THE ORGANIZATION OF RAPID MOVEMENT SEQUENCES AS A

Acta Psychologica 66 (1987) 237-250
North-Holland
237
THE ORGANIZATION OF RAPID MOVEMENT
AS A FUNCTION OF SEQUENCE LENGTH *
Adela GARCIA-COLERA
SEQUENCES
and Andras SEMJEN
Centre National de la Recherche Scientifique, Marseille, France
Accepted July 1987
An experiment was performed to test the predictions made by the subprogram retrieval model
(Stemberg et al. 1978) for the production of rapid movement sequences, and to search for the
maximum number of elements that can be planned in advance of sequence execution. Subjects
performed rapid sequences of 1 to 8 finger taps under both simple and choice RT conditions.
Increasing sequence length had no effect on choice RT, but caused simple RT to increase
nonlinearly, with the greatest effect between 1 and 3 taps. Intertap intervals did not increase as a
function of sequence length The sequences’ timing and force patterns suggested that sequences up
to 8 taps were organized as single performance units. The results indicate a fundamental
difference between activating a plan for a single tap and a sequence plan in which several elements
must be coordinated and timed. Increasing the number of elements beyond 3 does not necessarily
add processing steps in the selection and activation of the sequence plan, at least for sequences
involving the repetition of a simple element.
Since Lashley (1951) postulated the existence of a central nervous
mechanism that governs the production of action sequences, many
efforts have been directed at understanding the functioning of such a
mechanism. Motor plan or motor program have become the terms most
widely used to refer to the central representation of a movement
sequence. In the approach originally suggested by Henry and Rogers
(1960), motor programs may be assessed by measuring the reaction
time (RT) needed to begin sequences of varying complexity. From
variations in the time to initiate a movement sequence, as a function of
the characteristics of the whole sequence, one can draw an inference
about some properties of the process by which a plan for the entire
sequence is generated or activated.
* Requests for reprints should be sent to A. Garcia-Colera,
Aiguier, 13402 Marseille Ckdex 9, France.
CNRS-LNFl,
OOOl-6918/87/$3.50 0 1987, Elsevier Science Publishers B.V. (North-Holland)
31 Chemin Joseph-
238
A. Garcia-Colera, A. Semjen / RT and sequence length
The numerous studies inspired by the RT approach have yielded
inconsistent results due to the choice of manipulated factors, to whether
choice or simple RT procedures have been employed, and even to the
difficulty in appropriately defining movement complexity (for reviews
see Kerr (1978) and Marteniuk and MacKenzie (1980)). One of the
variables most often used as an index of complexity has been sequence
length. RT has been found to increase with the number of connected
movement parts (Henry and Rogers 1960; Fischman 1984), syllables
(Ericksen et al. 1970; Klapp et al. 1973) or stress groups (Stemberg et
al. 1978) to be pronounced, button presses (Rosenbaum and Patashnik
1980; Rosenbaum et al. 1984a), and keystrokes (Stemberg et al. 1978).
Sternberg et al. (1978) have proposed a model for the production of
rapid movement sequences. According to the model, a program for the
entire sequence, composed of a subprogram for each element (words to
be recited or letters to be typed in their experiments), is loaded into a
buffer in advance of execution. Prior to the execution of each element,
the corresponding subprogram must be found in the nonshrinking
buffer through a self-terminating sequential search. As the number of
elements in the sequence increases, the number of subprograms in the
buffer increases accordingly so that a longer search time is needed to
find the appropriate subprogram. Therefore, increasing sequence length
should result not only in a linear increase in RT, but also in a similar
increase in the intervals between the successive elements.
This model has received a great deal of attention and has been
successfully tested in various experimental situations. However, its
general applicability may be questioned on the basis of results such as
(a) the dependence of the RT increase upon the type of response
material (Knapp et al. 1979) and upon practice (Hulstijn and Van
Galen 1983), (b) the attenuation or even the disappearance of the
sequence length effect when length is varied within (choice RT) rather
than between (simple RT) trial blocks (Klapp et al. 1979; Rosenbaum
et al. 1984b), and (c) the lack of an effect of sequence length on
interresponse times (Hulstijn and Van Galen 1983; Stelmach et al.
