Journal of Experimental Psychology:
Human Perception and Performance
1999, Vol. 25, No. 5, 1316-1330
Copyright 1999 by the American Psychological Association, Inc.
0096-1523/99/S3.00
Correlations for Timing Consistency Among Tapping and
Drawing Tasks: Evidence Against a Single Timing Process
for Motor Control
Shannon D. Robertson, Howard N. Zelaznik, Dawn A. Lantero, Kathryn Gadacz Bojczyk,
Rebecca M. Spencer, Julie G. Doffin, and Tasha Schneidt
Purdue University
Three experiments were conducted to examine whether timing processes can be shared by
continuous tapping and drawing tasks. In all 3 experiments, temporal precision in tapping was
not related to temporal precision in continuous drawing. There were modest correlations
among the tapping tasks, and there were significant correlations among the drawing tasks. In
Experiment 3, the function relating timing variance to the square of the observed movement
duration for tapping was different from that for drawing. The conclusions drawn were that
timing is not an ability to be shared by a variety of tasks but instead that the temporal qualities
of skilled movement are the result of the specific processes necessary to produce a trajectory.
These results are consistent with the idea that timing is an emergent property of movement.
Skill clearly is a function of practice as well as a potential
to perform well. This potential, thought to be resistant to the
effects of practice, has been called an ability (Schmidt,
1988). Individuals who perform well on a particular task do
so because of extensive practice, high ability or, most likely,
a combination of the two. Common everyday experience
leads us to infer that certain individuals can perform well on
many motor tasks. It seems unlikely that practice is the
reason. Therefore, we intuit that these individuals must
possess an ability, that is, a potential, to perform well on
many, if not all, motor tasks. This concept, known as general
motor ability (see Schmidt, 1988), was disproved by Henry
and his students in the early 1960s (see Bachman, 1961;
Henry, 1960,1961, 1976; Lotter, 1961). Henry proposed the
hypothesis of the specificity of motor abilities, which
posited that these potentials, or abilities, were numerous—so numerous, in fact, that correlations among motor
tasks should be uniformly low. For example, Henry's
research program indicated that an individual's performance
on a balancing task, such as climbing the Bachman ladder,
was not correlated with performance on another balancing
task, the stabilometer balance task (Bachman, 1961).
During the past 15 years, Keele, Ivry, and colleagues have
challenged Henry's hypothesis of the specificity of motor
abilities (see Ivry & Hazeltine, 1995; Keele & Ivry, 1987).
Shannon D. Robertson, Howard N. Zelaznik, Dawn A. Lantero,
Kathryn Gadacz Bojczyk, Rebecca M. Spencer, Julie G. Doffin,
and Tasha Schneidt, Department of Health, Kinesiology, and
Leisure Studies, Purdue University.
Shannon D. Robertson is now at the Department of Exercise
Science and Physical Education, Arizona State University.
Special thanks are due to Daniela Corbetta, Richard Ivry, and
Lorraine Kisselburgh for comments on a draft of this article.
Correspondence concerning this article should be addressed to
Howard N. Zelaznik, Department of Health, Kinesiology, and
Leisure Studies, Purdue University, 1362 Lambert, West Lafayette,
Indiana 47907. Electronic mail may be sent to hnzelaz@purdue.edu.
They have proposed and have provided experimental evidence in support of the idea that certain fundamental
abilities can be shared by a variety of motor tasks. Their
research effort has focused on an examination of the nature
of timing as an ability. They have observed high correlations
among the performance of various timing tasks across
effector systems (finger and arm) and perceptual and motor
timing systems (Keele & Hawkins, 1982; Keele, Pokorny,
Corcos, & Ivry, 1985). Recently, Franz, Zelaznik, and Smith
(1992) have extended this notion by observing modest
correlations between speech and jaw timing consistency and
finger and arm timing consistency.
The collection of studies briefly described above is
theoretically important. First, these studies provide evidence
against a hypothesis of the specificity of motor abilities.
Second, these studies are consistent with the notion that
timing processes are imposed upon a movement or a
perceptual process. This idea, which we refer to as timing as
an abstract process, also is consistent with the idea that
movements are governed by abstract timing structures that
can be stretched or compressed in time to produce a new rate
of movement (see Heuer, Schmidt, & Ghodsian, 1995, and
Schmidt, 1988, for examples of these types of models).
On the other hand, timing can be viewed as the result of
movement control processes that act to constrain a movement trajectory. In other words, timing is an emergent
property of movement (Turvey, 1977). According to this
dynamic system perspective, timing is not "in" a construct
controlling movement; rather, the time course of a movement is the result of the dynamic processes at work (see
Wallace, 1996). Although this account has not been used to
explain and understand correlations among liming tasks, we
believe a dynamic system approach researcher would intuit
that there should be a high degree of specificity in motor
timing.
Ivry and Hazeltine (1995) examined the generality of
timing by examining whether the function relating variabil-
1316
TIMING CONTROL IN DRAWING AND TAPPING
ity in timing (timing variance) to the square of the observed
interval to be timed, a Weber function, was similar across
production and perception tasks. Can the same Weber
function describe perceptual and motor timing? Their results, in general, supported the notion of a common central
timing process in that perceptual timing tasks and movement
timing tasks appeared to obey the same Weber relationship.
However, their results did not bear on the prediction of high
correlations among different kinds of motor tasks. Is timing
performance on one task predictive of timing performance
on the same task performed at a different rate? Furthermore,
is timing performance for one type of task predictive of
timing performance for a different type of task? In Experiment 1, the above two questions were examined.
Experiment 1
In Experiment 1, we examined whether there is evidence
for a timing ability that is general across two different
tapping rates, 400 and 800 ms. If timing is a general ability
that can be shared across different movement rates, individuals who are consistent timers at the 400-ms rate also should
be consistent timers at the 800-ms rate. Furthermore, if
someone is a consistent timer at the 800-ms timing task, that
same individual should be a consistent timer in other
movements that require the production of an 800-ms rate.
These ideas were studied by examining correlations for the
performance of continuous tapping and drawing.1 If timing
processes are an integral part of the trajectory, low correlations should be observed between timing in finger tapping
and timing in repetitive drawing. In other words, each task
should demonstrate specificity in timing ability.
Method
Participants. Twenty-five undergraduate and graduate students at Purdue University (18 to 25 years old) volunteered to be
paid participants. There were 8 men and 17 women. All participants
had normal or corrected-to-normal vision. All participants provided
informed consent. The experiment was approved by the Purdue
University Committee on the Usage of Human Research Subjects.
Apparatus and tasks. For both the drawing and the tapping
tasks, participants used Mars-Staedtler 2-mm mechanical drawing
pencils containing 2H hardness graphite. A1-cm-diameter infraredlight-emitting diode (BRED) was affixed to the bottom of the
pencils. Adhesive tape was wrapped around each pencil to make
the diameter about 1 cm.
