Concatenating familiar movement sequences: the versatile cognitive processor

Acta Psychologica 106 (2001) 69±95

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Concatenating familiar movement sequences: the versatile cognitive processor Willem B. Verwey

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Institut fur Arbeitsphysiologie an der Universit at Dortmund, Ardeystraûe 67, D-44139 Dortmund, Germany Received 6 November 1998; accepted 4 June 1999

Abstract Earlier studies demonstrated that practicing a series of key presses in a ®xed order yields memory representations (i.e., motor chunks) that can be selected and used for sequence execution as if familiar key pressing sequences are single responses. In order to examine whether these motor chunks are robust in di€erent situations and whether preparation for one sequence may overlap with execution of another one, two experiments were carried out in which participants executed two highly practiced keying sequences in rapid succession in response to two simultaneously presented stimuli. The results con®rmed robustness of motor chunks, even when the sequences included only two elements, and showed that preparation (and in particular, selection) of a forthcoming sequence may occur during execution of the earlier sequence. Sequences including only two keys appeared to be slowed more by concurrent preparation than longer sequences. Together these results suggest that the execution of familiar keying sequences is predominantly carried out by a dedicated motor processor, and that the cognitive processor can be allocated to preparing a forthcoming sequence (e.g., during execution of an earlier sequence) or, some times, to selecting individual sequence elements in parallel to the motor processor. Ó 2001 Elsevier Science B.V. All rights reserved. PsycINFO classi®cation: 2330; 2340 Keywords: Motor skills; Sequential learning; Perceptual motor learning

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Tel.: +49-231-1084-313; fax: +49-231-1084-340. E-mail address: [email protected] (W.B. Verwey).

0001-6918/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 1 - 6 9 1 8 ( 0 0 ) 0 0 0 2 7 - 5

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1. Introduction This article has been written on the occasion of the retirement of professor Andries F. Sanders. One of the main themes in his work was disentangling the processing stages used in choice RT tasks, the merits of which should ``make sense beyond the realm of additive factor application'' in order to ``advance performance theory'' (Gopher & Sanders, 1984, p. 250). Based on a long line of research, Sanders (1980, 1990) proposed a model in which it is assumed that information processing in choice RT tasks involves six successive stages. In the present article, I shall extend SandersÕs line of thinking by reporting indications that the response selection and motor processing stages he proposed, may be carried out by two independent processors that can be active simultaneously. Let me start o€ by noticing that much of our daily life involves the virtually automatic production of series of actions. Intelligent, goal directed behavior would be impossible if we would continuously be engaged in controlling every minute aspect of our behavior. Several researchers have argued that we are capable of skilled action because, with extensive practice, behavioral sequences, such as pronouncing phonemes, writing letters, and typing short words are executed to an increasing degree as if they were single movements (e.g., Fowler, 1985; van Galen, 1991; Inho€, 1991). Elsewhere, I called these sequence-speci®c memory representations, motor chunks (Verwey, 1994). The availability of motor chunks would eliminate the need to select each element in a familiar keying sequence in a demanding and slow manner. The present article investigates, ®rst, the merits of the motor chunking concept in a situation that two familiar keying sequences are carried out in rapid succession. One possibility is that when familiar movement sequences are part of a longer behavioral sequence, the original motor chunks are still used for sequence control. In line with some older ideas, this would imply that familiar movement sequences constitute Ôbuilding blocksÕ of behavior (e.g., Eysenck & Frith, 1977; Gallistel, 1980; Paillard, 1960). Before the notion can be accepted that motor chunks underlie these building blocks of skilled behavior, there is a need to con®rm that motor chunks are robust in the sense that they can also be used in di€erent situations than the one they were practiced in. Alternatively, a new organization could develop and successive familiar sequences could be produced as a single, new sequence. This is especially likely when two successive sequences are short so that the elements of both sequences could be easily prepared together (Sternberg Monsell, Knoll & Wright, 1978; Verwey, 1996). In an earlier study, I reported how participants in a practice phase cycled through a series of nine key presses (Verwey, 1996). This series included a ®xed order of keys and participants were forced to wait for a relatively long time at two or three positions in the sequence. Subsequently, they were required to cycle through the sequence at maximum speed, that is, without waiting at any position. The results showed that even at maximum speed, the interkey intervals at the positions where the pauses used to be, were much longer than the remaining interkey intervals. I argued that during practice, the pauses had separated the sequences in parts, and that for each part a di€erent motor chunk had developed. Executing the sequence at maxi-

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mum rate forced participants to prepare the ensuing motor chunk at the positions in the sequence where they used to pause during practice. In the present study, I focus on a second ®nding in Verwey (1996), also see Verwey and Dronkert (1996): it turned out that execution rate of each sequence part between pauses had slowed too. This was attributed to the fact that at least part of the preparation of an oncoming sequence, overlapped with the execution of the preceding one. This was not unexpected as it is in line with other ®ndings that preparation of the forthcoming movement slows down the execution rate of the ongoing movements (e.g., Brown, McDonald, Brown, & Carr, 1988; Portier, van Galen & Meulenbroek, 1990). However, in another study, I found that when participants selected a key press during execution of a familiar keying sequence, execution rate was not a€ected by the compatibility of the imperative stimulus and the associated key press that immediately followed the familiar keying sequence (Verwey, 1995). How can we explain that the mere presence of concurrent preparation slows ongoing execution while the demands of concurrent preparation do not? The common explanation for interference between concurrent processes is that preparatory and motor processes tap the same limited processing resource (e.g., Kahneman, 1973). This was actually the explanation I advanced (Verwey, 1996), but in Verwey (1995), I had explained the ®nding that manipulation of response selection demands did not a€ect sequence execution by the notion that execution and preparation (in terms of selection) tap di€erent resources (e.g., Wickens, 1984). Obviously, it is unsatisfactory to assume a single-resource model for the comparison of execution with and without concurrent preparation, and a multiple-resource model for the situation in which the demands of concurrent preparation are manipulated. Therefore, a second purpose of this study is developing an alternative for the resource interpretation of slowed sequence execution. In line with various other models, I would like to propose that there are two di€erent processors, a cognitive and a motor processor (or system; e.g., Allport, 1980; MacKay, 1982; Pew, 1966; Schmidt, 1988). For example, Sha€er (1991) argued that skilled action ``is arranged at two levels in the brain, (a) in a cognitive system which plans and represents (symbolically) a goal structure of action, and (b) in a motor system with organizes movements appropriate to the goal'' (p. 372). An unfamiliar movement sequence would be controlled by a cognitive processor selecting individual sequence elements on the basis of a symbolic representation. A familiar movement sequence would be controlled by the cognitive processor in that it selects a single representation ± a motor chunk ± for the entire sequence which is subsequently read and executed by a dedicated motor processor. Compared to the production of unfamiliar sequences, this then reduces processing load on the cognitive processor. If an additional assumption is made, then this dual-processor model can explain why familiar sequences are slowed by concurrent preparation and not by the demands of concurrent preparation. The assumption is that when participants are asked to generate a single, familiar keying sequence as fast as they can (which is usually what they are instructed to do), they will have the cognitive and the motor processors operate in parallel in selecting the individual sequence elements. That is, the two processors will both produce the same information needed for executing an