1984).
One of the aims of the present study was to test the effects predicted
by the model of Stemberg et al. (1978) in a repetitive finger-tapping
task. Another purpose of the experiment was to search for the maximum number of elements that can be taken into account in the
advance planning of a rapid sequence of movements. Accordingly,
A. Garcia-Colera, A. Semjen
/ RT and sequence length
239
sequence length was varied over a wider range than that used in most
of the previous studies. Subjects produced sequences of 1 to 8 finger
taps under both simple and choice RT conditions. The rate of sequence
execution was also manipulated. In the Speed condition, the sequences
had to be executed as fast as possible, like in most of the previously
cited experiments. In the Cadence condition, the sequence elements
had to be paced according to a prespecified rate.
According to the model of Sternberg et al. (1978), both RT and the
intertap intervals should increase as a function of the number of taps to
be produced, up to a ceiling which should correspond to the maximum
number of elements able to be comprised in the sequence plan. The
upper limit of planning was also expected to be reflected in the timing
of the individual taps, with more fluent timing of the taps that were
planned in advance, followed by a slowing down of execution rate at
the point at which control was switched from the previously established
plan to the additional programming required for the remaining elements.
In order to gain a more complete picture of the subjects’ motor
performance, the force of the taps was also recorded. In previous work
we found that the initial and terminal taps of 5-element finger-tapping
sequences were stronger than the intermediate taps. Thus, the sequence
boundaries were marked by a small, spontaneous stress (Semjen and
Garcia-Colera 1986). In the present experiment, the produced force
patterns were examined as a further potential source of information on
whether long sequences were segmented into smaller subunits.
Method
Task
The subject sat at a table, facing a circular key (2 cm in diameter) on which the
tapping sequences were performed, and a digital display unit on which the warning and
reaction signals were presented.
The subject’s forearm rested on the table with the
tapping finger held just above the key, so that both wrist and finger movements
contributed
to the realization of the sequences. The finger used could be the index or
middle of the preferred hand, but it had to remain the same throughout the experiment.
The subjects were instructed to make very brief, ‘staccato’ taps, by just hitting the key
and releasing it immediately afterwards.
In the Cadence condition, each series of trials was preceded by the presentation
to
the subject, via headphones,
of a string of clicks separated by a constant 160-msec
240
A. Garcia-Colera, A. Semjen / RT and sequence length
interval. This model indicated the rate at which the taps had to be executed in a
sequence. In the Speed condition, the subjects were asked to execute the sequences as
fast as possible. Nevertheless,
the 160-msec interval model was also presented before
each trial series as a reference speed to remind the subjects that they should attempt to
tap faster than the model.
Every trial started with a warning signal, which consisted of three horizontal lines,
displayed for 500 msec. It was followed by a variable preparatory
period of one of
three equally likely values: 900, 1500, or 2100 msec. At the end of that period was
presented a digit, used as reaction signal (RS), which indicated the number of taps to
be executed in the sequence. The sequence had to be initiated as quickly as possible
after presentation
of the digit. During the intertrial interval, which lasted 4 set, the RT
of the sequence just performed was displayed on a television screen in front of the
subject.
Measurements
Any contact between the finger and the surface of the key triggered an electronic
circuit whose output served to identify the beginning and the end of each tap. The
force of each tap was measured as the peak output voltage of a strain gauge that was
incorporated
into the key. All experimental
events were automatically
controlled by a
PDP-12 computer. For each response sequence we recorded the force of each tap, the
time during which the finger was in contact with the key (tap duration), the interval
between the end of one tap and the beginning of the next (lift interval), and the RT.
RT was measured as the delay between onset of the digit used as RS and onset of the
first tap.
A test was automatically performed on the measurements
to determine whether each
sequence had been executed correctly. If the number of taps was other than the number
indicated by the RS, the trial was classified as an error. All the erroneous trials in a
block were repeated once at the end of the block.