All tasks were performed with the participant seated in front of a
79-cm-high table. In the tapping tasks, the participant tapped with
the pencil on a foam pad that was covered with black nonreflective
tape. The graphite was not protruding for these tasks. For the
drawing tasks, the participant drew the required shape(s) on
ll-by-15-inch (~28-by-~38-cm) white computer paper.
All tasks were paced by a computer-generated metronome. The
participant produced 12 movements with the metronome engaged;
this step was followed by an interval of time sufficient to allow for
30 movements that were not paced by the metronome to be
produced. During this unpaced portion of the trial, the participant
1317
attempted to maintain the goal movement interval as accurately and
as consistently as possible.
There were 11 drawing tasks. Three were unimanual tasks: line
drawing, circle drawing, and figure-eight drawing; all were performed with the nondominant hand. The period of motion for the
line and circle tasks was 800 ms, and the period of motion for the
figure-eight task was 1,600 ms. The line was drawn in the
anterior-posterior axis (the y-axis of the tabletop). The length of the
line and the diameter of the circle were 10 cm, as was the length of
the y motion for the figure eight. There were eight bimanual tasks:
circles, lines, a line and a circle (the line with the dominant hand
and the circle with the nondominant hand), and a circle and a line
(the circle with the dominant hand and the line with the nondominant hand); these four tasks were each performed in a symmetrical
mode of coordination (in-phase) and in an asymmetrical mode of
coordination (anti-phase). Symmetrical coordination for the lineline task was defined as the hands moving away from and then
toward the body in synchrony. For the circles-circle task, symmetrical coordination was defined along the x dimension, so that moving
in together and moving out together were symmetrical and the
hands moving toward the right together and moving toward the left
together were asymmetrical. For the line-circle and circle-line
tasks, symmetrical was defined in the y dimension. Symmetrical
was defined as the hands moving in the same y direction, such as
moving away from and then toward the body. Asymmetrical was
defined as one hand moving away from and the other hand moving
toward the body.
Procedures. After a participant was instructed and after he or
she provided informed consent, testing commenced. A trial began
when the experimenter told the participant to begin the appropriate
movement. One second later, the metronome was engaged for 13
beats (12 intervals), after which the participant continued to
perform the required task for the amount of time needed to produce
30 additional cycles. At the end of each trial, for the drawing
movements, the experimenter replaced the paper that was drawn
on. For all trials, (here was a 25-s intertrial interval. The entire
testing session required about 85 to 90 min.
Participants performed the 13 tasks in a fixed order.2 The order
was as follows: 400-ms tapping, 800-ms tapping, unimanual line,
unimanual circle, and unimanual figure eight. The bimanual tasks
were performed next. The order was as follows: symmetrical lines,
asymmetrical lines, symmetrical circles, asymmetrical circles,
symmetrical line-circle, asymmetrical line-circle, symmetrical
circle-line, and asymmetrical circle-line. In the mixed tasks, the
first shape name signifies the task performed by the dominant hand,
and the second shape name is for the task performed by the
nondominant hand.
The two tapping tasks were performed for 12 trials, and all other
tasks were performed for 6 trials.
Data acquisition and reduction. A Watsmart, Northern Digital
Inc., Waterbo, Ontario, Canada, system sampled the location of the
1
The original purpose of all of the conditions used in Experiment 1 was to develop a scale of task difficulty that we would use to
select tasks in future work on motor development. However, for the
sake of completeness, we report all of the drawing conditions.
2
We used a fixed order for the conditions in Experiment 1 and in
the other experiments so that the effects of practice would not
obscure the correlations between tasks. This technique follows the
traditions of the work of Keele and Ivry (1987). If the order of
conditions were randomized, then performance by different individuals on a particular task might depend on the order used. Because we
used a fixed order, each participant was affected by order in an
identical fashion.
1318
ROBERTSON ET AL.
lauit/ 1
i
Table
Average Computed Duration for Two Scorers (01 and 02) for 2 Participants in Tapping
Participant/
tapping duration
M(01)
M(02)
RMSEW
SD
(01)
SD
(02)
RMSEa
401
768
401
768
7
14
17
35
17
36
1.5
2.4
361
835
361
835
10
13
25
58
26
60
2.4
3.5
1
400
800
12
400
800
Note. RMSEw = root-mean-square error (RMSE) difference within a trial for the two scorers;
SD = average computed SD in interval duration for each scorer; RMSEa = average RMSE across
each of computed standard deviations for each scorer. All values are given in milliseconds.
IRED on each pencil at 256 Hz. Three-dimensional reconstruction
was done off-line with software provided with the Watsmart
system. The kinematic data from the drawing tasks were filtered, in
the forward direction and then in the backward direction, with an
8-Hz low-pass Butterworth filter.
Results
Tapping analyses. We used a graphic routine developed
in-house to determine when an individual tapped on the
tabletop. The routine displayed the unfiltered z-displacement
data and overlaid a low-pass-filtered (25 Hz) displacement
of the same tapping trial. The beginning of a tapping interval
was defined by the operator to be the location in the record
where the displacement record began to level off. The
operator used the mouse to position the crosshair to mark the
end of the downstroke of the tap (see Wing, 1980, for a
discussion of the dissection of a tap into components). This
method avoided the use of heavily low-pass-filtered (less
than 10 Hz) data, which would have made the tap downstroke the middle of the interval between the end of the
downstroke and the beginning of the upstroke.3 This method
was used in all three experiments. In order to determine the
accuracy and precision of the method, a second individual
also scored 2 participants from Experiment 1. Several
different computations were used to examine reliability and
accuracy.
First, the correlation within a trial of the marked points
was calculated. For each trial for the 2 participants (48 total
trials), the correlation for the sample value of the end of the
downstroke was greater than .99. This result is not surprising, because the sample number for successive downstrokes
must increase monotonically within a trial. Second, the
root-mean-square error in the standard deviation of tapping
duration across trials within a condition was computed.
Table 1 shows the results of these calculations. As indicated
in Table 1, the individual cycle durations within a trial
differed between scorers by less than 10 ms for the 400-ms
tapping task and less than 14 ms for the 800-ms tapping task.
However, an additional calculation demonstrated the functional accuracy of our scoring method. We calculated the
difference in average standard deviation for a condition
between the two scorers (last column of Table 1). This
difference was less than 4 ms. In other words, although the
scorers differed by about two samples for the 400-ms
tapping task and four samples for the 800-ms tapping task,
this difference was relatively consistent, as indicated by the
average standard deviation for the two scorers as well as the
very small difference in the root-mean-square errors between conditions. Thus, we are confident that our graphic
scoring method is accurate and precise in determining the
variance in timing. We did not perform this analysis for
Experiments 2 and 3, as the same data analysis technique
was used with the same Watsmart collection system and the
same individual scored the trials in all three experiments.
