool in RT
research if its assumptions could be veri®ed. Hence, it is easy to see why some more
contemporary RT researchers have developed rigorous distributional tests to check
the validity of the assumption of pure insertion (e.g., Ashby, 1982; Ashby &
Townsend, 1980; Roberts & Sternberg, 1992; see Schwarz, 1988 for further suggestions). For example, Ashby (1982) and Ashby and Townsend (1980) applied such
tests with success to memory scanning tasks, where the tasks compared are alike
except with respect to the number of items to be memorized. It seems quite plausible
that pure insertion may hold in this task, because there is no obvious qualitative
change in a memory scanning task when the number of memory set items is increased
(Sternberg, 1998a,b). However, such a qualitative di€erence is clearly much more
likely with the three tasks devised by Donders.
1.1. Tests of the assumption of pure insertion
Curiously, only a few di€erent tests of the validity of pure insertion involving the
original RT tasks have been reported in the literature to our knowledge. The ®rst test
was performed by Taylor (1966). He basically extended the original three tasks by
developing a modi®ed choice RT task in which participants did not need to identify
the stimulus but nevertheless were required to select a response to its nonappearance
at a more or less expected time. This additional task, termed the ``selection'' task
(Gottsdanker & Tietz, 1992), was held to require response selection but not stimulus
identi®cation. Because there were four tasks but only three unknown stage durations
to estimate, one degree of freedom was left. This enabled a comparison between the
observed and predicted stage durations (i.e., of the sum of stimulus identi®cation and
response selection). Taylor reported a nonsigni®cant di€erence between the observed
and the predicted durations and concluded that the assumption of pure insertion was
supported.
Gottsdanker and Tietz (1992) extended Taylor's work and in doing so provided
clear evidence against the validity of his proposed test of the subtraction method.
3
Given that few statistical tools were used in those times, one can easily imagine that sampling errors
inherent in sample means were falsely classi®ed as ``inconsistent'', especially when the subtraction method
yielded negative estimates of stage duration.
46
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
First, they enlarged the number of trials per participant to increase the statistical
power of the test. Second, they included choice RT tasks with both compatible and
incompatible mappings, based on arguments that compatibility should in¯uence the
outcome of Taylor's test. Finally, they employed a countdown procedure to provide
maximal temporal information about stimulus occurrence and thus to help the
participant execute a true nonstimulus response in the selection task. The results of
this extended study provided clear evidence that Taylor's test is not appropriate for
evaluating the assumption of pure insertion. First, as the authors expected and as
was suggested by a previous study (Broadbent & Gregory, 1962), the results did
depend heavily on S±R compatibility. Given that the duration of response selection
depends on the S±R mapping, it is dicult to argue that the selection and choice
tasks ± which use completely di€erent S±R mappings ± di€er only in the time required for stimulus identi®cation. Second, RTs in the choice task with the compatible mapping were generally faster than those in the selection task, contrary to
Taylor's assumption that the selection task requires one fewer stage (i.e., no stimulus
identi®cation).
A second and highly sophisticated test was suggested by Gottsdanker and
Shragg (1985). They split the informative and the imperative functions of a choice
stimulus. A visual precue speci®ed the correct response alternative and thus served
the informative function. The precue was followed by an auditory stimulus at
various precue-to-stimulus intervals. The auditory stimulus signalled that the
speci®ed response should be executed, and thus provided the imperative function.
When this interval was less than the mean di€erence between choice and simple
RT, it did not in¯uence the precue-to-response latency in the choice task. This
outcome is predicted when stimulus identi®cation and response selection are additional operations that would be purely inserted in the choice task. Unfortunately,
however, it seems quite possible that this prediction may also be made by alternative continuous models (e.g., McClelland, 1979), which deny the assumption of
strict serial processing. These models may mimic the behavior of serial stage
models on mean RT when stages are ``inserted'' (e.g. McClelland, 1979). Thus the
results of Gottsdanker and Shragg may be quite consistent with continuous models,
although in this case the second assumption of the subtraction method, namely
serial processing, would be violated and therefore its application to the analysis of
RT would be meaningless.
A third test of the assumption of pure insertion employed a pupillometric analysis
to assess whether response selection is involved in the go/nogo task. Since the time of
DondersÕs (1868) original study, RT researchers have been rather uneasy about his
assumption that the go/nogo task does not involve response selection. On introspective grounds, Wundt (1880) reasoned that participants in this task need to
choose between performing and inhibiting a response. In more recent years, Richer,
Silverman and Beatty (1983) utilized pupillary responses to provide some objective
evidence relevant to this conjecture. There is evidence that the size of the pupillary
response during cognitive processing provides an index of the load imposed on the
central nervous system by these processes (cf. Beatty, 1982). Richer et al. measured
the timecourse of the evoked pupillary response in both go and nogo trials of the go/
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
47
nogo task. Even in nogo trials, a phasic change of the pupillary response was obtained, and its size depended on the response demands in the go trials. Generally,
pupillary responses in nogo trials were smaller when responses in go trials had to be
delayed than when they were elicited immediately after the imperative stimulus had
occurred. From this and further results, the authors estimated that approximately
50% of the pupillary response is related to response selection and the remaining 50%
to motor preparation and execution in go/nogo tasks. This analysis led Richer et al.
to conclude that response selection is involved in the go/nogo task, contrary to
DondersÕs assumption.
Two recent studies (Jaskowski & Wlodarczyk, 1997; Miller, Franz & Ulrich,
1999) measuring response force may be considered as a fourth test of the assumption of pure insertion, although they were not designed for this purpose. For
example, Miller et al. measured the e€ects of stimulus intensity on response force to
infer potential post-perceptual e€ects of stimulus intensity. Although they were
mainly concerned with intensity e€ects, they also compared response force across
simple RT, go/nogo, and two-choice tasks in their ®rst experiment. In this experiment, the type of task did not a€ect the forcefulness of a response, consistent with
DondersÕs claim that response execution operates identically in all tasks. However,
this null e€ect could be due to a lack of sucient statistical power, since the experiment was not speci®cally designed to compare the level of response force between RT tasks. In the second and third experiments an auditory accessory
stimulus accompanied the imperative stimulus in a go/nogo and choice task. Only
the third experiment yielded a di€erence between tasks, with more forceful responses in the go/nogo task than in the choice task, contrary to the assumption that
response execution operates identically in these tasks. However, it is questionable
whether this e€ect generalizes to conventional RT tasks without an accessory, especially those studied by Donders. Thus, the outcomes of this study were somewhat
mixed; taken at face value, they suggest that response execution may operate
identically in all tasks with a single relevant stimulus but not when an irrelevant
accessory stimulus accompanies the imperative stimulus. Similarly, Jaskowski and
Wlodarczyk (1997) assessed the e€ects of sleep deprivation, stimulus quality,
knowledge of results, stimulus quality, and task on response force and RT. Their
main ®nding was that participants produced signi®cantly larger force amplitudes
when knowledge of results about RT was provided. Most important for the purposes of this paper, however, task (simple RT vs. choice RT) did not signi®cantly
a€ect response force. However, as in the previous study, this null result may simply
re¯ect a lack of statistical power. Moreover, because the go/nogo task was not
included, these results are incomplete with respect to the examination of DondersÕs
assumptions.
The studies just discussed tested DondersÕs insertion hypothesis for the classical
simple RT, go/nogo and choice RT tasks. Ilan and Miller (1994) went a step further
and tested the validity of pure insertion in a more complex task. Basically, they tested
the assumption that the operation of mental rotation is purely inserted into a normal
versus mirror-image discrimination task commonly used in studies of mental rotation (e.g., Cooper & Shepard, 1973). Their results suggest that in this task response
48
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
selection is altered when mental rotation is added, violating the assumption of pure
insertion.
1.2. The objective of the present experiments
This paper reports new experiments designed speci®cally to test DondersÕs hypothesis that insertion of a mental process does not a€ect other processes in the
simple RT, go/nogo and choice RT tasks. Like Richer et al. (1983), we feel that
psychophysiological measures provide the most powerful means of assessing this
assumption, especially given that the underlying model has too many free parameters to test using RT alone. In particular, response force seems an especially appropriate measure for assessing changes in operation of the motor system.