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element in the sequence. On a particular trial, the processor providing its output ®rst determines reaction time. Obviously, the cognitive processor is able to execute sequence elements as it had done so in early practice too. This notion stresses the versatility of the cognitive processor for, in case of familiar movement sequences, it may support the motor processor in producing the sequence elements and it may be allocated to other tasks. Of course, parallel operation of the cognitive and motor processors is likely only if it will actually speed up sequence execution. It appears that when the time taken by the cognitive and motor processors to produce their output is distributed and the distributions of both processors overlap, the average time to execute a single sequence element will reduce. This has been named statistical facilitation (Raab, 1962). In other words, execution rate will increase when two processors operate in parallel even when, on the average, one is slower than the other. The ®nding that execution rate was reduced by concurrent preparation, as compared to the condition without concurrent preparation (Verwey, 1996), can now be explained in terms of the cognitive processor being allocated to preparing the forthcoming sequence and, hence, being withdrawn from (assisting the motor processor with) sequence execution. The absence of an e€ect of the demands of concurrent preparation on execution rate (Verwey, 1995), is then explained by the notion that, once the cognitive processor had been allocated to another task, the actual demands placed upon the cognitive processor do not a€ect execution as execution was already controlled by the motor processor alone. In my view, the strength of this dual-processor model is not only that it provides an explanation for the e€ects of concurrent preparation on sequence execution, but also that it is in line with the parallel architecture of the brain (see Section 4). As interpretation of the execution rate e€ects in terms of the dual-processor model is still speculative at present, the purpose of the present study is testing some of its assumptions. First, it examines whether motor chunks are used also when two familiar sequences are executed in rapid succession. Next, it examines if preparation for one keying sequence overlaps with execution of the preceding keying sequence. Finally, it tests whether preparing a forthcoming sequence during execution of an earlier sequence, slows execution of the earlier sequence while the demands of concurrent preparation do not a€ect execution of the earlier sequence. 2. Experiment 1 The theoretical questions about chunk robustness and concurrent processing bring up the issue of how chunk robustness can be measured at all? Sternberg, Monsell, Knoll and Wright (1990) discussed a number of performance features that might indicate the use of chunks. Three of them are directly relevant for the present experiments: (a) Temporal grouping means that interkey intervals are shorter within familiar sequences than between successive familiar sequences. This feature has indicated chunk robustness with keying sequences in earlier studies (Verwey, 1996; Verwey & Dronkert, 1996, see Sternberg et al., 1990 for more references) and will be

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considered the prime indicator for chunk robustness. Two other features are the following: (b) Temporal structure refers to the observation that interkey intervals at di€erent positions within a sequence often di€er (e.g., Brown & Carr, 1989; Verwey, 1995). Robust motor chunks may be characterized by preservation of temporal structure (Sha€er, 1991). (c) Higher correlations of pairs of interkey intervals belonging to one as opposed to two familiar sequences, might also indicate motor chunk use (Schneider & Schmidt, 1995; Young & Schmidt, 1990). Two features that are not mentioned by Sternberg et al. (1990) and that might also indicate chunking in sequential keying tasks are (d) preservation of ¯uency denoting that the duration of familiar sequences is context independent and (e) preservation of the sequence length e€ect indicating that the sequence length e€ect on the average within-sequence interkey interval (WSIKI; e.g., Sternberg et al., 1978; Verwey, 1999) is found also if familiar sequences are carried out in a di€erent context. How can concurrent preparation be demonstrated? On basis of earlier experiments with keying sequences (Verwey, 1996; Verwey & Dronkert, 1996), the prime indicator for concurrent processing in various studies is (a) execution rate of a sequence, which is usually slowed if preparation for a forthcoming sequence overlaps with execution of that sequence. A second potential indicator for concurrent preparation is (b) the latency of the second sequence, which may be shorter as the preceding sequence is longer because preparation overlaps more with the preceding sequence. The third feature relates to the ®nding that reversing consistently practiced stimulus-sequence mappings, increases sequence latency substantially (Verwey, 1999). This suggests that (c) when the mapping of the second sequence is reversed and the stimulus to the second sequence is presented in advance of the ®rst sequence, a reduced reversal e€ect in the latency of the second sequence should be found in case of concurrent preparation, as compared to a single-sequence control condition. This manipulation also served to increase preparatory demands. Experiment 1 included three phases. In the ®rst phase, participants were familiarized with producing three keying sequences of two, three, and four key presses in response to a sequence-speci®c stimulus. In this phase, each key in the sequence was indicated by a key-speci®c cue. In a second practice phase, the participants learned producing these sequences (a) without key-speci®c cues, (b) responding with reversed stimulus-sequence mappings, and (c) producing sequences immediately following a so-called presequence. This presequence was included to prevent any advance preparation, which might conceal e€ects of practice (Verwey, 1996, 1999). It also made the task more realistically because preparation is often not possible in realworld tasks. Finally, in the third phase, which was the transfer phase, participants produced two of the three keying sequences in rapid succession in response to two simultaneously presented sequence-speci®c stimuli. This was the dual-sequence condition, which also included presequences, normal and reversed stimulus-sequence mappings, and no key-speci®c cues. This phase occasionally included production of one familiar sequence, which was the single-sequence control condition. So, Experiment 1 examined chunk robustness and e€ects of concurrent preparation. Temporal grouping and execution rate of the ®rst sequence were the prime indicators for chunk robustness and concurrent preparation, but the merits of some

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other potential indicators were assessed as well. Note that even though chunk robustness and concurrent preparation both predict an increase of interkey intervals, the predicted e€ects are clearly di€erent: chunk robustness would be indicated by a relatively long initiation latency of the second sequence and concurrent preparation would a€ect the execution rate of the ®rst sequence. Finally, the prediction that execution will slow down by concurrent preparation but not by increasing preparatory demands, was tested by examining the e€ect of reversing highly practiced stimulus-sequence mappings. 2.1. Method 2.1.1. Participants Nine students from the university of Dortmund served as participants. They were seven males and two females between 20 and 33 yr of age. They were paid 165 DM (approx. 85 ) for participation and the best three received a bonus of 25 DM (approx. 13 ). 2.1.2. Task Participants positioned the left little, ring, middle, and index ®nger on the y, d, f, g keys of a German PC keyboard, and the right thumb, index, middle, ring, and little ®nger on the space bar, and on the j, k, l, and - keys, respectively (German keyboards have reversed positions for y and z, and for - and / keys). These assignments were chosen such that each ®nger could easily press a di€erent key. The computer screen displayed bright green outlines of nine squares on a black background in the same spatial arrangement as the assigned keys. The outlines of nine squares remained visible during the entire block. Each practice trial started with presentation of a green Ô+Õ as ®xation symbol (see upper part of Fig. 1). After 1.5 s, the ®xation symbol was replaced by one of the three sequence-speci®c stimuli. After 300 ms, this was followed by the ®rst key-speci®c cue (S1 ), which involved ®lling one of the squares with green. The spatially corresponding key (R1 ) was depressed in response to this key-speci®c cue. Immediately after depressing this key, the content of the square became black again. Then the next square (S2 ) was switched on and the spatially corresponding key depressed (R2 ), and so on. The sequence-speci®c stimulus was erased only after the entire sequence had been produced. Each participant practiced a 2-, a 3-, and a 4-key sequence. For example, one participant produced Ô)JÕ in response to Ô7Õ, ÔDKÕ in response to Ô8Õ, and ÔGLYFÕ to Ô9Õ. Basically, the same sequences were carried out by all the participants. However, to prevent latencies and interkey intervals from being a€ected by ®ngerspeci®c e€ects, the keys were balanced across ®ngers for individual participants so that, across participants, each of the nine ®ngers contributed equally to each latency and interval in the sequences. Likewise, stimuli were always Ô7Õ, Ô8Õ, and Ô9Õ, but these were counterbalanced across sequence lengths. For example, a second participant produced ÔKÕ to Ô8Õ, ÔFLYÕ to Ô9Õ and ÔJ-DGÕ to Ô7Õ. Each of the nine keys