Drawing analyses. For the drawing data, the 8-Hz
low-pass-filtered displacement data were used. To determine
the cycle duration for drawing, an interactive computer
graphic routine was used to search for local minima in the
displacement record. The y dimension was used to determine
a cycle. A cycle in drawing was defined as the time between
successive local minima. In the bimanual conditions, the
cycle duration was calculated independently for the dominant and nondominant hands.
Descriptive data. Table 2 shows the relevant movement
time and spatial data.4 As indicated in Table 2, participants
performed the required tasks. The figure-eight task had a
much larger movement time because the participants completed half of the figure eight on each 800-ms beat of the
metronome.
Tables 3 and 4 show the reliability coefficients. These
were computed from intraclass correlation coefficients via
separate Subject X Trial for the best six trials on the tapping
tasks and the best four trials on the drawing tasks, as
determined by the detrended variance for the unpaced
portion of the trial. As indicated in Tables 3 and 4, reliability
was quite high, except for the nondominant hand in the
asymmetrical tasks and in the unimanual figure-eight tasks.
Correlational analysis. We computed the correlation
coefficients among all tasks for the detrended variance in
3
We thank one of the reviewers for pointing out the difficulty in
using filtered data for tapping.
4
In the present set of experiments the concern was for timing
variability capturing the most stable aspects of temporal precision.
Because in a long series of taps or repetitive drawing movements,
there can be a pause in the movement record, leading to increased
variability, we decided to use the average of the four best trials
(smallest detrended variance) in all conditions for all experiments.
1319
TIMING CONTROL IN DRAWING AND TAPPING
Table 2
Average Period of Motion (in Milliseconds) and Within-Subject Standard Deviation for
All Tasks and Average-Diameter Ratio and Length of Major Diameter (in Centimeters)
for All Drawing Tasks in Experiment 1
Dominant hand
Nondominant hand
Period of
motion (ms)
Task
400-ms tap
800-ms tap
Line
Circle
Figure eight
Line-line symmetrical
Line-line asymmetrical
Circle-circle symmetrical
Circle-circle asymmetrical
Line-circle symmetrical
Line-circle asymmetrical
Circle-line symmetrical
Circle-line asymmetrical
M
SD
398
13
802 ' 37
784
786
776
790
786
795
772
769
25
24
26
30
31
29
26
25
timing for the unpaced portion of the trial. Because there
were 21 movement types, which would result in a 21 X 21
correlation matrix (13 tasks plus the 8 nondominant hand
scores in bimanual conditions), we decided to depict the
pattern of correlations graphically instead of using a table.
Figure 1 depicts the pattern of correlations for the tapping
and unimanual drawing tasks. Consider each outer circle as
having a diameter of 1. A radius (i.e., a spoke) of the circle
represents a particular task, labeled at the circumference.
The solid-line radius represents the task that is being
correlated with all of the other tasks. The inner circle
represents the value of the correlation at the .05 level of
significance (r = .38). The value of the correlation is the
distance from the symbol to the center of the circle.
It is clear from the top two panels of Figure 1 that timing
precision in the 400-ms tapping task (left panel) was
marginally related to timing precision in the drawing tasks
and that timing precision in the 800-ms tapping task (right
panel) was not correlated with performance on the drawing
tasks. There was a low (r = .42), albeit significant, correlation for timing precision between the 400- and 800-ms
tapping tasks.
Table 3
Reliability of Coefficient of Variation for Each Task and
Hand Under Unimanual Conditions in Experiment 1
Coefficient of variation for:
Task
400-ms tap
800-ms tap
Line
Circle
Figure eight
Dominant
hand
Nondominant
hand
.97
.96
.60
.98
.37
Period of
motion (ms)
Ratio
.09
.11
.84
.76
.57
.56
.15
.13
Length
M
SD
Ratio
Length
13.6
13.8
12.1
13.0
15.3
15.4
13.9
14.8
801
794
1,487
784
784
777
789
786
795
772
769
27
30
54
27
26
27
32
33
35
28
25
.10
.85
.51
.07
.08
.86
.85
.15
.16
.60
.61
13.2
12.6
12.2
12.8
13.5
11.4
11.2
11.8
13.1
13.4
13.7
Examination of the bottom three panels of Figure 1
provides some interesting observations. First, for the figureeight task (center panel), timing performance was not related
to timing performance on any of the other tasks. For the line
and circle tasks (left and right panels, respectively), there
were significant correlations among many of the drawing
tasks. Unimanual line and unimanual circle drawing performances were correlated and, by and large, the bimanual
symmetrical conditions were significantly correlated with
the unimanual line and unimanual circle tasks.
Figure 2 shows the correlations for the bimanual drawing
tasks. The correlations for the nondominant hand are in the
lower half of each circle. The nondominant hand correlations are denoted by an unfilled circle, and the dominant
hand correlations are denoted by a filled circle. There was a
relationship for timing precision in these bimanual drawing
tasks. In the symmetrical conditions, individuals who were
consistent timers in one of these tasks were consistent timers
in other symmetrical dual-hand tasks. In the asymmetrical
Table 4
Reliability of Coefficient of Variation for Each Task and
Hand Under Bimanual Conditions in Experiment 1
Task
Coefficient of
variation for:
Dominant Nondominant Coordination Dominant Nondominant
hand
hand
mode
hand
hand
.97
Line
Line
Symmetrical
.95
Asymmetrical
.86
.60
Line
Line
Circle
Symmetrical
.96
.96
Circle
Asymmetrical
.90
Circle
Circle
.91
Line
.89
.82
Circle
Symmetrical
Asymmetrical
Line
Circle
.89
.63
Circle
.97
.98
Line
Symmetrical
Asymmetrical
Circle
Line
.81
.61
1320
ROBERTSON ET AL.
conditions, there was a tendency for the correlations to be
lower, perhaps because these conditions, in general, were a
bit more difficult, causing participants not to settle in on a
particular strategy for a condition. Finally, the task in which
a circle was drawn with the dominant hand and a line was
drawn with the nondominant hand in the asymmetrical
configuration (OLa in Figure 2) did not produce many
significant correlations.
Discussion
There were three theoretically important results in Experiment 1. First, consistency in timing on the 400-ms tapping
task was marginally related to consistency in timing on the
800-ms tapping task. Thus, in tapping, timing is not a unitary
process shared by these two different rates. Second, tapping
at the 800-ms rate was not correlated with any of the 800-ms
drawing tasks. Thus, the processes used for timing in tapping
were not the same as the processes related to timing in the
800-ms drawing tasks. Third, there were strong correlations
for timing precision among the drawing tasks. Because the
original purpose of Experiment 1 was not to examine these
drawing tasks for the pattern of correlations, they were not
chosen in such a way as to produce a principled account for
the correlational results.