Response force directly indexes motor activity and thus may supplement the previous inferences based on pupillary responses. It seems plausible that response force
provides a more speci®c index to probe the state of the motor system than pupillary
responses, which seem to probe the global processing demands on the CNS (Beatty,
1982). This is because response force directly assesses the force output of the responding limb, whereas pupillary responses are not directly linked with the motor
processing of the stimulus-associated response. 4 Thus, response force may specifically probe the motor system and thus assess potential di€erences (if any) between
the various RT tasks devised by Donders. In sum, if the type of task a€ects response execution, then response force should vary as a function of task, providing
evidence at odds with DondersÕs assumption of an invariant response execution
stage.
The present experiments extend the research of Miller et al. (1999) using designs
focusing on the e€ects of task ± as needed to test DondersÕs hypothesis ± rather than
on the e€ects of intensity. Speci®cally, participants performed simple RT, go/nogo
and two-choice RT tasks. In each trial, we measured the complete force±time pro®le
of the response. If this pro®le varies across tasks, then it will be safe to conclude that
response execution is not identical in all tasks.
The logic of our comparison assumes that di€erences in force demonstrate differences in motoric processing. This assumption seems indisputable because force is
clearly one manifestation of motor activity. If force di€ers across tasks, there must
necessarily have been some change in the operation of the motor system, whether it is
a change in the number of recruited motor units, their synchronization, the duration
of their outputs, or some other aspect of motor activity (Ulrich & Wing, 1991).
Admittedly, the cause of this change in motor activity cannot be immediately
identi®ed by examining force. Force di€erences might arise either because the motor
4
There is, however, evidence that the amplitude of the pupillary responses is sensitive to response force.
Richer and Beatty (1985) asked participants to press a lightly or heavily loaded key and found a larger
pupillary response when participants had to depress hard load conditions. This clearly indicates that
motoric processing demands contribute to the size of the pupillary response. However, it should be noted
that the response forces required in this study were very di€erent (100 vs. 1250 cN). Clearly, much smaller
di€erences (if any) in response force are expected between the RT tasks devised by Donders.
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
49
system itself functions somewhat di€erently in di€erent tasks or because the motor
system receives di€erent inputs (e.g., from the decision level) in di€erent tasks.
Whatever the mechanism, though, an observed change in force output would indicate some change in the motor system, and would thus weaken DondersÕs assumption of a task-invariant motor stage. Conversely, if response force is equal for all
tasks, DondersÕs assumption would clearly be strengthened.
It must be acknowledged that a di€erence in force±time pro®les will not prove that
the processing time of the response execution stage varies across tasks, which would
falsify DondersÕs assumption directly. The presumption that force changes also
imply duration changes appears to be quite plausible, however, not only theoretically
(Ulrich & Wing, 1991) but also empirically. First, when response force is manipulated by instructions, decreases in response force are associated with increases in RT
(Carlton, Carlton & Newell, 1987). Second, many factors that a€ect RT have also
been found to a€ect response force. For example, previous studies of response force
have indicated that force increases with stimulus intensity (Angel, 1973; Jaskowski,
Rybarczyk, Jaroszyk & Lemanski, 1995; Miller et al., 1999), with stimulus duration
(Ulrich, Rinkenauer & Miller, 1998), with response uncertainty (Mattes, Ulrich &
Miller, 1997), with temporal uncertainty of the stimulus (Jaskowski & Verleger,
1993; Mattes & Ulrich, 1997), with the level of arousal (Jaskowski, Wroblewski &
Jaroszyk, 1993; Ulrich & Mattes, 1996), with the number of stimuli (Giray & Ulrich,
1993; Mordko€, Miller & Roch, 1996), under time pressure (Jaskowski, Verleger &
Wascher, 1994), with word frequency in a lexical decision task (Abrams & Balota,
1991; Balota & Abrams, 1995), and with decreasing set size in memory scanning
(Abrams & Balota, 1991). Thus, response force is sensitive to a large number of
experimental manipulations that in¯uence RT.
This study provides four experiments to check for di€erences across tasks in response force. Each experiment compares the dynamics of the responses for two RT
tasks. Experiments 1 and 2 compare simple with choice tasks: Experiment 3, choice
with go/nogo; and Experiment 4, simple RT with go/nogo. Experiment 5 compared
the choice with the go/nogo task with a symbolic S±R mapping to test a speci®c
hypothesis that emerged from the results of Experiments 3 and 4. We included only
two tasks within each experiment to maximize the statistical power for its comparison and to minimize potential transfer e€ects between the tasks.
2. Experiment 1
The ®rst experiment employed visual imperative stimuli for both simple and
choice reaction times. A stimulus (the onset of an LED) appeared either on the left or
the right side of a central ®xation point. In the choice task, participants made a
corresponding left-hand response to the stimulus on the left and a right-hand response to the stimulus on the right. In the simple RT task, participants made a response to either stimulus with the same hand. If the two RT tasks do not di€er in the
execution of distal motor processes, response force±time pro®les should not di€er
between tasks.
50
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
2.1. Method
Participants. Thirty-six participants (16 females and 20 males; mean age: 26.3 yr)
were volunteers recruited from the campus of the University of Wuppertal. They
were tested in a single session and received 10 DM. All participants were naive about
the experimental hypothesis and all but 2 claimed to be right-handed.
Apparatus. Participants were seated in a dimly illuminated room. A microcomputer controlled stimulus presentation and recorded response force. A tone (440 Hz,
69 dB-SPL) served as the warning signal and was presented binaurally via headphones for 300 ms. A panel was attached at the top of the computer screen. A white
®xation cross was drawn in the middle of this panel. This ®xation cross was approximately at the participant's eye level. Two LEDs were mounted 8 cm (7.6°) to
the left and right of the ®xation cross. Both LEDs were green and had a diameter of
5 mm (0.48°). In each trial one LED was switched on for 150 ms, producing an
intensity of 77.3 cd/m2 , which served as the imperative stimulus. A chinrest provided
a constant viewing distance of 60 cm.
Response force was measured by means of a force key of the same sort used
previously (e.g., Giray & Ulrich, 1993). One end of a leaf spring (110 ´ 19 mm) was
held ®xed by an adjustable clamp, and the other end remained free. The participant's
forearm rested comfortably on a table while his or her index ®nger bent down the free
end of the leaf spring in response to the stimulus. A force of 10 N bent the free end by
about 1 mm. The resolution of this device was about 2 cN (approximately 2 g). Strain
gauges were attached to the leaf spring, so force applied to its free end caused changes
in an electrical signal that was digitized with a sampling rate of 500 Hz.
Procedure. Two tasks (simple RT and choice RT) were employed in a single session
lasting approximately 55 min. In the simple RT task, participants responded to any
imperative stimulus with the same index ®nger, and in the choice task they responded
with the index ®nger that corresponded to the side of the imperative stimulus.
Each task was run in a separate block of trials. There were four blocks per task
and task alternated from block to block. Each block contained 35 trials with imperative stimuli on the left side and 35 trials with stimuli on the right side. Both types
of trials were randomly intermixed within each block. The ®rst ten trials of each
block were considered practice, to familiarize participants with the new task and
therefore discarded from data analysis. Feedback on performance (mean RT and
percent correct) were provided after each block. Half of the participants responded
with their right hand in the ®rst block of the simple RT task and with the left hand in
the second block, whereas the reverse order was used for the other half of participants. The order of the four blocks was counterbalanced across participants.
A single trial started with the presentation of the warning signal. The temporal
interval between the onset of the warning signal and the onset of the imperative
stimulus (i.e., the foreperiod) was never less than 1.0 s. A random duration drawn
from the exponential distribution with a mean of 0.5 s was added to this 1.0 s interval
to prevent anticipatory responses (cf. Luce, 1986, p. 213). The next trial started 2 s
after the o€set of the imperative stimulus. The recording of response force started
50 ms before stimulus onset.