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Fig. 1. Events and intervals in a trial with a 2-key pressing sequence in the ®rst practice phase of Experiment 1 (upper part) and in the transfer phase (lower part). In the ®rst practice phase, `+' indicates the ®xation character, Sseq:-spec: is the sequence-speci®c stimulus, and S1 and S2 are key-speci®c cues. R1 and R2 denote key presses that belong to the 2-key sequence. In the transfer phase, Spn-1 and Spn are presequence stimuli indicating responses Rpn -1 and Rpn . Sseq:-spec:A and Sseq:-spec:B denote sequence-speci®c stimuli. Keyspeci®c cues were not presented in the transfer phase. The small o€sets between responses and subsequent key-speci®c cues and presequence stimuli indicate that key-speci®c cues and stimuli are presented immediately following the preceding response.

occurred once in the three sequences so each sequence contained only unique transitions between successive keys (cf. Cohen, Ivry & Keele, 1990). The task was slightly changed in the second practice phase. Each trial in this phase started with four to eight keys presses in random order (Rpnÿ2 , Rpnÿ1 and Rpn in the lower part of Fig. 1), this was called the presequence. These keys were indicated by white ®llings of the green squares on the display (Spnÿ1 and Spn ). Following this presequence, the sequence-speci®c stimulus was presented, but key-speci®c cues for the individual key presses were no longer displayed. In the third or fourth session of this phase, stimulus-sequence mappings of 2- and 4-key sequences were reversed. The mapping of the 3-key sequence was never changed. Finally, in the transfer phase participants executed either one familiar sequence or two familiar sequences in rapid succession in the single-sequence and dual-sequence conditions. The single-sequence condition included the three familiar sequences executed alone (A2 , A3 , A4 ; A standing for ÔaloneÕ and subscripts indicating sequence length, see Section 2.2 for a more extensive description of the abbreviations used). The dual-sequence condition involved the six combinations of familiar sequences (F2 S3 , F2 S4 , F3 S2 , F3 S4 , F4 S2 , and F4 S3 , F and S denoting Ô®rstÕ and ÔsecondÕ, respectively). Single- and dual-sequence conditions were mixed in the transfer phase. Each trial started with a presequence that was immediately followed by one sequence-speci®c stimulus in the single-sequence condition and two sequence-speci®c stimuli presented side by side in the dual-sequence condition (see lower part of Fig. 1). The sequence indicated by the left-hand sequence-speci®c stimulus was executed ®rst, followed by the sequence indicated by the right-hand stimulus (if present). Again, key-speci®c cues were not presented. This phase included two

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normal mapping sessions and two sessions with reversed stimulus-sequence mappings of the 2- and 4-key sequences. 2.1.3. Procedure Participants received a written instruction that was extended by oral explanation. They were asked to respond as rapidly as possible to the key-speci®c cues. They were told that they would receive a score at the end of each block that would show their performance, and that the best three out of nine participants would earn a bonus. After the ®rst two sessions, the experimenter urged all participants to take note of the sequence-speci®c stimulus, and not only to respond to the key-speci®c cues because they would later have to produce the sequences on basis of that stimulus alone. Participants worked in two alternating groups of two or three, each participant on one of three computers. Each participant carried out six 208-trial practice sessions on Day 1 and two such sessions on Day 2. Each session in this and other phases included a 22-s pause in the middle. The remaining four sessions on Day 2 involved the second practice phase (presequence, no key-speci®c cues). Each session in this second practice phase consisted of 128 trials. Three of these sessions involved normal stimulus-sequence mappings. In the third or fourth session mappings of the 2- and 4-key sequences were reversed. Day 3 started with a normal 208-trial practice session (i.e., key-speci®c cues, no presequence, normal stimulus-sequence mappings). This session was followed by ®ve dual-sequence transfer sessions, each including 108 trials. The ®rst of these sessions was considered practice, the second through ®fth sessions were the sessions of experimental interest. For half of the participants the second and fourth dual-sequence sessions had normal mappings whereas mappings of the 2- and 4-key sequences were reversed in the third and ®fth dual-sequence sessions. For the remaining participants, the order of normal and reversed mapping sessions was reversed. Each block was followed by a performance score which ranged from 0 to 100 points. Given that performance improvement obeys a power law (Newell & Rosenbloom, 1981), the score was determined with a logarithmic function so that late in practice, a relatively small improvement still yielded a perceivable increase: Score ˆ 130 + 70 ´ ln (50/((Duration/2) + 20 ´ Error), where Error ˆ 6 ) Error if Error < 3. Total sequence Duration was expressed in milliseconds and Error in percent. The formula shows that the accuracy a€ected scoring in that each deviation in error percentage from three equaled 20 ms slower responding. Participants were not informed of this procedure. To prevent cautious and therefore slow key pressing, error rates of less than 3% evoked the instruction to increase keying speed (unless the average RT per key was below 150 ms, which was exceptionally fast). 2.1.4. Apparatus The experiment was conducted on three MSDOS computers (80386SX, 40 MHz, Head Computers) with M77 (S.A.M. Computers) color VGA monitors. Stimulus presentation and response registration were controlled through micro-experimental laboratory software (MEL version 2.0; see e.g., Schneider, Zuccolotto & Tirone,

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1993). This software package is specially developed for running PC-based timecritical psychological experiments. At a typical viewing distance of about 65 cm, a square subtended a visual angle of approximately 1°. Visual angle of the sequence-speci®c stimuli was about 0.5° and the visual angle between both sequence-speci®c stimuli in the dual-sequence condition was about 0.8° so that both could easily be observed in a single ®xation. The stimuli were viewed under normal room illumination. The response keys were part of a normal AT-like keyboard (BTC). Input delays as measured by MEL ranged between 10.6 and 13.4 ms for the keys used. Although MEL can measure time with 1-ms precision by reprogramming the internal timer chip, variances caused by keyboard delays were found to add approximately 19 ms to the error variance which, given the large number of trials in the present study, is considered acceptable (Segalowitz & Graves, 1990). Three participants performed simultaneously on computers that were separated by wooden barriers, which prevented the participants from seeing each other. There they sat in front of a table on which the keyboard and a computer monitor were positioned. Participants were monitored by the experimenter through a closed video circuit. 2.2. Results of Experiment 1 In order to distinguish the various conditions and the interkey intervals, the following notations and terms will be used. In the transfer phase, the latency of the ®rst sequence is the time between onset of the sequence-speci®c stimulus and the ®rst key press (T1 in Fig. 1, lower part). Latency of the second sequence refers to the time between depressing the last key of the ®rst sequence and the ®rst key of the second sequence. Sequences in the normal mapping condition that are executed alone are denoted by ANn where n indicates the length of the sequence (i.e., AN2 , AN3 , and AN4 ). In the reversal condition, these sequences are denoted by ARn . Pooled across both the mapping conditions, and in Experiment 2, sequences are referred to as An . The ®rst and second sequences in the dual-sequence condition are called Fn (or FNn or FRn ) and Sn (or SNn or SRn ). Speci®c interkey intervals are indicated by a second subscript showing the intervalÕs position within the familiar sequence, for example, S41 (and SN41 and SR41 ) indicates the latency of a sequence in second position with length four. Average WSIKI of a sequence is referred to as, for instance, AN3WSIKI . Finally, speci®c sequence combinations are denoted by two letters plus subscripts indicating the length, e.g., F2 S4 or, when only the second of this combination is meant, …F2 †S4 . Analyses of the latencies and WSIKIs in the dual-sequence transfer phase were carried out on averages per participant, session, sequence, stimulus-sequence mapping and, sometimes, key position within the sequence. The ®rst four trials of each block and trials with errors were excluded from the interval analyses. Sequences were counted as error and not included in the analyses if they included depression of an inappropriate key, if they were followed by an illegal key press within 500 ms, or if