Experiment 1 does not refute the notion that timing
sometimes can be a shared process. There is ample evidence
from the drawing tasks for such sharing. We did find
significant correlations for symmetrical drawing conditions.
However, recall that there were no significant correlations
for 800-ms tapping and any of the 800-ms drawing tasks.
This result casts doubt upon what might be termed a strong
version of timing as a single, shared ability. Presumably,
tapping and drawing tasks would use the same timing
mechanism.
Experiment 2
On the basis of the results of Experiment 1, we concluded
that timing as an ability was not generalizable across tasks
that have qualitatively different spatial demands and that, at
least for the tapping tasks, there was marginal support for the
idea that timing ability was shared across the 400- and
800-ms tapping rates. On the basis of the results of
Experiment 1, one might assume that most drawing tasks
would show significant correlations in terms of timing
consistency. Experiment 1 did not provide a good test of that
idea, as all lines and circles were performed at the same rate
and were the same size. Thus, in Experiment 2, the
hypothesis about a generalized timing ability was examined
further by having participants tap at one of two rates, 550
and 800 ms, and then draw circles in which the diameter of
the circle was 2.5, 5, 10, or 20 cm at either the 550- or the
800-ms rate. This experiment provided a further test of the
generalizability of timing ability across two tapping tasks
with more similar movement time values. Furthermore, the
generalizability within a rate across tasks and within tasks
that vary on a parametric value, such as diameter, was
examined.
Method
Participants. Participants were 25 undergraduate and graduate
students (10 men and 15 women) at Purdue University; they were
18 to 25 years old. All participants had normal or corrected-tonormal vision and were without any known neurological impairments. All participants provided informed consent. The procedures
were approved by the Purdue University Committee on the Usage
of Human Research Subjects.
Apparatus and tasks. The tapping and unimanual circle drawing tasks were identical to those in Experiment 1. The circle
templates were 2.5,5,10, or 20 cm in diameter.
Procedures. After providing informed consent, each participant performed the 10 tasks in a fixed order. First, the 550-ms tasks
were performed: tapping tasks and then the 2.5-, 5-, 10-, and 20-cm
circle tasks. Then, the 800-ms tasks were performed in the same
order.
For each task, a trial began when the experimenter asked the
participant to begin. The metronome was then engaged, and the
participant performed the task, attempting to synchronize with the
metronome. After 16 beats (15 cycles), the metronome was
disengaged and the participant continued to perform and keep time
as though the metronome were still engaged. After enough time had
elapsed for the participant to perform 30 additional movements, the
trial ended. There was a 20- to 25-s rest period between trials. Six
trials were performed for each task. The entire session, including
instructions, required about 75 min.
Data collection. A Watsmart system collected the kinematic
data from the IRED at a 256-Hz sampling rate. The data from the
drawing tasks were filtered at 8 Hz.
Results
The same algorithms used to analyze the kinematic data
from Experiment 1 were used in Experiment 2. Only data
Figure 1 (opposite). Correlation values for the two tapping tasks and the three unimanual drawing
tasks with all other tasks in Experiment 1. Each circle is to be considered a unit circle. The distance
from a point to the center of the circle represents the value of the correlation between the task labeled
on the spoke (broken line) and the task represented by the solid line. The inner circle represents a
circle with a radius of .38 unit. That inner radius represents the value of the correlation that is
significant with 25 pairs of scores. Thus, the value of the correlation for 800- and 400-ms tapping
tasks is about .36, and the value of the correlation for unimanual circles with the LLs condition (the
dominant hand in the symmetrical bimanual line condition), shown in the right-hand panel beneath
the "Unimanual drawing task" heading, is about .96. L = line; O = circle; a = asymmetrical; s =
symmetrical. If the symbol is preceded by an N, then the correlation for the nondominant hand of the
bimanual conditions is being depicted on that particular spoke. All bimanual conditions are dominant
hand-nondominant hand. Thus, OL means that the dominant hand performed the circle task and LO
means that the dominant hand performed the line task.
1321
TIMING CONTROL IN DRAWING AND TAPPING
from the unpaced portion of each trial, in which the
metronome was not engaged, were analyzed. The four best
trials (lowest detrended variance) in each condition per
participant were analyzed.
Descriptive temporal and spatial results. As shown in
Table 5, participants appeared capable of meeting the
temporal demands of the task. The average durations for the
550- and 800-ms tapping conditions were 532 and 768 ms,
respectively, F(l, 24) = 1,441, p < .001, MSB = 1,929. For
the circle drawing tasks, the 550- and 800-ms tasks had
average durations of 537 and 768 ms, respectively, F(l, 24) =
1,067, p < .001, MSB = 9,955. There was an increase in
circle duration as diameter increased, F(3, 72) = 16.2, p<
.001, MSB = 2,925.
Tapping tasks
LLa
LLs
LLaLLs
OOs
OOa
OOa
NOLs
NLLa
N OOsN OOaN LOS
LOa
N OOiN OOa
Unimanual drawing tasks
LLaLLs
NL!
N OOift OOa
LLa
LOs
LLs
NLI
N OOiN OOa
LLa
LLs
OO:
N OOsN OOa
LOs
LOs
1322
ROBERTSON ET AL.
The coefficient of variation was higher for 800-ms tapping
than for 550-ms tapping, F(l, 24) = 41.17,p < .01, MSE =
6.99. For the circle drawing tasks, there was a significant
effect of goal duration, F(l, 24) = 41.76, p < .001, MSE =
53.85. There was a clear tendency for the coefficient of
variation to decrease as diameter increased, F(3, 72) =
177.64, p < .001, MSE = 0.75. This finding is contrary to
impulse variability theory (Meyer, Smith, & Wright, 1982;
Schmidt, Zelaznik, Hawkins, Frank, & Quinn, 1979), which
predicts that movement distance should have no effect on
timing variance. These results are consistent with Hancock
and Newell's (1985) proposed functions relating timing
variance to movement velocity.
The average diameter in the circle tasks was about 2.5, 5,
10, and 20 cm in the respective diameter conditions. The
diameter did not vary across movement rate, F(l, 24) < 1.
To assess the overall shape of the circles, the ratio of the
minor diameter to the major diameter (Franz, Zelaznik, &
McCabe, 1991) was computed. A perfect circle will have a
ratio of 1. As shown in Table 5, the ratios were all close to 1.
The longer-duration circles were more circular than the
shorter-duration ones, F(l, 24) = 19.4, p < .001, MSE =
.008, and the large-diameter circles were more circular than
the small-diameter ones, F(3, 72) = 6.8, p < .001, MSE =
0.003.
Correlational analysis. Reliability coefficients were .96
and .91 for the 550- and 800-ms tapping tasks, respectively.