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
51
Task instructions for each block were presented on the computer screen at the
beginning of each block, and participants initiated the block by pressing the space
bar when they felt ready to proceed. Participants were instructed to respond as
quickly as possible without making too many errors, and they were instructed not to
press the response key during the intertrial interval.
Method of Analysis. RT was de®ned as the ®rst moment at which force exceeded a
criterion of 50 cN (about 50 g) after imperative stimulus onset. This value was selected because it is approximately the force needed to trigger a response with many
common setups for measuring RT.
Two sets of dependent measures were derived from each recorded force±time
function to assess potential e€ects on response force. Fig. 1 provides example values
of these measures for three sample force±time functions. The ®rst set assessed the
dynamics of a response and included three force measures: (a) The maximal force
value attained in a single trial, i.e. peak force. (b) The total force integrated over time
in a single trial, i.e. the impulse size. (c) Time to peak force measured the speed of the
force output, that is, the temporal interval from force onset until the maximum of the
force output was achieved.
The second set of measures assessed the shapes of the force±time functions to
determine whether the task a€ects the shape of the force±time pro®les. Changes in
these pro®les may be expected when there is a qualitative change in the mode of force
control (see Ulrich & Wing, 1991; Ulrich, Wing & Rinkenauer, 1995). Shapes were
measured using central moments of the force±time pro®les (see Cacioppo & Dorfman, 1987). In brief, if the force±time function is normalized to have an area of one,
it can be thought of as analogous to a probability distribution, and its shape can be
described by standard measures of dispersion, skewness, and kurtosis (see Ulrich
et al., 1995). Dispersion assesses the duration of force output, skewness characterizes
the degree of asymmetry of the force pulse, while kurtosis measures its peakedness.
Each of these three descriptors was scored on the force±time function for each trial 5.
These measures were also used by Ulrich et al. (1995) to assess the shape of brief
force pulses and by Ulrich et al. (1998) to assess the e€ect of stimulus intensity and
stimulus duration on the timecourse of response force in a simple RT task.
For each trial, the force±time function was scored using the following steps. First,
the baseline of the force±time function was identi®ed as the average force value in the
interval from ÿ200 to ÿ190 ms before response onset, i.e. before response force
attained the criterion force of 50 cN. This baseline value was subtracted from every
force value in the whole force±time function to correct this function for baseline
shifts, which were in fact negligible in almost all cases. Second, the onset and the
o€set of the force pulse were determined for this baseline-corrected force±time
function. The onset t1 corresponded to the moment when force ®rst attained a value
5
A positive (negative) value of skewness indicates that the force pulse is skewed to the right (left). A
positive (negative) value of kurtosis usually indicates a peaked (¯at) force pulse relative to a normal
distribution, which has a kurtosis of zero. Both skewness and kurtosis are independent of the scale of
measurement and therefore have no measurement unit.
52
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
Fig. 1. Sample functions showing response force as a function of time. Stimulus onset is at t ˆ 0, and RT
is de®ned as the ®rst moment when response force exceeds the 50 cN criterion (horizontal line). For each
function a set of force measures (RT, peak force, impulse size, time-to-peak force, dispersion, skewness,
kurtosis) are computed and used as dependent measures. These measures are (266, 888, 92, 116, 49,
0.44,ÿ0.079), (342, 561, 78, 79, 57, 0.62, 0.076) and (227, 551, 131, 88, 57, 0.02,ÿ0.622) for the displayed
curves, A, B and C, respectively.
of 20 cN, and the o€set t2 corresponded to the ®rst subsequent moment when it fell
back below this value. Third, peak force and time to peak force were determined
within the interval from t1 to t2 . (Time to peak force is the time interval from t1 to the
moment of maximum force output). Fourth, the force±time function was normalized
within the interval from t1 to t2 such that the area under this function was equal to
one. Fifth, dispersion, skewness and kurtosis were computed for the normalized
force±time function from t1 to t2 , as described by Cacioppo and Dorfman (1987).
Finally, for each participant, mean values of each force measure, as well as mean
RTs, were computed across all correct-response trials within each condition
(task ´ side of hand). These individual-participant means were analyzed using re-
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
53
peated-measures ANOVAs with factors of task and hand, separately for each dependent measure.
2.2. Results and discussion
There were a total of 0.9% premature responses (RTs < 100 ms) and 0.3% misses
(RTs > 1000 ms); in the choice task, there were 0.7% wrong hand responses. These
trials were discarded from further data analysis.
Table 1 shows the mean value for each dependent measure in each task, followed
by a 95%-con®dence interval for the di€erence between the simple and the choice
tasks for that dependent measure. This interval was computed using the error term
from a paired t-test, which was applied to the di€erence scores of the participants.
For each measure, the table also shows the F-value of the corresponding ANOVA
and the statistics for a Wilcoxon matched-pairs signed-ranks test. The latter nonparametric test uses only the ranks of the di€erences between the simple and the
choice task for each participant. It is thus less sensitive than the ANOVA to a small
number of participants producing large di€erences, and it therefore provides a check
whether signi®cant F-values are due to such outliers. Nevertheless the statistical
power of this nonparametric test is comparable to corresponding parametric tests
(Wonnacott & Wonnacott, 1977).
As expected, mean RT was shorter in the simple than in the choice task. Consistent with previous research (Kerr, Mingay & Elithorn, 1963; Woodworth &
Schlosberg, 1954, p. 40; Ulrich & Stapf, 1984) the RT di€erence of 3 ms between the
left and right hand was small and did not di€er signi®cantly, F …1; 35† ˆ 1:5; p > 0:1.
There was no signi®cant interaction of task and hand on RT, F < 1. Within the
simple RT task, responses were 4 ms faster when the stimulus appeared on the same
side as the responding hand than when it appeared on the opposite side,
F …1; 35† ˆ 13:3; p < 0:01. This 4 ms disadvantage for contralateral responses agrees
fully with previous studies (e.g., Po€enberger, 1912) and has been attributed to the
additional time required to transfer neuronal information from the stimulated cerebral hemisphere to the opposite one, which generates the response (cf. Bashore,
1981). 6
Most important and in agreement with DondersÕs assumption of pure insertion,
the dynamics of the response and shape of the response pro®le were virtually
identical for both the simple and the choice task, because neither peak force, integrated force nor time to peak force was in¯uenced by RT task. The values of peak
force and integrated force were in close agreement with those reported in previous
studies (Giray & Ulrich, 1993; Ulrich et al., 1998). The grand mean of time to peak
force was 98 ms and thus only slightly longer than the minimal attainable value of
about 90 ms (Freund & B
udingen, 1978; Ulrich et al., 1995); a similar grand mean
was obtained in other RT studies (Ulrich & Mattes, 1996; Ulrich et al., 1998). Thus,
the force output of the response developed very rapidly. As found in previous studies
6
Ironically, this conclusion also requires the assumption of pure insertion.
261
683
111
97
0.24
ÿ0.40
56
298
653
110
99
0.23
ÿ0.44
57
38 ‹ 7
ÿ30 ‹ 54
ÿ1 ‹ 10
2‹3
ÿ0.01 ‹ 0.02
ÿ0.04 ‹ 0.04
1‹1
105.7
1.3
0.01
1.4
5.6
2.7
2.6
F-value
D ‡ HW
Simple
Choice
ANOVA
Task
p < 0:001
n.s.
n.s.
n.s.
p < 0:05
n.s.
n.s.
p
5.2
0.7
0.5
1.1
1.0
1.8
1.6
Z-value
Wilcoxon test
p < 0:001
n.s.
n.s.
n.s.
n.s.
n.s.
n.s.
p
Notes: The degrees of freedom for each F-value are 1 and 35. A two-tailed p-value was used for the Wilcoxon matched-pairs signed-ranks test. The fourth
column gives the mean di€erence D and the half-width, HW, of the corresponding con®dence interval.
a
RT (ms)
Peak force (cN)
Integrated force (cN s)
Time to peak force (ms)
Skewness
Kurtosis
Dispersion (ms)
Dependent variable
Mean value of each dependent measure as a function of task, in Experiment 1, and results of the ANOVA and the Wilcoxon test for e€ect of taska
Table 1
54
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
55
(Ulrich et al., 1995, 1998), the shape analysis of the force±time functions revealed
positive values of skewness and negative values of kurtosis. There was a small yet
reliable e€ect of RT task on skewness; force pulses were slightly more skewed to the
right in the simple than in the choice task. However, the Wilcoxon matched-pairs
signed-ranks test did not produce a signi®cant di€erence. Hence, the signi®cant Fvalue may re¯ect a Type II error, which may arise from the multiple comparisons
within such an extended set of dependent measures tested with both parametric and
nonparametric tests.