Subjects
and design
The subjects were 8 paid volunteers. All subjects participated
in three experimental
sessions. Session 1 was devoted to training for all subjects. The Cadence condition was
presented first. Fight series of trials were run following the simple RT (SRT) procedure. In the first, the digit 1 was presented in 9 successive trials. The following digits, in
ascending order, were presented in the same manner. Afterwards,
a choice RT (CRT)
block was run. It comprised 72 trials in which each digit from 1 to 8 was presented 9
times in a pseudo-random
order. After a rest period, the same SRT and CRT blocks
were run in the Speed condition.
Sessions 2 and 3 were each devoted to either the Cadence or the Speed condition.
The subjects were divided into two equal groups which performed the two conditions in
opposite order. The series of trials run were the same as in session 1, but there were two
CRT blocks of 72 trials each. Half of the subjects in each group started with the two
CRT blocks, followed by the eight SRT series, and the other half did the same in the
A. Garcia-Colera,A. Semjen / RT and sequence length
241
reverse order. The order of presentation of the eight SRT trial series was varied,
according to a latin square design, for each of the subjects.
Data analyses were conducted only on the data from sessions 2 and 3. The first trial
from each SRT series and the first eight from each CRT block were considered as
warm-up trials and, therefore, were not included in the computation of the individual
means.
Reaction time
The group means for SRT and CRT in the Cadence and Speed conditions are
shown in fig. 1 as a function of the number of taps in the sequence. The CRT means
are presented separately for each of the two CRT blocks. The individual mean CRTs
were subjected to a 2 x 2 X 8 analysis of variance (ANOVA) with the factors Timing
Condition (Cadence or Speed), Block (First and Second), and Number of Taps. The
effect of Block was significant, F&7) = 23.34, p < 0.01, indicating that CRT was
significantly shorter in the second than in the first block. No other effect was found
significant at the 0.05 probability level or better. The RT values observed in the SRT
condition and those from the second block in the CRT condition were subjected to a
2 x 2 x 8 ANOVA which tested the effects of Timing Condition, Block (SRT vs. CRT)
and Number of Taps. The only significant main effect was that of Block, I;(1,7) = 58.01,
REACTION
TIME
CADENCE
SPEED
,p.~ ...O--Q ..,,
o..o..o...o
250
p”‘0”
9
.‘b
.:’
SRT
O..d
6
i
200
_
12345676
12345670
NUMBER
Fig. 1. Mean RT in the
each timing condition.
OF TAPS
SRT and the two CRT blocks, as a function of the number of taps, for
242
A. Garcia-Colera, A. Semjen / RT and sequence length
p < 0.001, indicating that the CRT was significantly longer than the SRT. Significant
interactions were found between Timing Condition and Block, F(1,7) = 16.03, p < 0.01,
and between Number of Taps and Block, F(7,49) = 5.16, p < 0.001. The latter interaction denotes the fact that Number of Taps reached the significance level only in the
SRT condition, F(7,49) = 4.21, p < 0.01
Tests of linearity were performed on the SRT data for each timing condition
separately. The linear component was nonsignificant in the Speed condition, but it did
reach significance in the Cadence condition, F(1,7) = 5.96, p < 0.05. A closer inspection of the data suggested that the significant effect of sequence length in the SRT
condition was mainly due to the difference between one-tap and two-tap sequences in
the Speed condition, and between two- and three-tap sequences in the Cadence
condition. In the Cadence condition, SRT increased 17 msec from the two- to the
three-tap sequences, but only 11 msec from the three- to the eight-tap sequences. This
11 msec increase failed to reach significance, as shown by an additional test of linearity
(F&7) = 1.61). In the Speed condition, SRT increased 29 msec between the one-tap
and two-tap sequences, but only 14 msec from the two- to the seven-tap sequences.
Again, the linear trend in this 14 msec increase proved to be nonsignificant (F(1,7) =
1.93).
Sequence timing
The mean duration of the interval between the onset of a tap and the onset of a
subsequent tap in the sequence was calculated for each individual subject. Thus, these
interval measurements include the time during which the finger was in contact with the
key to produce a given tap (tap duration), plus the interval during which the finger was
raised between the end of a tap and the onset of the following one (lift interval). These
interval data for sequences from 2 to 8 taps were analyzed with seven separate
ANOVAs, one for each sequence length. The differences between the intervals produced in the SRT and CRT blocks proved to be nonsignificant in all of the analyses.