For the 550-ms circle drawing task, the reliability coefficients were .94, .96, .95, and .93 for the 2.5-, 5-, 10-, and
20-cm-diameter conditions, respectively. For the 800-ms
circle drawing task, the reliability coefficients were .92, .96,
.93, and .96 for the 2.5-, 5-, 10-, and 20-cm-diameter
conditions, respectively.
The dependent variable for this analysis was the correlation between pairs of tasks for the detrended variance. These
are displayed in Figure 3 in a manner identical to that used in
Experiment 1. Performance on the tapping tasks was not
related to performance on the circle drawing tasks, and
tapping performance on the 800-ms task was marginally
related to tapping performance on the 550-ms task (r = .53).
These results are very similar to those from Experiment 1.
There were some significant correlations in timing performance within the drawing tasks. These correlations appear
to be related to the difference in the diameters of the circles.
As indicated in the two left panels on the bottom of Figure 3,
only one of the other drawing tasks was related to the 20-cm,
550-ms circles, and no tasks were related to the 20-cm,
800-ms circles. The only other significant correlations were
for the 10-cm, 800-ms, the 5-cm, 800-ms, and the 5-cm,
550-ms tasks.
Discussion
Like Experiment 1, Experiment 2 demonstrated that
temporal performance on a tapping task was not related to
temporal performance on a drawing task. Furthermore,
within the circle drawing tasks, there was specificity. Timing
consistency for the 20-cm-diameter circles was not related to
timing consistency for the smaller-diameter circles. Further-
more, there were not as many significant correlations as in
Experiment 1. This difference across experiments can be
explained by the fact that all circle and line drawing tasks in
Experiment 1 were 10 cm in diameter (circles) and 10 cm in
length (lines). In Experiment 2, the smallest difference
between diameters was twofold within each rate of movement. We do not know whether the higher correlations for
drawing in Experiment 1 were based upon the similarities of
the total length of the y motion or whether they occurred
because there was only about a 1.5-fold difference between
the circumference (length) of a circle and the length of the
repetitive line.
One simple idea is that timing processes can be shared
only if movements belong to the same class. For example, a
class can be defined as a spatial-temporal characteristic (see
Schmidt, 1975), or as a movement topology (Franz et al.,
1991). Using the above notions of class, we assumed that
tapping and drawing are different movement classes. Thus,
significant correlations might not be observed between
tapping and drawing. Because not all circle drawing tasks
were correlated with each other and, in fact, there were not
many significant correlations, the idea of movement class is
not sufficient to explain correlations among tasks in terms of
timing precision. Instead, it seems that the dynamic similarity determined by the nature of the trajectory as well as the
forcefulness of the movement is an important consideration
for understanding the pattern of correlations. Experiment 3
examines this issue as well as one further test concerning the
sharing of timing processes across tapping and drawing
tasks.
Experiment 3
In Experiments 1 and 2, we examined what can be called a
very strong version of timing as a single ability to be shared
across motor tasks. This strong model assumes that only one
type of timing process is shared by all motor tasks. In
Experiment 2, changes in duration and diameter were large;
thus, it is possible that timing processes are shared, but only
within a small range of task differences. Recall that Experiment 1 did show significant correlations among drawing
tasks that were performed at the same rate, with the same
length, or with the same diameter. Thus, correlations across
rates might be observed if a much smaller range of
movement rate conditions were used.
Also, it is well known that timing variability increases as
the duration to be timed increases (Schmidt et al., 1979). In
fact, increases in timing variability follow well-defined
mathematical descriptions. Ivry and Hazeltine (1995) took
advantage of this fact in the examination of common timing
processes for production and perception. In their study,
participants produced or estimated timed intervals of 325,
400,475, or 550 ms. The timing-timing variability function
was best described by a Weber function in which the
variance in timing was related linearly to the square of the
timed interval. Across three experiments, the production and
estimation tasks displayed similar Weber functions. The
slope of the Weber function captures the central component
in timing. If two timing tasks share a central component,
1323
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ROBERTSON ET AL.
Table 5
Mean Duration, Coefficient of Variation (CV), Average
Diameter, and Diameter Ratio for Circle Tasks as a
Function of Circle Diameter and Goal Duration
in Experiment 2
Circle diameter (cm)
Parameter
M(ms)
CV
Diameter (cm)
Ratio
2.5
5
550ms
520
535
3.9
3.2
2.2
0.88
4.7
0.88
10
20
539
2.6
9.5
0.89
555
2.5
18.8
0.91
772
3.0
9.5
0.93
788
2.5
19.0
0.93
800ms
M(ms)
CV
Diameter (cm)
Ratio
749
4.8
2.4
0.91
763
3.8
4.7
0.93
Note. For tapping tasks, the means were 535 and 777 ms and the
CVs were 3.5 and 4.4 at 550 and 800 ms, respectively.
then the slope of their Weber functions should be equal.
Because Ivry and Hazeltine found equal slopes, they concluded that perception and production tasks share a common
central time-keeping component.
In this study, the technique developed by Ivry and
Hazeltine (1995) was used. Participants tapped at one of five
timed intervals, 325, 400, 475, 550, and 800 ms, and drew
10-cm-diameter circles at these intervals. Three questions
were asked. First, is the strength of the correlation among
tasks related to the degree of similarity in the movement
duration? Second, is the characteristic function relating the
variance in timing to the duration squared in circle drawing
equivalent to the function in tapping? To answer the second
question, the Weber analysis of Ivry and Hazeltine (1995)
was used. If in fact timing is controlled by a common
process or set of processes across various rates of production, the slope relating variance to duration for drawing
should be the same as the slope for tapping. Third, in more
limited-duration movements, which presumably are controlled via open-loop processes, are the correlations between
tapping and drawing still low?
Method
Participants. Participants were 25 undergraduate students (10
men and 15 women) at Purdue University. All except 1 woman
were right-handed. Each participant was paid $10 for participation.
Participants were recruited, provided informed consent, and were
tested in accordance with the procedures approved by the Purdue
University Committee on the Usage of Human Research Subjects.
Apparatus and tasks. The drawing task apparatus and drawing
task were identical to those in Experiment 2. For the tapping task,
the participant used the index finger of the dominant hand, the palm
of which rested on the tabletop and the thumb of which was
abducted; the other three digits were curled back to the palm. An
IRED was placed on the tip of the dominant-hand index finger. The
tapping task required that the index finger touch the tabletop with a
flexion movement coincident with the metronome beat. The
participant continued to tap at this rate when the metronome was
disengaged. In the circle drawing task, the participant drew 10-cm
circles in rhythm with the metronome beat and then continued to
draw at the same rate when the metronome was disengaged.
Kinematic data were sampled at 256 Hz by a Watsrnart system, and
data were analyzed in a manner identical to that used in Experiments 1 and 2.