Furthermore, kurtosis did not systematically vary with task, suggesting that the
peakedness of the force pulse was unin¯uenced by task. Finally, the duration of the
force output was virtually identical in both tasks as indicated by the measure of
dispersion. Thus, the analysis of the shape descriptors indicates no substantial e€ect
of task on either the shape or duration of the force pulse. In addition, within the
simple RT task, force was una€ected by whether the stimulus appeared on the same
or opposite side from the responding hand.
Interestingly enough, the hand factor also produced no signi®cant main e€ects on
these variables, suggesting that left- and right-hand responses did not di€er in force
output. However, there was a signi®cant hand by task interaction on time to peak
force, F …1; 35† ˆ 29:7; p < 0:01; for the left hand, mean time to peak force was
virtually identical for both the choice and the simple RT task (100 vs. 99 ms). For
right-hand responses, however, mean time to peak force was slightly faster in the
simple than in the choice task (95 vs. 100 ms). This small di€erential hand e€ect
might re¯ect a better synchronization of force units (Ulrich & Wing, 1991) for the
right than for the left hand due to more practice. However, this hand di€erence
seems to vanish when the activation of force units has to be delayed because of the
intervening response selection stage.
In conclusion, then, the present results are quite compatible with the hypothesis of
pure insertion, because the force output of the response seems to be rather unin¯uenced by whether participants perform a simple or a choice task. The next experiment was performed with auditory stimuli to test the generality of this
conclusion.
3. Experiment 2
Experiment 2 was identical to the ®rst experiment, except that loud auditory
imperative stimuli were employed. It has been well documented that loud auditory
stimuli increase choice RT yet reduce simple RT (van der Molen & Keuss, 1979; van
der Molen & Orlebeke, 1980). One explanation of this asymmetrical e€ect is that
loud auditory stimuli increase immediate arousal, which interferes with response
selection in choice RT tasks (van der Molen & Keuss, 1981). It seems quite possible
that this interference might extend to the motor system and a€ect the execution of a
response and thus its force output. Hence, the present experiment was a critical test
to see whether the results found in Experiment 1 would generalize to intense auditory
imperative stimuli.
56
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
3.1. Method
Participants. A fresh sample of 36 participants (16 females and 20 males; mean
age: 27.7 yr) was recruited from the same population as in Experiment 1. All participants were naive about the experimental hypothesis and all but two claimed to be
right-handed.
Apparatus. The apparatus was identical to the one of Experiment 1, except that
the left (right) visual imperative stimulus was replaced by a tone (1000 Hz, 80 dB-A,
150 ms) presented monaurally to the left (right) ear via a headphone.
Procedure. The procedure and the method of data analysis was identical to Experiment 1.
3.2. Results and discussion
There were a total of 0.8% premature responses (RTs < 100 ms) and 0.2% misses
(RTs > 1000 ms); in the choice task, there were 0.7% wrong hand responses. These
®gures are almost identical to those obtained in Experiment 1. As in the previous
experiment, these trials were discarded from further data analysis.
The main e€ect of task on the dependent measures is shown in Table 2. Note
that these results clearly replicate the results obtained in Experiment 1 and thus
reinforce the conclusion that RT task does not a€ect the force output of the response. As in Experiment 1, there was no signi®cant e€ect of response hand on any
dependent measure. In addition, this time the hand by task interaction was not
signi®cant.
We also performed a Modality (Experiment 1 vs. 2) by Task (Simple vs. Choice) by
Response Hand (left vs. right) ANOVA to further increase the statistical power for
detecting a task e€ect and also to assess the e€ect of stimulus modality. 7 This analysis
of course yielded a highly signi®cant main e€ect of task on RT, F …1; 70† ˆ 224:3;
p < 0:001, but it yielded virtually no e€ect of task on force measures. Overall, for the
simple and choice RT tasks, mean peak forces were 696 and 669 cN, integrated force
118 and 117 cN s, time to peak force 101.7 and 101.6 ms, skewness 0.26 and 0.24,
kurtosis ÿ0.39 and ÿ0.41, and dispersion 59.4 and 59.6 ms, respectively. The main
e€ect of task was signi®cant only in the ANOVA test of skewness, F …1; 70† ˆ 4:2;
p ˆ 0:04, though it was insigni®cant with the Wilcoxon test, z ˆ 1:14; p ˆ 0:254. As
discussed in the previous experiment, this e€ect appears too small to justify an interpretation, and a Type II error for the F-test seems likely because many tests were
conducted and because this e€ect was not con®rmed by the Wilcoxon test.
This combined analysis also yielded some e€ects of modality. There was a highly
signi®cant e€ect of modality on RT, F …1; 70† ˆ 24:2; p < 0:001; as one might expect,
7
In this comparison, the e€ect of modality is not purely sensory, but may also be confounded to some
extent with di€erences in stimulus intensity, the required discrimination, the arousing properties of the
stimuli, and so on. Since the most important e€ects are the same across both modalities, however, it seems
unnecessary to attempt to disentangle these confounded factors.
206
708
125
106
0.26
ÿ0.38
63
258
686
124
104
0.26
ÿ0.40
62
52 ‹ 6
ÿ22 ‹ 48
ÿ1 ‹ 10
ÿ2 ‹ 3
ÿ0.01 ‹ 0.02
ÿ0.02 ‹ 0.04
ÿ1 ‹ 1
277.1
0.9
0.03
2.1
0.3
0.5
2.6
F-value
D HW
Simple
Choice
ANOVA
Task
p < 0:001
n.s.
n.s.
n.s.
n.s.
n.s.
n.s.
p
5.2
0.4
0.4
1.8
0.9
0.7
0.9
Z-value
Wilcoxon test
p < 0:001
n.s.
n.s.
n.s.
n.s.
n.s.
n.s.
p
Notes: The degrees of freedom for each F-value are 1 and 35. A two-tailed p-value was used for the Wilcoxon matched-pairs signed-ranks test. The fourth
column gives the mean di€erence D and the half-width, HW, of the corresponding con®dence interval.
a
RT (ms)
Peak force (cN)
Integrated force (cN s)
Time to peak force (ms)
Skewness
Kurtosis
Dispersion (ms)
Dependent variable
Mean value of each dependent measure as a function of task, in Experiment 2, and results of the ANOVA and the Wilcoxon test for e€ect of taska
Table 2
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
57
58
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
participants responded faster to auditory than to visual stimuli. In addition, the RT
di€erence between the choice and the simple RT task was signi®cantly larger for
auditory than for visual stimuli, F …1; 70† ˆ 8:9; p < 0:01. Modality did not have a
signi®cant e€ect on peak force or on integrated force (p's > 0.14) nor were there
interactions of modality with task (p's > 0.38).
There were also some statistically signi®cant though small interactive e€ects which
we cannot interpret. First, for the left hand time to peak force was 2 ms shorter for
the simple compared to the choice task. However, the reverse 2 ms e€ect was obtained for the right hand, F …1; 70† ˆ 6:9; p ˆ 0:01. Second, for the visual modality
the right hand reached peak force faster (by 2 ms) than the left hand. However, for
the auditory modality this e€ect reversed, F …1; 70† ˆ 4:3; p ˆ 0:043. Finally, the
three-way interaction of hand, modality and task on peak force just attained statistical signi®cance F …1; 70† ˆ 4:0; p ˆ 0:050. This interaction seems to be due to a
somewhat increased force output of the right hand in the simple RT task when
auditory stimuli were employed.