On the contrary, the effect of Timing Condition was significant in all of them. The
difference between the mean interval durations produced in the Cadence and Speed
conditions can be seen in fig. 2. Here the interval values are averaged over the SRT and
CRT blocks, and presented as a function of the number of taps in the sequence. The
mean interval in the Cadence condition barely increases as the number of taps in the
sequence increases, but a more pronounced augmentation is observed in the Speed
condition. This observation could seem to go in the direction predicted by the
Stemberg et al. model. However, a closer look at the origin of this effect affords a more
complete picture of the timing structure of these sequences that is not compatible with
such a model.
In table 1 are presented the mean interval durations as a function of the number of
taps in the sequence, and of the serial position of the intervals in each sequence. For all
sequences longer than three taps, the first interval was always longer than the second
and the last interval was always the longest. In the Cadence condition, the duration of
the intermediate intervals was very similar, with a trend for the interval next to the last
to be slightly longer than the intermediate ones. A different pattern appeared in the
Speed condition in which the intervals displayed a progressive lengthening from the
A. Garcia-Colera, A. Semjen / RT and sequence length
O-O
243
.0-.&o
.0-o
CADENCE
k
5
0
160 J
A
a
SPEED
I
234
567
NUMBER
6
OF TAPS
Fig. 2. Mean duration of the interval between taps’ onsets in sequences of 2 to 8 taps, for
timing condition.
Table 1
Mean interval duration (msec) in each timing condition as a function of the number of taps and
the serial position of the interval in the sequence.
Number
of taps
Serial position
1
2
3
4
5
6
I
Cadence
2
3
4
5
6
I
8
182
181
185
186
185
186
186
183
180
178
182
181
181
189
181
184
183
183
190
183
182
183
196
185
183
194
187
196
Speed
2
3
4
5
6
7
8
145
152
154
156
155
156
157
144
150
148
151
149
150
154
153
154
153
154
156
158
155
155
161
157
156
162
157
162
A. Garcia-Colera, A. Semjen / RT and sequence length
244
Table 2
Mean tap duration (msec) in each timing condition as a function of the number of taps and the
serial position of the taps in the sequence.
Number
of taps
Cadence
1
2
3
4
5
6
I
8
Speed
1
2
3
4
5
6
I
8
Serial position
1
2
3
4
5
6
7
8
14
65
66
63
65
61
62
61
61
60
54
53
54
53
51
69
55
55
54
54
53
63
55
53
53
51
60
55
54
52
59
54
52
58
51
55
65
54
50
49
49
50
48
65
51
50
49
48
48
58
48
49
48
41
51
48
48
41
55
41
48
52
48
54
IO
56
56
54
51
54
56
55
to the last. It must be noted that, whereas the difference between the second
and the last interval increased with sequence length, the variations in the duration of
the intervals in the same serial position were very small and did not show a systematic
increase with sequence length.
These observations indicate that the very slight increase in mean interval duration,
seen in fig. 2 for the Cadence condition, is mainly due to variations in the lengthening
of the last and of the next-to-last intervals. The sharper increase in mean interval
duration with sequence length, observed for the Speed condition, simply reflects the
progressive deceleration over the successive intervals within a sequence. Hence, in
neither condition did we observe an overall lengthening of each intertap interval as a
function of increasing sequence length, as should have occurred according to the
Stemberg et al. model.
To further look for possible effects of sequence length on the timing of the
successive elements, tap duration and lift intervals were also analyzed separately. The
mean tap duration values are presented in table 2 as a function of the number of taps
and of the taps’ serial position in each sequence. Overall, tap duration was a little
longer in the Cadence condition than in the Speed condition. In both conditions and
for all sequence lengths, the first and last taps were longer than the intermediate ones.
The duration of the intermediate taps was remarkably stable across sequence lengths
and serial positions. Given this pattern of tap durations, the lift intervals differed from
second
245
A. Garcia-Colera, A. Semjen / RT and sequence length
the whole intervals as presented above in that the first lift interval was not longer than
the intermediate ones. The lift intervals displayed, therefore, a more continuous
decelerating pattern from the first to the last tap, but, again, those sharing the same
serial position were not systematically lengthened across sequences of different length.