Procedures. A trial was performed in a fashion similar to that
used in Experiment 2. Sixteen paced metronome beats (15 cycles)
were followed by a time interval sufficient to allow 30 movements
to be performed without the metronome. The order of conditions
was fixed. The tapping tasks were performed first, in sets of seven
trials. The order was 325, 400, 475, 550, and 800 ms. The circle
drawing tasks were performed next, in the same duration order. The
entire 70-trial session required about 75 min to complete. Participants were given rest intervals equal to the duration of the trial or
longer, if they so desired.
Results
Descriptive data. Table 6 shows the relevant data.
Except for the 325-ms circle drawing condition, in which the
average period of motion was 368 ms, participants were
capable of producing the cyclical movements with the
appropriate average duration. Of greater interest are the
coefficients of variation. First, all values were less than 10%.
In fact, for the circle drawing tasks, all values were about
3%. In other words, producing this rhythmical movement
with a trajectory constraint produced a much more consistent temporal rhythm than producing a simpler, tapping
movement. The tapping movements had coefficients of
variation of greater than 5%, and these values increased as
the goal duration increased, F(4, 96) = 4.11, p < .01,
MsE = 38.56.
In the circle drawing tasks, participants were capable of
producing the required spatial paths. At all five movement
rates, participants produced circles that were almost 10 cm
in diameter. The average y diameter was between 8.1 and 8.8
cm for the five duration conditions. There was an effect of
the goal duration, F(4, 96) = 9.58, p < .01, MsE = 0.96.
The 325-ms circles were smaller than circles at the other
four rates of movement. The shape of the circles was
measured by the index of circularity, computed on a
cycle-by-cycle basis (Franz et al., 1991). The ratio was about
.88, and a significant effect of movement rate, F(4, 96) =
3.59, p < .01, MSE = 0.004, appeared to be the result of a
small increase in the ratio for the 800-ms movement rate
condition.
Weber function analysis. If a common timing process is
shared across tasks, the function relating the variance in
timing to the duration squared should be the same for both
tapping and circle drawing. This issue was examined by
conducting two analyses, an analysis of variance in which an
interaction between duration and task was the test for a
common function and a regression analysis that tested for
the equality of slopes of die Weber function for the two
tasks. Figure 4 shows the relevant data. There was an
interaction between the type of timing task and the goal
duration, F(4, 96) = 31.64, p < .001, MSE = 3,662,765.
This interaction also was observed when the 800-ms tasks
were removed from the analysis, F(3, 72) = 49.93, p <
TIMING CONTROL IN DRAWING AND TAPPING
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ROBERTSON ET AL.
Table 6
Mean Duration and Coefficient of Variation (CV)for
Tapping Tasks and Drawing Tasks in Experiment 3
Value at a goal duration (ms) of:
Goal
duration
325
400
475
550
800
474
6.4
544
6.4
788
8.7
Tapping tasks
Mean duration (ms)
CV (%)
320
5.2
403
6.2
Circle tasks
Mean duration (ms) 368
415
473
533
765
CV (%)
3.2
2.9
2.9
3.0
3.4
Major diameter (cm)
8.8
8.1
8.6
8.8
8.8
Minor diameter (cm)
7.8
7.8
7.9
8.0
8.3
Ratio
.88
.87
.87
.86
.90
Note. For circle drawing tasks, the average diameter ratio and the
y diameters also are included.
.001, MSB = 721,446. Thus, these analyses do not support
the notion that a common timing process is responsible for
timing in tapping and drawing. We used a regression
procedure in which the detrended variance was regressed
against the observed duration squared. The slopes of the
regression were .0034 for the tapping tasks and .0009 for the
circle drawing tasks. The significant regression analysis,
F(2, 246) = 151.57, p < .001, MSE = 144,493, indicated
that the slopes were significantly different. The same analysis with the 800-ms tasks removed revealed the slopes to be
.0030 for the tapping tasks and .0004 for the circle drawing
tasks. This regression analysis also was significant, F(2,
196) = 285.47, p < .001, MSE = 25,732. It is interesting to
note that the slope for the tapping tasks did not change much
when the 800-ms tasks were removed from the analysis but
that the slope for the drawing tasks was about half as large.
Both sets of analyses converge to cast strong doubt on the
idea that timing processes can be shared over a wide variety
of tasks.
Correlational analysis. The detrended variance was
used for the correlational analysis of timing performance.
The reliability coefficients were .93, .93, .93, .91, and .82 for
the 325-, 400-, 475-, 550-, and 800-ms tapping tasks,
respectively. The reliability coefficients were .91, .93, .94,
.93, and .99 for the 325-, 400-, 475-, 550-, and 800-ms circle
drawing tasks, respectively.
Figure 5 shows the pattern of correlations among all tasks.
Temporal precision in tapping was not related to temporal
precision in circle drawing. Within the tapping tasks, there
was evidence for the generalization of timing ability. Except
for the low correlations for the 325-ms task, there were
significant correlations among the other tapping tasks. In the
circle drawing tasks, a similar pattern of correlations was
observed. On average, there were significant correlations
among all of the drawing tasks, except for the drawing tasks
paired with the 325-ms drawing task and there was a
reduction in the strength of the correlations between the 325to 550-ms tasks and the 800-ms drawing tasks.
Discussion
There were two major findings in Experiment 3. First,
timing performance in tapping tasks was not related to
timing performance in circle drawing tasks. Second, within
tapping and drawing tasks, there was evidence for a sharing
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Figure 4. Relation between duration squared (T2) and variance (ms2) for the tapping and the circle
drawing tasks in Experiment 3. Standard errors are depicted by the error bars.
TIMING CONTROL IN DRAWING AND TAPPING
Circle drawing tasks
Tapping tasks
55<Ma£__475tap
800 tap
325 circle (
1327
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400 tap
---
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400 circle
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800 circle
475 circle
circle
325 circle
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400 circle'
00 circle
475 circle
circle
Figure 5. Correlation between tapping and circle drawing tasks in Experiment 3. The left panel
represents the correlations for the tapping tasks with all the other tasks, and the right panel represents
the correlations for the circle drawing tasks with all the other tasks. The symbol that shows a 1.00
correlation (the symbol on the outer circumference) is the correlation of that task with itself and thus
is the symbol to look for to see the correlation of that task with the other tasks. For example, the solid
circles in the left panel represent the correlations between the 325-ms tapping task and the other
tasks.
of timing processes among the different durations. The first
finding and the findings of Experiments 1 and 2 lead to the
inference that timing at a particular duration does not have to
be a process shared across different kinds of motor tasks.