Intermediate conclusions. The outcomes of Experiment 1 and 2 strongly suggest
that the execution of a keypress response is almost completely invariant across RT
tasks and thus support DondersÕs assumption of pure insertion. This inference is
based on the present ®ndings that force output of a speeded response does not (or at
least not strongly) depend on whether a participant performs a simple or a choice RT
task, although the task manipulation strongly in¯uenced RT. This conclusion was
also supported by an ANOVA combining Experiments 1 and 2 to increase statistical
power. Furthermore, the conclusion seems to hold whether auditory or visual stimuli
are employed as imperative stimuli.
The next two experiments compare the go/nogo task with the simple and choice RT
tasks to examine whether the present conclusion also generalizes to the go/nogo task.
4. Experiment 3
This experiment was identical to Experiment 1, except that the simple RT task
was replaced by the go/nogo task. Therefore, this experiment investigates whether
response dynamics di€er between the choice and go/nogo tasks.
4.1. Method
Participants. A fresh sample of 36 participants (24 females and 12 males; mean
age: 25.4 yr) was recruited from the same population as in the previous experiments.
All participants were naive about the experimental hypothesis and all but ®ve
claimed to be right-handed.
Apparatus. The apparatus was identical to the one of Experiment 1.
Procedure. The procedure and the method of data analysis was identical to Experiment 1 with the only exception that the simple RT task was now replaced by a
go/nogo task. In each block of the go/nogo task, one hand was designated as the
response hand. Participants were instructed to respond whenever the LED ipsilateral
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
59
to the respond hand went on (go trial) but to withhold the response to the onset of
the contralateral LED (nogo trial). Before each block they were also explicitly told to
®x their gaze on a small white spot between both LEDs.
4.2. Results and discussion
There were a total of 0.4% premature responses (RTs < 100 ms) and 0.3% misses
(RTs > 1000 ms). In the choice task, there were 0.1% wrong hand responses. These
®gures are quite similar to the ones obtained in the previous experiments. In the go/
nogo task there were only 1.2% false alarms in nogo trials. As before, these trials
were discarded from further data analysis.
The main e€ect of task on the dependent measures is shown in Table 3. Although
mean RTs were slightly faster in the go/nogo than in the choice task, this di€erence
was not signi®cant. The lack of a signi®cant RT di€erence may be expected with such
a highly compatible spatial S±R mapping as the one employed in this experiment,
since such a mapping should strongly facilitate response selection and therefore
would greatly reduce the RT di€erence between the choice and go/nogo tasks (cf.
Kornblum, Hasbroucq & Osman, 1990).
Although RT did not di€er signi®cantly between the two tasks, participants
produced signi®cantly more forceful responses in the go/nogo task than in the choice
task. Task also produced tiny yet signi®cant e€ects on kurtosis and dispersion. The
force±time functions in the choice task were slightly more stretched along the time
axis and also slightly ¯atter than those in the go/nogo task. There was no main e€ect
of the hand factor (p's > 0.18) nor did factor hand modulate the above signi®cant
main e€ects of task (p's > 0.24).
It is remarkable that the results of the choice task were almost identical to the
ones in Experiment 1 when the choice task was paired with the simple RT task. This
particular result indicates that the present results are not amenable to context e€ects,
i.e. the results of the choice task appear to be unin¯uenced by its pairing with a go/
nogo or a simple RT task.
To summarize, the present experiment indicates that the go/nogo task involves
more powerful responses as compared to responses in a choice task. The next experiment therefore tests whether the same conclusion can be reached when the go/
nogo task is compared with the simple RT task.
5. Experiment 4
This experiment was identical to Experiment 3, except that the choice RT task was
replaced by the simple RT task.
5.1. Method
Participants. A fresh sample of 36 participants (19 females and 17 males; mean
age: 26.6 yr) was recruited from the same population as in the previous experiments.
291
688
120
106
0.24
ÿ0.39
60
295
645
116
106
0.23
ÿ0.42
61
4‹7
ÿ44 ‹ 37
ÿ4 ‹ 8
0‹3
ÿ0.1 ‹ 0.02
ÿ0.4 ‹ 0.03
1‹1
1.8
5.6
1.0
0.3
0.1
4.1
5.3
F-value
D HW
go/nogo
choice
ANOVA
Task
n.s.
p < 0:05
n.s.
n.s.
n.s.
p < 0:05
p < 0:05
p
1.5
2.2
1.0
0.4
1.1
2.1
2.3
Z-value
Wilcoxon test
n.s.
p < 0:05
n.s.
n.s.
n.s.
p < 0:05
p < 0:05
p
Notes: The degrees of freedom for each F-value are 1 and 35. A two-tailed p-value was used for the Wilcoxon matched-pairs signed-ranks test. The fourth
column gives the mean di€erence D and the half-width, HW, of the corresponding con®dence interval.
a
RT (ms)
Peak force (cN)
Integrated force (cN s)
Time to peak force (ms)
Skewness
Kurtosis
Dispersion (ms)
Dependent variable
Mean value of each dependent measure as a function of task, in Experiment 3, and results of the ANOVA and the Wilcoxon test for e€ect of taska
Table 3
60
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
61
All participants were naive about the experimental hypothesis and all except two
claimed to be right-handed.
Apparatus. The apparatus was identical to the one of Experiment 1.
Procedure. The procedure and the method of data analysis was identical to Experiments 1 and 3. The simple RT task and the go/nogo task were identical to the
ones employed in Experiments 1 and 3, respectively.
5.2. Results and discussion
There were a total of 0.4% premature responses (RTs < 100 ms) and 0.6% misses
(RTs > 1000 ms). In the go/nogo task 1.7% false alarms resulted in nogo trials. These
®gures are similar to the ones obtained in the preceding experiments.
The e€ect of task on the dependent variables is summarized in Table 4. As expected, simple RTs were signi®cantly faster than RTs in the go/nogo task. Theoretically more revealing, however, is that task signi®cantly a€ected the force output
of the responses. In accordance with the preceding experiment, participants produced signi®cantly more forceful responses in the go/nogo task. Both the amplitude
and the area under the force±time function were larger in the go/nogo task as
compared with the simple RT task, though the shape of the force±time function was
virtually una€ected by task. The estimates of the shape parameters and time to peak
force were remarkably consistent with the ones obtained in the preceding experiments.
Participants produced signi®cantly more response force with their right hands
than with their left hands (peak force: 725 vs. 647 cN, F …1; 35† ˆ 6:8; p < 0:05; integrated force: 123 vs. 139 cN s, F …1; 35† ˆ 7:2; p < 0:05†. However, these main
e€ects did not interact with factor task (p's > 0.47). The hand factor produced neither
any further signi®cant main e€ect (p's > 0.17) nor any signi®cant interaction
(p's > 0.15) with task on the remaining dependent measures.
6. Experiment 5
The preceding two experiments demonstrated that responses are more forceful in
the go/nogo task than in the simple and choice RT tasks. These results certainly
suggest that the response execution process operates di€erently in the go/nogo task
than in the other two tasks, contrary to DondersÕs assumption of pure insertion.
Before concluding that pure insertion was de®nitely violated in this situation,
however, it is necessary to consider whether the increased response force in the go/
nogo task can be attributed to changes in apparent brightness.