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an interkey interval exceeded 4 s. The data were analyzed with within-participant designs. Notice that the results of the transfer phase generally showed no Session e€ects. 2.2.1. Robustness: temporal grouping Table 1 gives an overview of the main results in the transfer phase. It shows that latencies of the second sequence in the dual-sequence condition were larger than WSIKIs of the ®rst and second sequences. These di€erences appeared as a highly signi®cant Part main e€ect in a Part (3: FnWSIKI ; Sn1 ; SnWSIKI ) ´ Mapping (2: normal, reversed) ´ Sequence_Combination (6: F2 S3 , F2 S4 , F3 S2 , F3 S4 , F4 S2 , F4 S3 ) ´ Session (2) ANOVA [F …2; 16† ˆ 159:9, P < 0.001]. Planned comparisons of Sn1 versus FnWSIKI =SnWSIKI con®rmed that this main e€ect was caused by the di€erence between WSIKIs of both sequences and latency of the second sequence [F …1; 8† ˆ 161:6, P < 0.001]. 2.2.2. Robustness: preservation of ¯uency A Length (3: 2, 3, 4) ´ Context (5) ´ Mapping (2) ´ Session (2) ANOVA was carried out on average WSIKI with the following Context levels: alone (i.e., A2 , A3 , A4 ), Table 1 Latency and average WSIKIs for the normal (upper half) and reversal (lower half) mapping conditions in Experiment 1 Alone, ®rst sequence

Second sequence

Latency

Average WSIKI

Latency

Average WSIKI

2-key

AN2 : 852 ms FN2 …SN3 †: 967 ms FN2 …SN4 †: 998 ms

AN2 : 104 ms FN2 …SN3 †: 133 ms FN2 …SN4 †: 132 ms

…FN3 †SN2 : 425 ms …FN4 †SN2 : 446 ms

…FN3 †SN2 : 120 ms …FN4 †SN2 : 115 ms

3-key

AN3 : 935 ms FN3 …SN2 †: 1012 ms FN3 …SN4 †: 1005 ms

AN3 : 137 ms FN3 …SN2 †: 156 ms FN3 …SN4 †: 154 ms

…FN2 †SN3 : 495 ms …FN4 †SN3 : 547 ms

…FN2 †SN3 : 134 ms …FN4 †SN3 :152 ms

4-key

AN4 : 912 ms FN4 …SN2 †: 965 ms FN4 …SN3 †: 963 ms

AN4 : 139 ms FN4 …SN2 †: 146 ms FN4 …SN3 †: 146 ms

…FN2 †SN4 : 477 ms …FN3 †SN4 : 477 ms

…FN2 †SN4 : 138 ms …FN3 †SN4 : 151 ms

2-key

AR2 : 1126 ms FR2 …SN3 †: 1201 ms FR2 …SR4 †: 1181 ms

AR2 : 110 ms FR2 …SN3 †: 148 ms FR2 …SR4 †: 146 ms

…FN3 †SR2 : 562 ms …FR4 †SR2 : 514 ms

…FN3 †SR2 : 125 ms …FR4 †SR2 : 125 ms

3-key

AN3 : 971 ms FN3 …SR2 †: 1048 ms FN3 …SR4 †: 1047 ms

AN3 : 141 ms FN3 …SR2 †: 163 ms FN3 …SR4 †: 164 ms

…FR2 †SN3 : 474 ms …FR4 †SN3 : 547 ms

…FR2 †SN3 : 140 ms (FR4 )SN3 : 160 ms

4-key

AR4 : 1134 ms FR4 …SR2 †: 1196 ms FR4 …SN3 †: 1181 ms

AR4 : 147 ms FR4 …SR2 †: 158 ms FR4 …SN3 †: 159 ms

…FR2 †SR4 : 548 ms …FN3 †SR4 : 652 ms

…FR2 †SR4 : 150 ms …FN3 †SR4 : 154 ms

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preceding the shortest of the two alternative sequences [F2 …S3 †; F3 …S2 †; F4 …S2 †], preceding the longest of the alternative sequences [F2 …S4 †; F3 …S4 †; F4 …S3 †], following the shortest of the alternative sequences […F3 †S2 ; …F2 †S3 ; …F3 †S4 ], and following the longest of the alternative sequences […F4 †S2 ; …F4 †S3 ; …F2 †S4 ]. This ANOVA showed that Context had an e€ect on WSIKI [Fig. 2; F …4; 32† ˆ 13:2, P < 0.001]. Planned comparisons con®rmed that sequences were generally carried out more slowly in the dual-sequence than in the single-sequence condition [F …1; 8† ˆ 16:7, P < 0.01] and that sequences executed ®rst were slowed more than those in second position [slowing relative to single-sequence condition: 20 versus 9 ms; F …1; 8† ˆ 10:7, P ˆ 0.01]. 2.2.3. Robustness: preservation of sequence length e€ect An initial Length (3) ´ Mapping (2) ´ Session (2) ANOVA on the single-sequence (ÔaloneÕ) condition con®rmed the expected sequence length e€ect on WSIKI [Fig. 2; F …2; 16† ˆ 4:3, P < 0.05]. Planned comparisons indicated that this e€ect was caused solely by the di€erence between 2-key sequences on the one hand and the 3- and 4-key sequences on the other hand [Fig. 2; A2WSIKI versus A3WSIKI and A4WSIKI : F …1; 8† ˆ 8:5, P < 0.05; A3WSIKI versus A4WSIKI : F …1; 8† ˆ 0:1, P > 0.20]. According to a planned comparison that followed a Length (3) ´ Context [5: AnWSIKI ; FnWSIKI …Sshorter †; FnWSIKI …Slonger †; …Fshorter †SnWSIKI ; …Flonger †SnWSIKI Š ´ Mapping (2) ´ Session (2) ANOVA, the di€erence between 2- and 3-/4-key sequences was larger in the single- than in the dual-sequence condition [single-sequence condition: 34 ms, dual-sequence condition: 21 ms; F …1; 8† ˆ 12:2, P < 0.01]. Additional planned comparisons showed that the WSIKI di€erence between 2- and 3-/4-key sequences reached signi®cance for the second sequence, but not for the ®rst sequence [121 versus 147 ms, F …1; 8† ˆ 8:6, P < 0.05; 140 versus 156 ms, F …1; 8† ˆ 0:9, P > 0.20, respectively]. This distinction, however, did not reach signi®cance [F …1; 8† ˆ 1:1, P > 0.20].