Force and error patterns
The mean force of the taps is presented in table 3 as a function of the number of
taps and of each tap’s serial position in a sequence. Overall, the taps were stronger in
the Speed condition than in the Cadence condition. In both conditions, the strongest
tap was the last one and the next strongest was the first one. In the Cadence condition,
force decreased from the first to the second tap, showed a slight increasing trend over
the successive taps, and a more abrupt increase from the next-to-last to the last tap. In
the Speed condition, the force level of the fist tap was always higher than the level of
the first tap in the Cadence condition. It decreased gradually from the first to the third
tap, where it approached the level of the third tap in the Cadence condition, then it
showed a small but progressive increase over the successive taps, and a much larger
increase on the last tap. The jump in force level from the next-to-last to the last tap was
much greater in the Speed than in the Cadence condition.
Table 3
Mean force (arbitrary units) in each timing condition as a function of the number of taps and the
serial position of the tap in the sequence.
Number
of taps
Serial position
1
2
3
4
5
6
1
8
141
128
126
124
129
122
128
121
142
119
115
113
112
109
107
143
123
120
111
115
114
150
127
111
115
110
154
117
119
112
140
120
110
142
114
136
162
149
139
141
145
143
147
138
162
137
130
127
130
132
125
149
125
117
121
119
108
173
127
124
125
117
178
130
129
120
182
139
125
172
126
176
Cadence
1
2
3
4
5
6
7
8
Speed
1
2
3
4
5
6
7
8
246
A. Garcia-Colera, A. Semjen
/ RT and sequence length
Table 4
Number of errors in each timing condition and trial block as a function of number of taps in the
sequence.
Number of taps
Total
1
2
3
4
5
6
I
8
Cadence
TRS
TRCl
TRC2
5
1
2
3
2
1
10
5
8
13
5
4
5
3
10
5
10
9
3
11
6
4
12
15
48
49
55
Speed
TRS
TRCl
TRC2
2
2
8
6
3
7
9
I
8
10
1
10
9
5
10
16
12
11
10
13
18
12
8
14
14
51
86
The subjects performed sequences with fewer or more taps than required in 9.9% of
the total number of trials. Over 80% of the errors were due to the execution of one tap
more or one tap less than the number required. The number of errors as a function of
Timing Condition, Trial Blocks and Number of taps, is presented in table 4. More
errors were committed in the Speed than in the Cadence condition. Most importantly,
the errors in the SRT condition did not increase systematically
as the required number
of taps increased from 3 to 7 or 8. Therefore, the lack of a significant linear trend in the
SRT increase over this range of taps cannot be accounted for by a trade-off between
speed of sequence initiation and precision of sequence execution.
Discussion
One of the aims of this experiment was to test whether the effects of
sequence length on RT and intertap intervals were those predicted by
the model of Sternberg et al. (1978). Differences were observed in the
timing of the successive taps as a function of the taps’ serial position.
However, for any interval in a given serial position no systematic
increase was observed as a function of sequence length. This observation agrees with the previously cited results of Hulstijn and Van Galen
(1983) and Stelmach et al. (1984). Rosenbaum et al. (1984a) also failed
to observe an effect of sequence length upon the timing of the responses beyond the first one.
The RT increased as a function of sequence length in the SRT
condition. However, the greatest increase occurred between 1 and 3
taps. Beyond 3 taps, the increase was very small and did not show a
A. Garcia-Colera, A. Semjen / RT and sequence length
241
significant linear trend. Although this result is contrary to the model
proposed by Sternberg et al. (1978), it is very close to their own
one-hand typing results which showed a large increase in RT when the
letters to be typed increased from 1 to 2, and a nonlinear and very
small further RT increase when the number of keystrokes augmented
from 2 to 5. The present results also resemble those obtained by Inhoff
et al. (1984: exp. 1) and Inhoff (1986: exp. l), who found a nonlinear
increase in RT when the number of elements increased from 1 to 3. It
must be noted that in several other studies that have reported an RT
lengthening as a function of the number of elements, the number tested
did not exceed 2 or 3 elements (Rosenbaum and Patashnik 1980;
Rosenbaum et al. 1984a,b). This seems therefore to be the range within
which the RT variations as a function of the number of elements are
strongest and can be most reliably reproduced.