In the previous two experiments, the imperative stimuli were two LEDs to the left
and right of ®xation. With such stimuli, it seems optimal to divide spatial attention
between these two LEDs in both the simple and choice RT tasks, because both of
these tasks require speeded responses to both LEDs. In the go/nogo task, however, it
seems advantageous to focus spatial attention at the ``go'' side LED, because this is
the only LED requiring a speeded response. It is possible that this extra focusing of
262
660
126
99
0.22
ÿ0.49
59
292
711
137
100
0.22
ÿ0.46
60
30 ‹ 7
52 ‹ 43
11 ‹ 8
1‹3
ÿ.01 ‹ .03
0.01 ‹ 0.03
0‹1
69.6
5.9
8.3
0.7
0.1
1.9
0.3
F-value
D HW
simple
go/nogo
ANOVA
Task
p < 0:001
p < 0:05
p < 0:01
n.s.
n.s.
n.s.
n.s.
p
5.2
2.1
2.4
0.9
0.6
0.8
1.2
Z-value
Wilcoxon test
p < 0:001
p < 0:05
p < 0:05
n.s.
n.s.
n.s.
n.s.
p
Notes: The degrees of freedom for each F-value are 1 and 35. A two-tailed p-value was used for the Wilcoxon matched-pairs signed-ranks test. The fourth
column gives the mean di€erence D and the half-width, HW, of the corresponding con®dence interval.
a
RT (ms)
Peak force (cN)
Integrated force (cNs)
Time to peak force (ms)
Skewness
Kurtosis
Dispersion (ms)
Dependent variable
Mean value of each dependent measure as a function of task, in Experiment 4, and results of the ANOVA and the Wilcoxon test for e€ect of taska
Table 4
62
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
63
attention in the go/nogo task would increase the apparent brightness of the stimulus
(Downing, 1988) in this task as compared to the other two tasks. Because brighter
stimuli produce more forceful responses (Angel, 1973; Ulrich & Mattes, 1996; Experiment 3), this attentional hypothesis might explain why participants produced
especially forceful responses in the go/nogo tasks of the preceding experiments, even
if response execution processes operated identically in all tasks.
Experiment 5 was designed to test this attentional hypothesis. The stimuli were
letters, always presented at the same location, and letter identity determined the
correct response (go/nogo or left/right hand in the choice task). Since all stimuli
appeared at the same location, stimuli in both the go/nogo and the choice RT task
should have had the same degree of focused attention and therefore the same apparent brightness. Thus, according to the above attentional hypothesis, response
force should not di€er between the go/nogo and the choice RT tasks.
6.1. Method
Participants. Another sample of 36 participants (20 females and 16 males; mean
age: 26.2 yr) was recruited. Two participants claimed to be left-handed.
Apparatus. The apparatus was identical to Experiment 1 except for the stimuli,
which were the letters X and S presented in the center of the computer monitor. Each
letter subtended a visual angle of 2.1° ´ 1.6° and had an intensity of 3.1 cd/m2 . The
intensity of the background was 0.25 cd/m2 .
Procedure. The procedure and data analysis were identical to Experiment 3 except
for the stimulus set and S±R mapping. In the choice RT task, half of the participants
responded with the left hand to the letter X and with the right hand to the letter S;
this mapping was reversed for the other half. In the go/nogo task, the assignment of
letters to go and nogo trials was de®ned analogously to Experiment 3. Thus, the
stimulus that de®ned the right (left) hand response in the choice task also de®ned a
``go'' trial when participants responded with the right (left) hand in the go/nogo task.
6.2. Results and discussion
A total of 0.2% premature responses (RTs < 100 ms) and 0.5% misses (RTs > 1000
ms) were obtained. In the choice task, there were 0.7% wrong hand responses, and in
the go/nogo task there were 1.8% false alarms in nogo trials. These ®gures are quite
similar to the error pattern observed in Experiment 3.
Table 5 shows the main e€ect of task on the dependent measures. Compared to
Experiment 3, there was a clearer RT di€erence between the choice and go/nogo
tasks. Such a strong e€ect of task was expected, because the symbolic S±R mapping
in the present experiment is much less compatible than the spatial mapping S±R
employed in Experiment 3 (Kornblum et al., 1990).
Although the S±R mapping clearly di€ers between Experiment 3 and the present
one, the e€ects of task on response dynamics were almost identical. Most important,
participants again produced larger force amplitudes in the go/nogo task than in the
choice task. This ®nding strongly argues against the attentional hypothesis consid-
339
614
100
100
0.27
ÿ0.35
60
412
575
100
102
0.26
ÿ0.38
61
73 ‹ 9
ÿ38 ‹ 33
0‹7
2‹4
ÿ0.01 ‹ 0.03
ÿ0.02 ‹ 0.05
ÿ2 ‹ 1
262.7
5.6
1.0
0.4
0.6
1.5
6.7
F-value
D HW
go/nogo
choice
ANOVA
Task
p < 0:001
p < 0:05
n.s.
n.s.
n.s.
n.s.
p < 0:05
p
5.2
2.5
0.9
0.8
0.8
1.3
2.8
Z-value
Wilcoxon test
p < 0:001
p < 0:05
n.s.
n.s.
n.s.
n.s.
p < 0:01
p
Notes: The degrees of freedom for each F-value are 1 and 35. A two-tailed p-value was used for the Wilcoxon matched-pairs signed-ranks test. The fourth
column gives the mean di€erence D and the half-width, HW, of the corresponding con®dence interval.
a
RT (ms)
Peak force (cN)
Integrated force (cN s)
Time to peak force (ms)
Skewness
Kurtosis
Dispersion (ms)
Dependent variable
Mean value of each dependent measure as a function of task, in Experiment 5, and results of the ANOVA and the Wilcoxon test for e€ect of taska
Table 5
64
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
65
ered earlier. Moreover, this dissociation suggests that the task e€ect on response
force is not generated at the level of response selection. If it were, one would expect a
change in S±R compatibility to a€ect response force as well as RT. Thus, it seems
most likely that the generally heightened force output in the go/nogo task is due to a
processing stage that is located at the distal end of the processing chain. (This
conjecture is further elaborated in Section 7.)
Only two further e€ects were signi®cant. First, there was a one millisecond e€ect
of task on dispersion. As in the analogous Experiment 3, force pulses were slightly
less stretched along the time axis in the go/nogo compared to the choice task. Second, there was a main e€ect of hand on dispersion, F …1; 35† ˆ 5:8; p < 0:05; lefthand responses produced a somewhat less dispersed (by 3 ms) force pulse than
right-hand responses. There was neither any further main e€ect (p's > 0.07) nor any
signi®cant interaction (p's > 0.40) on the remaining dependent measures.
6.3. Conclusions from go/nogo task
The outcomes of Experiment 3, 4 and 5 clearly suggest that participants produce
more forceful responses in the go/nogo task than in the two other RT tasks, which
themselves do not produce di€erences in force output.
7. General discussion
In this study, we sought to examine whether the type of RT task a€ects response
force. Speci®cally, participants performed simple RT, go/nogo and two-choice RT
tasks, and in each trial we measured the complete force±time pro®le of the response. We reasoned that if this pro®le varies across tasks, response execution must
not operate identically in all tasks, weakening DondersÕs hypothesis that the motor
system consumes the same amount of time regardless of task. In contrast, if force±
time pro®les are the same in all tasks, this would clearly strengthen the assumption
that this system operates identically ± and thus consumes the same time ± in all
tasks.
The two main ®ndings of this study can be summarized as follows: First, the
force±time pro®les of the responses of simple and choice RT tasks are virtually indistinguishable. This conclusion applies to both visual and auditory stimuli (Experiments 1 and 2, respectively). Second, participants produce more forceful
responses in the go/nogo than in the choice or simple RT tasks (Experiments 3, 4 and
5). Most surprisingly, the tasks most di€erent in terms of RT, i.e. simple and choice
RT, produced virtually identical response outputs, suggesting that the response execution process does indeed operate identically in these two tasks, as Donders assumed.
Because the present force results from simple and choice RT tasks are in accordance with DondersÕs assumption, they argue against the idea that response activation di€ers between these two tasks, as suggested by continuous models (cf. Balota
& Abrams, 1995). For example, under the plausible assumption that di€erences in
66
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
the rate of response activation produce di€erences in observable response force,
McClelland's (1979) cascade model predicts the highest rate of response activation in
the simple RT task, a lower rate in the go/nogo task, and the lowest rate in the choice
RT task (see the appendix for a detailed analysis of this prediction). The present
results, however, are clearly inconsistent with this prediction.