Fig. 2. Average WSIKIs as a function of sequence length pooled over normal and reversal mapping conditions in Experiment 1.

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Fig. 3. WSIKIs as a function of position, context, mapping, and sequence length in Experiment 1.

2.2.4. Robustness: preservation of temporal structure Fig. 3 shows that, in general, 3- and 4-key sequences were carried out with increasing rates. However, Key (2/3) ´ Context (5) ´ Mapping (2) ´ Session (2) ANOVAs did not show signi®cant Key main e€ects or interactions with Key [3-key: F …1; 8† ˆ 0:1; 4-key: F …2; 16† ˆ 0:7, P > 0.20]. Moreover, temporal structure was not the same in all dual-sequence conditions: In FN3 …SN2 †; FR3 …SR2 †; …FN2 †SN4 , and …FR2 †; SR4 , the ®rst WSIKI was shorter than the second, rather than larger. 2.2.5. Robustness: correlations between individual elements On the assumption that correlations between WSIKIs should be higher with intervals within a familiar sequence than between successive sequences, correlations were computed on basis of the raw data, per participant, between each pair of successive interkey intervals. Correlations between WSIKIs were compared in F2 S4 , F3 S4 , F4 S2 , and F4 S3 . These correlations were based on pairs of WSIKIs with one intermediate interval (e.g., in F2 S4 : between-sequence WSIKIs F22 and S42 , withinsequence WSIKIs S42 and S44 ). A Within_Between (2) ´ Mapping (2) ´ Sequence_Combination (6: F2 S3 , F2 S4 , F3 S2 , F3 S4 , F4 S2 , F4 S3 ) ANOVA showed that correlations within and between familiar sequences did not di€er signi®cantly [within: r ˆ 0.20; between: r ˆ .08; F …2; 8† ˆ 2:6, P > 0.10]. 2.2.6. Concurrent processing: ®rst sequence Planned comparison following a Context [3: An1 ; Fn1 …Sshorter †; Fn1 …Slonger †] ´ Length (3) ´ Mapping (2) ´ Session (2) ANOVA on latencies of the ®rst sequences, showed that these latencies were longest in the dual-sequence condition [An1 : 900 ms, Fn1 : 985 ms; F …1; 8† ˆ 83:8, P < 0.001]. This dual-sequence e€ect did not interact with

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length of the ®rst or second sequence [F …2; 16† ˆ 1:7, P > 0.20; F …1; 8† ˆ 0:1, P > 0.20] (nor with mapping, see below) and may have been caused by increased perceptual load or by preparing dual-sequence control. Average WSIKI was also larger in the dual- than in the single-sequence condition [150 versus 130 ms; F …1; 8† ˆ 18:9, P < 0.01]. Relative to the single-sequence condition shorter sequences were slowed more than longer ones [2-key: 33 ms, 3-key: 20 ms, 4-key: 9 ms; F …2; 16† ˆ 7:7, P < 0.01]. 2.2.7. Concurrent processing: second sequence Planned comparison following the Context [3: An1 ; …Fshorter †Sn1 ; …Flonger †Sn1 ] ´ Length (3) ´ Mapping (2) ´ Session (2) ANOVA showed that latencies of the second sequences were much smaller than in the single-sequence condition [514 ms versus 988 ms; F …1; 8† ˆ 368:1, P < 0.001]. These latencies were not a€ected by the sizes of the ®rst [F …2; 16† ˆ 2:2, P > 0.10] and second sequences [F …2; 16† ˆ 1:7, P > 0.20]. As evidenced by longer WSIKIs, the sequences in second position were executed more slowly than in the single-sequence condition, but the di€erence was small [AnWSIKI : 130 ms, SnWSIKI : 139 ms, F …1; 8† ˆ 7:8, P < 0.05]. This e€ect was caused mainly by the 2-key sequence [15 ms, F …1; 8† ˆ 10:6, P < 0.05] and was not statistically signi®cant with both other sequences [6 ms; F …1; 8† ˆ 1:7, 2.7, P > 0.13]. However, this di€erence between sequences was not supported by a signi®cant Length ´ Context interaction [F …1; 8† ˆ 2:6, P > 0.10]. Further planned comparisons showed that WSIKIs of sequences in the second position were still faster than those in ®rst position [F …1; 8† ˆ 10:7, P < 0.05]. 2.2.8. Concurrent processing: mapping reversal As mappings of the 3-key sequences were never reversed, there was no signi®cant reversal e€ect of 3-key sequences in the single- [F …1; 8† ˆ 2:8, P > 0.10] and dualsequence conditions [®rst sequence: F …1; 8† ˆ 2:7, P > 0.13; second sequence: F …1; 8† ˆ 0:0, P > 0.20]. Therefore, separate analyses were carried out on the second sequence of the combinations with two reversed mappings [i.e., …FR2 †SR4 and …FR4 †SR2 : consistent R-mapping] and those with one reversed mapping […FN3 †SR2 and …FN3 †SR4 : mixed R-mapping]. A Context [2: An1 ; Sn1 ] ´ Length (2: 2-, 4-key) ´ Mapping (2) ´ Session (2) ANOVA on the latencies in the consistent R-mapping condition showed that the reversal e€ect in the second sequenceÕs latency was substantially smaller than in the single-sequence latency [70 versus 248 ms; F …1; 8† ˆ 40:0, P < 0.001]. This was also found in the mixed R-mapping condition with a Context (2: An1 ; Sn1 ) ´ Length (2: 2-, 4-key) ´ Mapping (2) ´ Session (2) ANOVA [156 versus 248 ms; F …1; 8† ˆ 10:7, P ˆ 0.01]. The reversal e€ect in the latency of the second sequence was smaller in the consistent than in the mixed R-mapping sequence combination [70 versus 156 ms; F …1; 8† ˆ 9:0, P < 0.05] suggesting that more time was needed for selecting the second sequence in the mixed than in the consistent R-mapping condition. A Length-First (2: Fshorter , Flonger ) ´ Length-Second (2: S2 , S4 ) ´ Mapping (2) ´ Session (2) ANOVA on latencies of the second sequence showed with a LengthFirst ´ Length-Second ´ Mapping interaction that the reversal e€ect was larger in