The second aim of this experiment was to search for the maximum
number of elements that could be comprised in the advance planning
of sequences of repeated finger taps. At first glance, the breaking-point
observed in the SRT function when the number of taps equaled 2 or 3
could be considered as indicative of the upper limit of planning that we
had looked for. However, other studies have shown that the advance
planning of rapid movement sequences may extend up to 5 or 6
elements. In experiments in which subjects had to choose between
movement sequences that differed in the serial ordering of their constituents, RT was influenced by the characteristics of the last two
responses in a sequence of 5 or 6 button presses or taps (Inhoff et al.
1984: exp. 3; Semjen and Garcia-Colera 1986: exp. 4). In rapid speech
production, the capacity of the ‘program buffer’ has been estimated at
7 or 8 items, a value similar to the memory span (Monsell 1984). It
would be surprising if the storage capacity for simple repeated finger
taps was limited to only 2 or 3 items. Instead, the sharp SRT increase
between one and two or three taps may be interpreted as an index of
the basic difference between preparing for a single movement or having
to activate a sequence plan in which a beginning, an intermediate, and
a terminating element are to be coordinated and timed. The lack of a
further significant increase in RT for longer sequences would indicate
that adding intermediate elements to such a simple sequence does not
require additional processing operations before sequence initiation.
In this experiment, the difference between CRT and SRT was
relatively small for an 8-choice task, which may reflect the relative
248
A. Garcia-Colera, A. Semjen / RT and sequence length
simplicity of the plan selection process in the case of sequences of
repeated elements. The most striking aspect of the CRT data was,
however, the complete absence of any sequence length effect. Other
investigators have also reported a decrease or a total absence of
sequence length effects under the CRT paradigm, as compared to the
SRT paradigm (Klapp et al. 1979; Rosenbaum et al. 1984b; Inhoff
1986). The fact that in this study the CRT of a single tap was as long as
that of sequences of any length suggests that, in the context of
preparation for sequence production, the selection of a plan for a single
tap involves the same operations as the selection of any other plan.
Furthermore, the lack of an effect of sequence length over the whole
range of lengths tested suggests that the representation of the sequence
size was accessed in a single step rather than structured in a serial
fashion. Otherwise, longer sequences should have had longer CRT.
The timing and force data collected in this experiment lend support
to the hypothesis that the sequences were planned in advance, rather
than organized step-by-step in the course of their execution. A possible
division of the longer sequences into subunits was expected to appear
as a disruption in the timing of the taps at the transition from one
subunit to the next. Instead, a very stable timing pattern was observed
across sequences of different lengths. This pattern was characterized by
a lengthening of the first and last intervals with respect to the intermediate ones, and a trend for progressive deceleration from the second
to the last interval, particularly in the Speed condition. Such deceleration can be interpreted as a preparation for the stop, which probably
poses a greater difficulty in this faster condition than in the Cadence
condition. This is a further indication that the sequence end was
anticipated at least several steps before its actual execution.
The lengthening of the intervals at the beginning and the end of
movement sequences has been systematically observed by us in sequences of 4 to 5 taps (Semjen et al. 1984; Semjen and Garcia-Colera
1986), as well as by other authors in different experimental situations
(Povel 1977; Shaffer et al. 1985). It has been interpreted as a characteristic of ‘coherent sequences’ that constitute a perceptual-motor unit. In
the present experiment, the lengthening of the intervals at the sequence
boundaries was also accompanied by a longer duration of the first and
last taps, and a stronger force on these same taps. The fact that none of
these ‘boundary markers’ was observed for any of the intermediate
taps, even in sequences of up to eight taps, gives further support to the
A. Garcia-Colera, A. Semjen
/ RT and sequence length
249
conclusion that the tapping sequences were organized as single units of
performance.
This conclusion, together with the failure to observe the main effects
predicted by the subprogram
retrieval model (Stemberg
et al. 1978),
lead us to question the general validity of this model. Even from a
logical standpoint,
it is not clear why a buffer should be searched to
find the subprogram
corresponding
to the element to be performed
next, when such element is the same throughout the sequence.
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