The ®nding that the go/nogo task produces especially vigorous responses extends
the pattern reported by Miller et al. (1999). As mentioned in the Introduction, these
authors measured response force to assess whether stimulus intensity a€ects postperceptual processes in the simple, go/nogo, and choice tasks. Although the authors
were mainly concerned with intensity e€ects, they also compared response force
across RT tasks. In their ®rst experiment employing all three tasks, response force
did not vary across task.
This null e€ect may be attributed to insucient statistical power, because all three
tasks were run within a single session. In the second and third experiments an auditory accessory stimulus accompanied the imperative stimulus in a go/nogo and
choice task. As in the present study, in both of theses experiments more vigorous
responses were found for the go/nogo task, although this e€ect was only highly
statistically reliable in their third experiment. It should be stressed that the study of
Miller et al. (1999) not only employed an accessory stimulus but also a less direct
stimulus-response mapping than in the present set of experiments. Thus, the conclusion that the go/nogo task produces relatively forceful responses is obviously
fairly robust.
There seem to be at least three plausible accounts of why participants produced
relatively more forceful responses in the go/nogo task. First, one might argue that in
a go/nogo task a response is not required in each trial and hence the motor system
has, on average, more time to recover from the previous response. Assuming that
force increases with the length of the recovery period, this would clearly explain
especially forceful responses in a go/nogo task, since in both simple and choice RT a
response is required in each trial and so the recovery period is never more than one
intertrial interval. Alternatively, one might argue that participants become more
responsive as more nonresponse trials precede a trial with an imperative stimulus
(e.g., perhaps because arousal increases). Although it is dicult to discriminate this
from the recovery explanation, both make the same testable prediction. Immediate
response repetitions in a go/nogo task should produce less forceful responses than
responses following nogo trials. In order to test this prediction, we analyzed response
force for repetitions vs. nonrepetitions in the go/nogo tasks employed in Experiments
3, 4 and 5. These additional analyses revealed no repetition e€ect on the strength of a
response, thus leading us to reject these accounts. 8
As a second possible explanation, one might be tempted to argue that participants
may for some reason raise the level of muscle tension during the foreperiod more in
8
Peak force was 668 cN for repetitions and 677 cN for nonrepetitions and this di€erence was
nonsigni®cant, F …1; 107† ˆ 2:3, p ˆ 0:130; in addition, integrated forces were 120 and 119 cNs,
respectively, and the di€erence between these was also nonsigni®cant, F …1; 107† ˆ 1:1, p ˆ 0:294.
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
67
the go/nogo than in the other tasks. Thus the force output before stimulus onset may
be slightly more increased toward the criterion force of 50 cN in the go/nogo task
compared with the other tasks. Hence, the force±time functions may be started from
a slightly higher base-line level in the go/nogo task. An increase in the maximal
produced force level would be quite a reasonable consequence of a heightened baseline level due to preload force (Ulrich & Wing, 1991). To test this explanation, we
investigated whether the base-line level of response force before stimulus onset differed across tasks. Mean force output was computed over the interval from 100 to
110 ms before the RT on each trial, and the average force in this interval was virtually identical in all three tasks. 9 Hence, it seems implausible that participants
produced more force in the go/nogo task because they started from a higher force
level.
The third and at this point most attractive explanation involves the motor
readiness model (N
a
at
anen, 1971; Niemi & Naatanen, 1981) and, speci®cally, to a
further development of this model to account for response probability e€ects on
response force (Mattes et al., 1997). Mattes et al. reported that participants produced more forceful responses when the probability of a go trial was low than
when it was high. They interpreted this ®nding in terms of an extended motor
readiness model. According to this extension, the distance between motor activation and a threshold for action is relatively large when response probability is low,
and a large increment is needed to exceed this threshold, resulting in slow but
forceful responses. A similar explanation might apply to the present ®nding that
participants produce more forceful responses in the go/nogo task. In this task,
participants might be forced to keep motor activation low in order to avoid false
alarms on nogo trials. If motor activation were high (i.e., close to the threshold for
motor action), nonspeci®c activation elicited by the nogo stimulus might propagate
through the S±R system and occasionally trigger a false alarm. Note that nonspeci®c activation is especially likely to trigger false alarms in the go/nogo task. In
simple RT, there is no irrelevant stimulus to produce nonspeci®c activation. In
choice RT, each stimulus selectively activates one response channel and reciprocal
inhibition would quickly dampen or even eliminate activation in the other channel
(Zorzi & Umilta, 1995), so even a high initial level of motor activation would rarely
trigger erroneous responses.
The motor readiness account also explains the paradoxical ®nding that the RT in
a go/nogo task can sometimes even be longer than the RT in a corresponding choice
situation (cf. Luce, 1986, p. 213). According to this explanation, the response system
must generate more activation to produce a response in the go/nogo task than in the
choice task. It is plausible that extra time would be needed to generate this additional
activation.
9
An ANOVA including Experiment 3, 4 and 5 revealed that the average preload force within this
window was only 0.7 cN larger in the go/nogo task than in the other tasks, F < 1. Virtually identical
results were obtained in an analysis of mean force output over a wider interval preceding RT.
68
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
Since the introduction of DondersÕs subtraction method, the go/nogo task has
been a major cause of debate about the validity of DondersÕs scheme (cf. Luce, 1986;
Welford, 1980). The present results provide direct empirical support for the existing
notion that the go/nogo task does not ®t well into this scheme. As discussed in the
Introduction, the traditional concerns about the go/nogo task revolve around
DondersÕs assumption that this task does not necessitate the process of response
selection. Speci®cally, beginning with Wundt (1880), several authors have argued on
introspective and logical grounds that the go/nogo task does require response selection ± contrary to DondersÕs analysis ± because the observer must choose whether
to respond or not. As far as we know, however, the only empirical support for this
view comes from the pupillometric studies mentioned in the introduction, and this
evidence is rather indirect, as already discussed. The present results neither support
nor contradict the idea that the go/nogo task requires a response selection process,
but they do suggest an alternative account of why the go/nogo task might not ®t
within DondersÕs scheme.
In conclusion, the present experiments partially support but partially contradict
DondersÕs assumption that the response execution system operates identically in all
three RT tasks of his scheme. In particular, the go/nogo task is an exception, because
more force is generated in this task.
Acknowledgements
This work was supported by the Deutsche Forschungsgemeinschaft (UL 116/3-2)
and by a research cooperation fund of the Deutsche Forschungsanstalt f
ur Luft-und
Raumfahrt e.V. (NZ 08). We thank Frauke Becker and Hiltraut M
uller-Gethmann
for running the experiments. We appreciate the helpful comments of Richard Ridderinkhof, A.F. Sanders, Robin Thomas, and three anonymous reviewers on previous versions of this paper. Requests for reprints should be addressed to Rolf
Ulrich, Phychological Institute, University of T
ubingen, Friedrichstr. 21, 72072
T
ubingen, Germany, or to Je€ Miller, Department of Psychology, University of
Otago, Dunedin, New Zealand.
Appendix A. Predictions of cascade model
In the main text we have emphasized the null e€ects of task on response force
predicted from serial stage models and DondersÕs assumption of pure insertion. In
this appendix we consider the predictions of an alternative continuous model known
as the ``cascade model'' (McClelland, 1979). This alternative model rejects the
assumptions of serial stages and of pure insertion and, as we will show, suggests that
the response execution stage should vary with task complexity. Speci®cally, it suggests that the response force should decrease as task complexity increases. This
prediction is developed in the remainder of this Appendix A.
It seemed important to consider the predictions of continuous models as well as
discrete ones. Some theorists consider continuous models to be more plausible than
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
69
discrete stage models, because the former seem more compatible with current ideas
about brain structure and neural mechanisms (e.g., Smith, 1995; but see Roberts &
Sternberg, 1992). McClelland's (1979) cascade model was chosen for study because it
is the classic and seemingly most prominent continuous model in RT research, and
because it is one of the few continuous models that are speci®ed precisely enough to
derive such predictions (cf. Roberts & Sternberg, 1992).