The significant correlations within each movement class
lead us to believe that the sharing of timing is related to the
similarity of the movement dynamics, in this case, the rate of
movement. We could not draw this conclusion from Experiments 1 and 2 because of the larger disparity in tapping rates
used and because of the very large differences in diameters
in Experiment 2.
across the three experiments for tapping were negative. This
finding lends support to the applicability of the WingKristofferson (1973) model to the tapping data. Second, in
Experiments 1 and 3, the covariances at lags greater than 1
were negative, providing evidence that feedback might be
involved in timing. Across the three experiments, such was
not the case for movements of less than 800 ms. However,
this finding does not explain the low correlations for timing
at the two rates in Experiments 1 and 2, as Experiment 2
showed that the covariances across lags 2 through 5 were
equal to zero. Thus, not all of the 800-ms tapping tasks
appeared to be under feedback control.
Covariance Analysis Across the Three Experiments
In the Wing-Kristofferson (1973) model of timing, the
covariance between the durations of interval n and interval
« + 1, called the lag 1 covariance, should be negative.
Assuming that the timing of the tapping intervals was under
open-loop control, their model predicts that the covariances
at lags greater than 1 should be equal to zero. However, if in
fact a participant adjusted subsequent intervals to correct for
perceived errors in previous intervals, then the covariances
at lags greater than 1 should be negative. Thus, the
covariance structure for lags greater than 1 (Wing, 1980) is
used to determine whether an open-loop model of timing has
strong support.5
A potential criticism of Experiment 1 is that the two rates
of tapping might involve different control processes. Specifically, the 400-ms rate might produce open-loop timing
behavior, and the 800-ms rate might produce closed-loop
timing behavior. Although this criticism is not as serious for
Experiment 2 and certainly does not hold for Experiment 3,
the nature of the covariance structure should be examined.
For all three experiments, the covariance structures for
lags 1 through 5 were computed. Figure 6 shows the results
of these computations. First, all of the lag 1 covariances
General Discussion
On the basis of the results of these three experiments, a
strong model of a central common timing process for motor
production was not supported. In all three experiments, we
found that temporal precision in tapping was not related to
temporal precision in drawing movements. If timing were an
abstract process, a temporal plan could be imposed upon a
variety of spatial trajectories. Thus, individuals who tap
consistently at a particular rate should also draw consistently
at that same rate because both tasks use the same abstract
timing process. This situation did not occur in the three
experiments.
Significant correlations were observed between the drawing movements of Experiment 1, between some similarly
sized and timed circles in Experiment 2, and between circles
5
We did not perform the lag covariance analyses for drawing
because more than 50% of the trials exhibited a lag 1 covariance
that was greater than zero. In other words, the Wing-Kristofferson
(1973) model did not apply to these drawing movements. This
finding for drawing provides further evidence that drawing and
tapping timing processes do not overlap.
1328
ROBERTSON ET AL.
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0
-100
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•
325 ms
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400ms
475 ms
550ms
800 ms
-300
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-500
100
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400 ms
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-300
Experiment 2
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100
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0
-100
T 800 ms
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-200
-300
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1
2
3
4
5
Covariance Lag
Figure 6.
Lag n covariance for tapping tasks for the three experiments.
drawn at different rates in Experiment 3. Why did Experiment 2 not show the same strength of correlations among
drawing as Experiment 3? Experiment 2 manipulated movement diameter from 2.5 to 20 cm, with each diameter level
being double the previous diameter level. In Experiment 3,
the manipulation of rate was much smaller than the changes
in movement diameter in Experiment 2. Thus, Experiment 3
used more similar tasks than did Experiment 2.
Correlations will be observed among timing tasks when
the tasks involve not just the same timed interval, as we
found for tapping and drawing, but similar dynamic demands. According to dynamic approaches to motor production, timing is the result of the assembly of oscillatory
processes (Kugler, Kelso, & Turvey, 1982; Turvey, 1990),
perhaps based on a pendulum system (Holt, Hamill, &
Andres, 1990) or a damped-mass spring system with a
driving component (Schmidt, Beek, Treffner, & Turvey,
1991). Similar movements (such as 10-cm circles and lines)
performed at similar rates could use similar oscillatory
processes, so that their temporal variability is related across
small changes in movement rate. As movements become
less and less dynamically similar, the two tasks will share
fewer common oscillatory mechanisms. Therefore, we believe that our results clearly support the notion that timing is
an emergent property of movement dynamics and is not
specified by an agent external to a movement's trajectory.
The above approach to motor timing processes helps us
better understand the previous results of Franz et al. (1992).
In that study, there were modest correlations for timing
variability for finger and jaw movements. These correlations, although significant, were much lower than those
found for finger and arm tapping by Keele et al. (1985). The
1329
TIMING CONTROL IN DRAWING AND TAPPING
reason why Franz et al. (1992) found significant, but lower,
correlations is that there was less sharing of finger and jaw
movement dynamic processes than of those of finger and
arm. When the timing variance was parceled into a central
duration-dependent component and a peripheral durationindependent component (Ivry & Hazeltine, 1995; Wing &
Kristofferson, 1973), the pattern of the correlational data did
not substantially change. Thus, the lower correlations were
not attributable just to a different effector peripheral apparatus for jaw and limb movements but could be attributable to
a different configuration of timing processes, that is, oscillators with different properties that produce the observed rate.
Our results are not in accordance with the conclusions of
Ivry and Hazeltine (1995), who argue for a common timing
process between perception and production and for an
interval-based process rather than a beat-based process. The
interval-based process is analogous to a centrally based
clock-like mechanism; Ivry and Hazeltine describe beatbased timing as an oscillatory process. Support for the
interval-based model was derived from the results of their
Experiment 4, in which timing in a brief, continuous
paradigm was no better (statistically) than that in a discrete,
discontinuous paradigm. If timing were beat (oscillatory)
based, the continuous condition should have produced better
timing than the discrete condition. Such was not the case.
However, there are two problems with their interpretation.
First, the continuation condition in fact was numerically
better in that it possessed less variance than the discrete
condition. Second, the multiple-presentation condition (only
four intervals) was numerically better than the singlepresentation condition. Finally, little is known about the
timing of the first several taps in a long sequence of taps, as
most experiments examine behavior only after participants
have become stable. Riding a bike clearly is cyclical, but the
first two or three revolutions from a standing start might not
appear to be very cyclical. It is clear that biological systems
have "start-up costs" for any oscillatory process. Future
work is needed to resolve this issue.
Why do perception and production share common timing
processes (Ivry & Hazeltine, 1995; Keele & Ivry, 1987) but
tapping and drawing (our experiments) apparently do not?
Our intuition is that tapping and perceptual timing tasks
require participants to estimate time. There are dwell times
at the beginning and end of tapping movements. The
participant needs to estimate when to bring the finger down
to contact the device to measure time or to produce the
sound of the tap coincident with the metronome. The rest of
the tapping movement does not have any particular trajectory constraint. The same lack of a trajectory constraint
occurs in perceptual tasks. However, the continuous drawing
tasks that we have studied do not have pause and dwell
times. In drawing, the entire trajectory is crucial for producing timing consistency. Thus, drawing depends much more
so on motor output processes than does tapping.