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…F3 †S21 than in …F4 †S21 (136 versus 68 ms) whereas it was smaller in …F2 †S41 than in …F3 †S41 [72 versus 175 ms; F …1; 8† ˆ 8:9, P ˆ 0.01]. This third-order interaction suggests that the reversal e€ect in Sn1 is larger when the earlier sequence has another mapping, rather than when the ®rst sequence is shorter. Reversal slowed execution of the ®rst sequence only in case of a ®rst 2-key sequence, that is, in F2WSIKI …S3 † and F2WSIKI …S4 † (see Table 2). So, this occurred irrespective of the mapping of the second sequence. Across all sequences, however, the reversal e€ect on WSIKIs of the ®rst sequence did not reach signi®cance [F …1; 8† ˆ 0:1, P > 0.20]. A further test examined if perhaps execution of the 3-key sequence, which was never reversed, was a€ected by the reversal of the second sequence. This was investigated with a Context [2: F3WSIKI …S2 †; F3WSIKI …S4 †] ´ Mapping (2) ´ Session (2) ANOVA on average WSIKI of the 3-key sequence; WSIKIs of the 3key sequence took only 9 ms longer when the 3-key sequence was followed by a sequence with reversed stimulus-sequence mappings as compared with a normal mapping [F …2; 16† ˆ 0:1, P > 0.20]. Thus, the higher selection demands associated with reversed mapping of the second sequence had no signi®cant e€ect on execution of the ®rst sequence. Of course, the latency of the ®rst sequence also showed a reversal e€ect in the reversal condition. This was con®rmed by a Context [3: An1 ; Fn1 …Sshorter †; Fn1 …Slonger †] ´ Length (3) ´ Mapping (2) ´ Session (2) ANOVA [see Table 2; F …1; 8† ˆ 92:1, P < 0.001]. The e€ect was, obviously, signi®cantly bigger for the 2and 4-key sequences than for the 3-key sequence [F …1; 8† ˆ 111:1, P < 0.001]. A Context (3: An ; Fn ) ´ Length (2: 2, 4) ´ Mapping (2) ´ Session (2) ANOVA revealed that the latency of the ®rst sequence was not a€ected by the second sequenceÕs Table 2 Sizes, F-values (d.f. ˆ 1, 8), and signi®cance levels of the reversal e€ect on latencies and WSIKIs in Experiment 1 3-Key sequencesa

2-Key sequences Seq.

Latency

WSIKI

Seq.

Latency

WSIKI

Seq.

Latency

WSIKI

A2

274 ms 77.1 234 ms 33.5 184 ms 63.7 136 ms 12.5 68 ms 9.3

7 ms 4.2‡ 15 ms 10.9 15 ms 19.9 5 ms 0.8 10 ms 2.6

A3

36 ms 2.8 37 ms 3.0 41 ms 1.9 )22 ms 0.7 )1 ms 0.0

4 ms 0.3 7 ms 1.3 11 ms 2.3 5 ms 0.6 8 ms 1.5

A4

222 ms 23.8 231 ms 31.1 218 ms 33.1 72 ms 3.5‡ 175 ms 33.2

8 ms 1.6 12 ms 3.1 13 ms 3.3 11 ms 4.0‡ 3 ms 0.27

F2 …S3 † F2 …S4 † …F3 †S2 …F4 †S2 a

4-Key sequences

F3 …S2 † F3 …S4 † …F2 †S3 …F4 †S3

F4 …S2 † F4 …S3 † …F2 †S4 …F3 †S4

There was no stimulus-sequence mapping reversal for 3-key sequences. P < 0.05. ** P < 0.01. *** P < 0.001. + P < 0.10. *

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mapping [F …1; 8† ˆ 0:9, P > 0.20]: when the second sequence also had a reversed mapping [i.e., in FR21 …SR4 † and FR41 …SR2 †], the reversal e€ect in the latency of the ®rst sequence amounted to 208 ms. When the second sequence had a normal mapping [i.e., in FR21 …S3 † and FR41 …S3 †], the reversal e€ect in the latency of the ®rst sequence amounted to 226 ms. In addition, the length of the ®rst sequence did not in¯uence the reversal e€ect [F …1; 8† ˆ 1:9, 0.2, respectively, P > 0.20]. A ®nal analysis on mapping e€ects concerned the question why the reversal e€ect in the latency of the second sequence had not entirely disappeared. The data suggest that execution of the ®rst sequence did not take long enough to allow preparation to be ®nished in time. With respect to the 2-key sequence, just the reversal e€ect amounted to 274 ms, implying that even more time was needed for response selection. However, execution of the ®rst sequence (excluding latencies) lasted 319 ms in F3 …S2 † and 455 ms in F4 …S2 †. Together with the ®nding that the latency of the ®rst sequence was not a€ected by the mapping of the second sequence, this suggests that the preparation for the second sequence started after initiation of the ®rst sequence had been completed and that preparing the second sequence took longer than execution of the ®rst sequence. In short, the reversal e€ect in the latency of the second sequence was smaller than in the ®rst sequence or in the single-sequence condition. It was also smaller with two reversed mappings than when only the second mapping was reversed. Execution of the ®rst sequence was not slowed by mapping of the second sequence. Latency of the ®rst sequence was, obviously, a€ected by mapping of the ®rst, but it was not a€ected by mapping of the second sequence or length of the ®rst sequence. Finally, the size of the reversal e€ect was quite large relative to the time available to execute the ®rst sequence. 2.2.9. Errors Arcsine transformed errors frequencies were analyzed with a Context [5: An ; Fn …Sshorter †; Fn …Slonger †; …Fshorter †Sn ; …Flonger †Sn ] ´ Mapping (2) ´ Session (2) ´ Key (2-4) ANOVA per sequence length. Only errors that occurred ®rst in a sequence were included in the error analyses; later errors were ignored. To improve independence of means and variances, arcsine transformations were carried out on error proportions per cell before subjecting these to ANOVAs (Winer, Brown, & Michels, 1991). For the 2-key sequence this yielded a Mapping ´ Key interaction [F …1; 8† ˆ 8:3, P < 0.05] indicating that more errors were made at initiation of the ®rst sequence with reversed mappings (FR21 : 4.9%, FR22 : 0.2%) than with normal mappings (FN21 : 2.3%, FN22 : 0.7%). The 3-key sequence analysis showed no signi®cant e€ects. For the ®rst key presses in a sequence, average error percentage was 2.2%. For the second and third key presses, these percentages amounted to 2.9%. Finally, more errors were made at the ®rst and second key press of the 4-key sequence in the reversal condition than in the normal mapping condition [per key, normal mapping: 2.1%, 1.8%, 3.4%, 0.6%; reversed mapping: 4.1%, 3.4%, 2.8%, 1.1%; F …3; 24† ˆ 4:7, P < 0.05] and more errors were made in …F3 †S4 than in the other four contexts [4.2% versus 1.9%; F …4; 32† ˆ 5:1, P < 0.01].