In some respects, the cascade model resembles discrete stage models. Like discrete
models, it assumes that activation passes unidirectionally through a set of functionally ordered stages such as stimulus detection, stimulus identi®cation, response
selection, and response execution. It di€ers fundamentally from stage models,
however, regarding the transmission of activation from one stage to the next. The
cascade model holds that a single stage transmits its output continuously to the
subsequent stage, which starts processing as soon as partial activation is available
from its predecessor stage. Thus, when a stimulus is presented, activation gradually
increases throughout the whole system until a threshold is crossed in a ®nal motor
stage, triggering the motor response.
As has been noted previously (e.g., Balota & Abrams, 1995; Ulrich et al., 1998), a
natural elaboration of the cascade model is required to account for the recent
®ndings that experimental manipulations a€ect not only RT but also the dynamics of
the response itself. For example, it has repeatedly been documented that participants
respond not only faster but also more forcefully to intense stimuli than to weak
stimuli (Angel, 1973; Jaskowski et al., 1995; Mattes & Ulrich, 1997; Miller et al.,
1999; Ulrich et al., 1998).
Within the standard cascade model, increasing stimulus intensity would increase
the activation ¯ow throughout the system, because the strength of a stage's input
determines the strength of its output. Even if force is monotonically related to response-level activation, however, this would not explain the e€ect of intensity on
response force. As mentioned before, in the standard cascade model a response is
emitted when the accumulated activation at the ®nal response stage reaches a certain
threshold value that is independent of intensity. Thus, all responses would be initiated at the same criterion activation value regardless of stimulus intensity, and response force would not increase with intensity.
It is, however, plausible to elaborate the cascade model by assuming that force
production somehow re¯ects continuing response activation after the criterion is
crossed. Moreover, there is evidence in support of this assumption (Ulrich et al.,
1998). Such an elaboration could explain why intense stimuli cause more forceful
responses. For example, it seems quite plausible that an increased rate of response
activation after criterion crossing would recruit more motor units, which in turn
would increase the amplitude of the force output (cf. Ulrich & Wing, 1991). Thus, if
response force is assumed to depend on the rate of continued response activation
after the response criterion is crossed, the cascade model would not only account
for RT results but also provide a framework to make predictions about the dynamics of the response itself. The predictions of this elaborated cascade model
regarding the e€ect of task complexity on both response force and RT will be
analyzed next.
70
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
The ¯ow of activation predicted by McClelland's cascade model is depicted in
Fig. 2 for various levels of task complexity. In each panel, the solid curve represents
the activation level of the response execution stage. First, examine panels A, B and C
on the left side of the ®gure. These show how response activation is in¯uenced by the
insertion of nonmotoric stages, in accordance with DondersÕs analysis of the simple
RT, go/nogo, and choice RT tasks. Panel A shows the activation functions for a twostage version of the cascade model, which might be suitable for a simple RT task
(e.g., stimulus detection and response execution). Panel B shows the activation
functions for a three-stage version of the model that might be suitable for a go/nogo
task, with an intermediate stage (e.g., stimulus identi®cation) added between the two
stages of the version shown in Panel A. Note that the growth of response activation
in the response execution stage is slowed, relative to that shown in Panel A, when this
intermediate stage is inserted. Finally, Panel C shows the activation functions for a
four-stage version of the model that might be suitable for a choice RT task, with an
additional intermediate stage (e.g., response selection) beyond that present in Panel
B. Note that insertion of this additional stage further slows the growth of response
activation. Thus, continuous models suggest that response activation would increase
more slowly as the number of nonmotoric stages increased, contrary to DondersÕs
assumption of pure insertion.
Panels D, E and F show that the response activation function is also ¯attened if ±
contrary to DondersÕs analysis ± task complexity reduces the rate of accumulation
¯ow within a central stage instead of in¯uencing the number of stages. Panel D
shows a model for simple RT; information is processed at a high rate within the
central stage because the task puts little demand on that stage. Panel E shows a
model for the go/nogo task, where there is more demand on the central stage and
thus a lower rate of information growth in this stage. Once again, making the task
more complex slows the growth of response activation, just as it did when increasing
complexity added new stages rather than slowing an existing one. Panel F shows a
model for the choice task, with even more demand on the central stage and even
slower activation growth in it, resulting in even slower activation growth in the ®nal
stage.
The ¯attening of the response activation function illustrated in panels A-C and
again in panels D±F can be demonstrated more formally. Let i denote the ith
…i ˆ 1; . . . ; n† stage within a chain of n successive processing stages. Speci®cally, let n
be the ®nal processing stage, which corresponds to the response activation process.
As shown by McClelland (1979, p. 294), the response activation function an …t† is
given by the general gamma function (McGill, 1963)
an …t† ˆ 1 ÿ
n
X
Ki exp …ÿki t†;
…A:1†
iˆ1
where ki is the rate associated with the ith stage and the constant Ki is computed as
n
Y
kj
:
…A:2†
Ki ˆ
kj ÿ ki
jˆ1
j6ˆi
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
71
Fig. 2. Activation functions predicted by the cascade model. Each panel shows activation functions for
various information processing stages. The top panels (A and D) show hypothetical systems for a simple
RT task, the middle panels (B and E) for a go/nogo task, and the lower panels (C and F) for a choice RT
task. The left panels demonstrate how the response activation function (solid curve in each panel) becomes
¯atter as more stages are inserted before the response execution stage. The right panels show how the
response activation function becomes ¯atter when task complexity increases the processing time of a
central stage within a hypothetical system with three stages. In all panels, the rate constant ki of the response execution stage is 1=120 msÿ1 and the asymptotic activation value is 1. In panels A, B and C the
rates of stimulus detection, stimulus identi®cation and response selection are 1/90, 1/80 and 1=70 msÿ1 ,
respectively. The rate of the central processing stage in D, E and F is 1/30, 1/110 and 1=170 msÿ1 , respectively; the rate of the detection stage is 1=60 msÿ1 in all three panels. The following indices can be
computed for the response activation functions in each panel: (a) RT (ms) for a criterion value of c ˆ 0:5,
(b) slope (1/ms) of the response activation function at c ˆ 0:5, (c) the spread of the response activation
function (ms) ± cf. Appendix A, and (d) the duration (ms) it takes to increase response activation from a
value of 0.1 to a value of 0.9. These indices (a, b, c, d) are (176, 0.00298, 150, 354) for Panel A, (257,
0.00254, 170, 412) for Panel B, (329, 0.00231, 184, 451) for Panel C, (179, 0.00334, 138, 321) for Panel D,
(255, 0.00251, 174, 418) for Panel E and (305, 0.00205, 216, 516) for Panel F.
72
R. Ulrich et al. / Acta Psychologica 102 (1999) 43±75
(Note that information is processed more slowly in stage i when ki is small than when
it is large.)
The general gamma function can be conceived as the cumulative distribution
function of a sum of n exponentially distributed random variables with rates
k1 ; . . . ; kn (McGill, 1963). Therefore, the slope of an …t† corresponds to the probability
density function of the general gamma function
n
X
d
Ki ki exp …ÿki t†
an …t† ˆ
dt
iˆ1
…A:3†
and thus the spread (i.e., the standard deviation) of the activation function an …t† is
s
n
X
1
:
…A:4†
SD ˆ
2
k
i
iˆ1
Hence, all other things being equal, the spread of an …t† increases and the response
activation function an …t† becomes ¯atter in two cases: (1) as more stages precede the
®nal stage, that is, as n increases (i.e., as illustrated in panels A±C); and (2) as there is
a decrease in the rate ki of any stage i 2 f1 . . . n ÿ 1g that precedes the ®nal stage n
(i.e., as illustrated in panels D±F).
In summary, the cascade model suggests that response activation accumulates
more slowly within the motor system in more complex tasks, whether increasing task
complexity adds new stages, as Donders suggested, or slows existing ones. Assuming
that response force is larger when motor activation accumulates at a higher rate, in
either case the model thus suggests that responses are most forceful in the simple RT
task, less forceful in the go/nogo task, and least forceful in the choice RT task. This
particular prediction is clearly at variance with the results of our experiments.
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