Experiment 1 showed significant correlations for symmetrical movement tasks but not for asymmetrical tasks. Symmetrical movements are in-phase and thus are more stable
(Kelso, 1995). This increased stability might mean that these
processes are easily shared across different types of coordi-
nation tasks, whereas asymmetrical (anti-phase) movements, being less stable, might need to be assembled anew
for each task.
Although we have no a priori reason why tapping and
circle drawing tasks should not have exhibited significant
correlations, some recent thinking from Ivry and Hazeltine
(1992) provides an interesting direction to follow. They
argue that one can consider two distinct types of timing
processes, timing with a timer versus timing without a timer.
We cannot rule out the possibility that tapping involves a
process of timing with a timer and thus involves some
centrally based clock-like mechanism. On the other hand,
the trajectory constraints of circle drawing may produce
temporal behavior that emerges from the trajectory constraints themselves, much in the same manner that Viviani
and Schneider (1991) argue that the 2/3 power law relating
velocity to curvature arises from the movement trajectory
characteristics. Thus, circle drawing and line drawing involve timing without a timer. At the present time, we have no
way of predicting why tapping should involve a different set
of timing processes than circle drawing. Thus, we are forced
to conclude that the three experiments, taken as a whole,
clearly show that timing processes are not shared across a
wide variety of motor tasks. Rather, timing appears to have a
large specific component based upon the similarity of the
tasks in question.
References
Bachman, J. C. (1961). Specificity vs. generality in learning and
performing two large muscle motor tasks. Research Quarterly,
32,3-11.
Franz, E. A., Zelaznik, H. N., & McCabe, G. (1991). Spatial
topological constraints in a bimanual task. Acta Psychologica,
77, 137-151.
Franz, E. A., Zelaznik, H. N., & Smith, A. (1992). Evidence of
common timing processes in the control of manual, orofacial,
and speech movements. Journal of Motor Behavior, 24, 281287.
Hancock, P. A., & Newell, K. M. (1985). The movement speedaccuracy relationship in space-time. In H. Heuer, U. Kleinbeck,
& H. Schmidt (Eds.), Motor behavior: Programming, control,
and acquisition (pp. 153-188). Berlin: Springer-Verlag.
Henry, F. M. (1960). Factorial structure of speed and static strength
in a lateral arm movement. Research Quarterly, 31, 440-447.
Henry, F. M. (1961). Reaction time-movement time correlations.
Perceptual and Motor Skills, 12, 63-66.
Henry, F. M. (1976). The second dimension of individual differences. Perceptual and Motor Skills, 43, 370.
Heuer, H., Schmidt, R. A., & Ghodsian, D. (1995). Generalized
motor programs for rapid bimanual tasks: A two-level multiplicative-rate model. Biological Cybernetics, 73, 343-356.
Holt, K. G., Hamill, J., & Andres, R. A. (1990). The force-driven
harmonic oscillator as a model for human locomotion. Human
Movement Science, 9, 55-68.
Ivry, R. B., & Hazeltine, R. E. (1992). Models of timing-with-atimer. In F. Macar, V. Pouthas, & W. Freidman (Eds.), Time,
action, and cognition (pp. 183-189). Amsterdam: Kluwer
Academic.
Ivry, R. B., & Hazeltine, R. E. (1995). Perception and production of
temporal intervals across a range of durations: Evidence for a
1330
ROBERTSON ET AL.
common timing mechanism. Journal of Experimental Psychology: Human Perception and Performance, 21, 3-18.
Keele, S. W., & Hawkins, H. L. (1982). Explorations of individual
differences relevant to high level skill. Journal of Motor
Behavior, 14, 3-23.
Keele, S. W., & Ivry, R. I. (1987). Modular analysis of timing in
motor skill. In G. H. Bower (Ed.), The psychology of learning
and motivation (Vol. 21, pp. 183-228). San Diego, CA: Academic Press.
Keele, S. W., Pokorny, R. A., Corcos, D. M., & Ivry, R. (1985). Do
perception and motor production share common timing mechanisms: A correlational analysis. Acta Psychologica, 60, 173-191.
Kelso, J. A. S. (1995). Dynamic patterns. Cambridge, MA: MIT
Press.
Kugler, P. N., Kelso, J. A. S., & Turvey, M. T. (1982). On the
control and co-ordination of naturally developing systems. In
J. A. S. Kelso & J. E. Clark (Eds.), The development of movement
control and co-ordination (pp. 5-78). New York: Wiley.
Lotter, W. S. (1961). Specificity or generality of speed of systematically related movements. Research Quarterly, 31, 55-62.
Meyer, D. E., Smith, J. E. K., & Wright, C. E. (1982). Models for
the speed and accuracy of aimed movements. Psychological
Review, 89, 449^82.
Schmidt, R. A. (1975). A schema theory of discrete motor skill
learning. Psychological Review, 82, 225-260.
Schmidt, R. A. (1988). Motor control and learning: A behavioral
emphasis (2nd ed.). Urbana, EL: Human Kinetics.
Schmidt, R. A., Zelaznik, H. N., Hawkins, B., Frank, J. S., & Quinn,
J. T., Jr. (1979). Motor-output variability: A theory for the accuracy of
rapid motor acts. Psychological Review, 86, 415-451.
Schmidt, R. C., Beek, P. J., Treffner, P. J., & Turvey, M. T. (1991).
Dynamical substructure of coordinated rhythmic movements.
Journal of Experimental Psychology: Human Perception and
Performance, 17, 635-651.
Turvey, M. T. (1977). Preliminaries to a theory of action with
reference to vision. In R. E. S. J. Bransford (Ed.), Perceiving,
acting and knowing (pp. 211-265). Hillsdale, NJ: Erlbaum.
Turvey, M. T. (1990). Coordination. American Psychologist, 45,
938-953.
Viviani, P., & Schneider, R. (1991). A developmental study of the
relationship between geometry and kinematics in drawing movements. Journal of Experimental Psychology: Human Perception
and Performance, 17, 198-218.
Wallace, S. A. (1996). Dynamic pattern perspective of rhythmic
movement: An introduction. In H. N. Zelaznik (Ed.), Advances
in motor learning and control (pp. 155-194). Champaign, IL:
Human Kinetics.
Wing, A. M. (1980). Timing of movement phases of a repeated
response. Journal of Motor Behavior, 12, 113-124.
Wing, A. M., & Kristofferson, A. B. (1973). The timing of
interresponse intervals. Perception & Psychophysics, 13, 455460.
Received December 1, 1997
Revision received July 20,1998
Accepted August 27, 1998