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3. Experiment 2 Experiment 1 showed evidence for motor chunk robustness in terms of the prime chunking indicator, temporal grouping. The other indicators for motor chunks did not indicate use of motor chunks. Concurrent preparation was indicated by the prime indicator, slowed execution of the ®rst sequence in the dual-sequence condition, and also by the reduced mapping e€ect in the latency of the second sequence. The remaining indicators for concurrent preparation did not show indications for concurrent preparation. So, it seems that the proposed, relatively new indicators for motor chunking and concurrent preparation are not useful. Evidence against resource models and in favor of the dual-processor model was found in that execution of the ®rst sequence was slower in the dual-sequence than in the single-sequence condition whereas reversal of the second sequenceÕs mapping did not a€ect execution of the ®rst sequence. An interesting ®nding was that execution rate of 2-key sequences appeared generally more susceptible to dual-sequence conditions than 3- and 4-key sequences. This suggests that the cognitive processor had a greater contribution in executing the 2-key sequence than in the longer sequences. Experiment 2 examined, again, the potential of the earlier proposed indicators for chunk robustness and concurrent processing but now for 2- and 6-key sequences. Furthermore, it tested the notion that short sequences su€er more from concurrent preparation than long sequences. Experiment 2 did not include mapping reversal. 3.1. Method 3.1.1. Participants Participants were 18 students from the University of Utrecht (12 males and 6 females). They were paid 240 Dutch guilders (109 ) for participating in the entire experiment and the best six received a bonus of 25 Dutch guilders (11 ). 3.1.2. Task and procedure The task was a simpler version of the one used in Experiment 1 and was the last transfer phase of an experiment reported elsewhere (Verwey, 1999). Di€erences with Experiment 1 pertained to the use of two 2-key sequences and one 6-key sequence and the absence of a reversed mapping condition. The two 2-key sequences, where necessary indicated by ÔaÕ and ÔbÕ, included di€erent keys, but they were not intended to be di€erent in any other respect. Thus, Experiment 2 included three sequences in the single-sequence condition …A2a ; A2b ; A6 †, and six sequence combinations in the dual-sequence condition …F2a S2b ; F2b S2a ; F2a S6 ; F2b S6 ; F6 S2a ; and F6 S2b †. Examples of sequences produced by one participant are ÔLÕ given in consistent response during practice to the digit Ô2Õ, ÔDFÕ in response to Ô6Õ, and ÔGLZ/KÕ in response to Ô3Õ. This time, some keys occurred in more than one sequence so that transitions were not entirely unique. Again, these sequences were preceded by a presequence, involved no key-speci®c cues, and were balanced across participants and stimuli to cancel out any ®nger- or stimulus-speci®c e€ects.

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In Experiment 2, participants simultaneously worked in groups of seven or less in seven di€erent 2:4  2:5  2 m sound-attenuated rooms. Each time a group had completed a session, another group of seven or less started in the same room. This resulted in a rest and test schedule for each participant of 15±20 min. Each participant in Experiment 2 had carried out six 168-trial practice sessions on Day 1, seven on Day 2, and two on Day 3. The experiment was conducted on seven identical IBM-AT compatible (G2, 80386SX) computers with NEC Multisync VGA 3D color monitors running the same MEL software as in Experiment 1. Further details are described in Verwey (1999). 3.2. Results The ®rst analysis involved comparison of the two 2-key sequences in a Version (a versus b) ´ Context [5: A2 ; F2 …S2 †; F2 …S6 †; …F2 †S2 ; …F6 †S2 ] ´ Key (2: latency, WSIKI) ´ Session (2) ANOVA to investigate whether any di€erences would exist between the two 2-key sequences. No signi®cant main e€ect or interactions with Version (P > 0.15) was found indicating that both the versions had comparable latencies and execution rates in the various contexts (Version a: 784 ms, 145 ms; Version b: 827 ms, 129 ms). Therefore, further analysis involved the pooled latencies and WSIKIs of both 2-key sequences. 3.2.1. Robustness: temporal grouping As shown in Table 3, latencies of the second sequence in the dual-sequence condition were larger than average WSIKIs of the ®rst and second sequences. Planned comparison of Sn1 versus FnWSIKI =SnWSIKI following a Part (3: FnWSIKI ; Sn1 ; SnWSIKI ) ´ Sequence_Combination (3: F2 S2 ; F2 S6 ; F6 S2 ) ´ Session (2) ANOVA showed a di€erence between WSIKIs of both sequences and latency of the second sequence [F …1; 17† ˆ 126:1, P < 0.001] and no di€erence between WSIKIs of the ®rst and second sequence [F …1; 17† ˆ 0:3, P > 0.20]. Moreover, Sn1 reduced more with Session than FnWSIKI =SnWSIKI [57 ms versus 17 ms; F …1; 17† ˆ 11:6, P < 0.001]. Table 3 Latency and average WSIKIs in Experiment 2a Alone, ®rst sequence

a

Second sequence

Latency

Average WSIKI

Latency

Average WSIKI

2-key

A2 : 955 ms F2 …S2 †: 1116 ms F2 …S6 †: 1109 ms

A2 : 113 ms F2 …S2 †: 141 ms F2 …S6 †: 145 ms

…F2 †S2 : 374 ms …F6 †S2 : 474 ms

…F2 †S2 : 138 ms …F6 †S2 : 149 ms

6-key

A6 : 929 ms F6 …S2 †: 994 ms

A6 : 177 ms F6 …S2 †: 183 ms

…F2 †S6 : 492 ms

…F2 †S6 : 190 ms

Data are collapsed across the two versions of the 2-key sequence.

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3.2.2. Robustness: preservation of ¯uency Both the 2- and 6-key sequences were carried out more slowly in the dual-sequence condition [F …1; 17† ˆ 23:6, 7.6, P < 0.05]. Whether a sequence was ®rst or second in the dual-sequence condition did not have a signi®cant e€ect on WSIKIs of 2- and 6-key sequences [F …1; 17† ˆ 0:2, 2.1, P > 0.17]. 3.2.3. Robustness: preservation of sequence length e€ect The single-sequence condition showed a sequence length e€ect on average WSIKI [Table 3; F …1; 17† ˆ 56:8, P < 0.001]. Planned comparisons following the Context (3: AnWSIKI ; FnWSIKI ; SnWSIKI ) ´ Length (2) ´ Session (2) ANOVA indicated that the sequence length e€ect was smaller in the dual-sequence condition [in AnWSIKI : 64 ms, in FnWSIKI : 40 ms, in SnWSIKI : 47 ms; F …1; 17† ˆ 12:3, P < 0.001], but the sequence length e€ect on WSIKI remained signi®cant in the dual-sequence condition [F …1; 17† ˆ 24:3, P < 0.001]. Sequence length did not have a signi®cant latency e€ect in the single-sequence condition [F …1; 17† ˆ 0:6, P > 0.20]. 3.2.4. Robustness: preservation of temporal structure Fig. 4 suggests that the temporal structure of the 6-key sequence was quite robust across conditions. A Context (5: A6 ; F6 …S2a †; F6 …S2b †; …F2a †S6 ; …F2b †S6 † ´ Key (5) ´ Session (2) ANOVA on individual WSIKIs con®rmed signi®cance of the temporal structure by a Key main e€ect [F …4; 68† ˆ 8:5, P < 0.001], but a Context ´ Key interaction [F …16; 272† ˆ 4:0, P < 0.001] indicated that temporal structure was signi®cantly di€erent in the ®ve conditions. Planned comparison showed that temporal structure of the 6-key sequence was di€erent when it was at ®rst and second position of the dual-sequence condition [F …4; 68† ˆ 6:6, P < 0.001]. Detailed analyses showed that Context had signi®cant e€ects on the third and the sixth key press [F …4; 68† ˆ 5:7, 5.2, P < 0.01], but not on the remaining key presses [F …4; 68† < 2.0, P > 0.10]. The temporal structure of the 6-key sequence was not a€ected by the

Fig. 4. WSIKIs in the 6-key sequence as a function of context in Experiment 2. Data are collapsed across the two versions of the 2-key sequence.

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version of the 2-key sequence [®rst position: F …4; 68† ˆ 2:1, P > 0.08; second position: F …4; 68† ˆ 1:6, P > 0.17]. 3.2.5. Robustness: correlations between individual elements Correlations were computed for each participant, sequence combination, and session between WSIKIs with a mutual distance of two. That is, correlations were computed between F22 and S62 (i.e., between-sequence) and between S62 and S64 , S63 and S65 , and S64 and S66 (i.e., within-sequence). Similarly, correlations between F66 and S22 were compared with the average correlations between F62 and F64 , F63 and F65 , and F64 and F66 . Planned comparison following the Within-Between (4) ´ Sequence_Combination (2: F2 S6 , F6 S2 ) ´ Session (2) ANOVA revealed no signi®cant di€erences between within- and between-sequence correlations. Correlations were below 0.20 and di€erences did not reach signi®cance [F …1; 17† ˆ 0:9, P > 0.20]. 3.2.6. Concurrent processing: ®rst sequences A Context (2: An1 ; Fn1 ) ´ Length (2: 2, 6) ´ Session (2) ANOVA showed that sequences at the ®rst position in the dual-sequence condition had larger latencies than in the single-sequence condition [1051 versus 942 ms; F …1; 17† ˆ 52:7, P < 0.001]. Furthermore, latency of the 2-key sequences increased more in the dual-sequence condition than latency of the 6 key-sequence [F …1; 17† ˆ 10:8, P < 0.01]. According to a Context [2: F21 …S2 †; F21 …S6 †] ´ Session (2) ANOVA, latency of the ®rst 2-key sequence was not a€ected by the length of the second sequence [F …1; 17† ˆ 0:2, P > 0.20]. Planned comparison following the earlier mentioned Context (3: AnWSIKI ; FnWSIKI ; SnWSIKI ) ´ Length (2) ´ Session (2) ANOVA showed that execution of 2-key sequences was slowed more in the dual-sequence condition than the 6-key sequence [30 versus 6 ms; F …1; 17† ˆ 7:3, P < 0.05]. 3.2.7. Concurrent processing: second sequence Planned comparison following the Context [5: A21 ; A61 ; …F2 †S21 ; …F6 †S21 ; …F2 †S61 ] ´ Session (2) ANOVA revealed that latencies of second sequences were smaller than of sequences in the single-sequence condition [F …1; 17† ˆ 100:5, P < 0.001]. Latency of 2-key sequences at second position were shorter when they followed another 2-key sequence than when they followed a 6-key sequence [F …1; 17† ˆ 15:6, P < 0.01]. Planned comparison following the earlier mentioned Context (3: AnWSIKI ; FnWSIKI ; SnWSIKI ) ´ Length (2) ´ Session (2) ANOVA showed that WSIKIs were longer in the second position of the dual-sequence condition than in the single-sequence condition [172 versus 145 ms; F …1; 17† ˆ 22:8, P < 0.001]. The dual-sequence condition caused more slowing in the 2-than in the 6-key sequences [30 versus 13 ms; F …1; 17† ˆ 10:3, P < 0.01]. WSIKIs appeared to be slowed more when a 2-key sequence was preceded by the other 2-key sequence than by the 6-key sequence [F …1; 17† ˆ 4:6, P < 0.05].

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3.2.8. Errors Again, error analysis involved only errors that occurred as ®rst in a sequence and error proportions were transformed before subjecting them to ANOVAs. These ANOVAs showed no systematic e€ects. Error rates per key in F2 S6 sequences averaged 2.5%, for F6 S2 sequences 3.3%, and for F2 S2 sequences 2.0%. For sequence in the single-sequence condition, average error rates were 1.9% for A2 , and 2.1% for A6 .

4. Discussion The main purpose of this study was investigating whether a model assuming that a cognitive and a motor processor may produce sequences in parallel can explain performance when two familiar keying sequences are executed in rapid succession. Research questions pertained to the robustness of motor chunks and to the e€ects of concurrent preparation and mapping reversal on sequence execution. Also, the merits were examined of various potential indicators for motor chunks and concurrent preparation. The main results of Experiments 1 and 2 are (a) latencies of the second sequences were longer than WSIKIs of the ®rst and second sequence, (b) relative to the single-sequence condition, execution rates of the ®rst and second sequences were reduced in the dual-sequence condition, (c) relative to the single-sequence control condition, the reversal e€ect in the latency of the second sequence in Experiment 1 reduced substantially in the dual-sequence condition while latency and execution rate of the ®rst sequence were not a€ected by reversal of the second sequence. These results suggest that even with two 2-key sequences, motor chunks are robust in the sense that they are used for executing familiar sequences. The e€ects of the second sequence and of mapping reversal on execution rate of the ®rst sequence can be considered evidence for a dual-processor model but as will be described below, full explanation of the data in terms of the dual-processor model requires additional assumptions. Lastly, it appeared that the various alternative data features proposed in the Introduction to Experiment 1 were not reliable indicators for chunk robustness and concurrent preparation in the present tasks. 4.1. Robustness Experiments 1 and 2 showed that latency of the second sequence was much longer than the within-sequence interkey intervals (WSIKIs) of the ®rst and second sequences. As this is in line with earlier research (Sternberg et al., 1990; Verwey, 1996), it is interpreted as evidence that execution of both familiar sequences was indeed based on using two motor chunks. It appeared that even when two 2-key sequences were executed in succession, which could have allowed advance preparation of the four sequence elements (Sternberg et al., 1978), temporal grouping still indicated use of motor chunks. Even though not mentioned explicitly as an indicator for chunk robustness, the execution rates of the sequences also seem too high (average WSIKIs

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were below 160 ms) for assuming that the individual elements were selected after one another at a cognitive level. As to the other indicators for chunk robustness, temporal structure appeared relatively stable with the 6-key sequence in Experiment 2, but there was still a signi®cant context e€ect. In Experiment 1, temporal structure was not consistent across conditions (Fig. 3). Hence, temporal structure was not a reliable indicator for chunk robustness in the present experiments. A next potential indicator for chunk robustness, the sequence length e€ect on execution rate, appeared to be smaller in the dual-sequence conditions of both experiments. Only in Experiment 2, with its large di€erence in sequence lengths, the sequence length e€ect remained signi®cant. So, preservation of the sequence length e€ect also has limited value for indicating chunk robustness. The two remaining potential indicators for chunk robustness, preservation of ¯uency and correlations between within-key intervals, did not indicate motor chunk usage at all. The fact that correlations in familiar sequences were so small suggests that higher correlations are found with explicit timing requirements only (cf. Schneider & Schmidt, 1995; Young & Schmidt, 1990). Notice that the low correlations between intervals within the same sequence support the assumption of the dual-processor model that the time taken by the motor processor to produce its output is distributed, that is, it is subject to noise (Heuer, 1988; Meyer, Smith, Kornblum, Abrams & Wright, 1990; van Gemmert & van Galen, 1997). 4.2. Concurrent processing The prime indicator for concurrent preparation, reduced execution rate of the ®rst sequence, suggests that concurrent preparation had indeed taken place. This is con®rmed by the relatively small reversal e€ect in the latency of the second sequence in Experiment 1, which entails unambiguous evidence that selection of the second sequence occurred during execution of the ®rst sequence selection. The possibility that selection of the second sequence took place before initiation of the ®rst one can be rejected, as the latency of the ®rst sequence was not a€ected by mapping of the second sequence. Slowed execution of the ®rst sequence due to concurrent preparation is basically in line with both the dual-processor model and with single-resource models. However, as with a single key press following a familiar sequence (Verwey, 1995), increasing selection load by mapping reversal did not a€ect execution of the ®rst sequence. The ®nding that increased response selection demands did not a€ect execution of the ®rst sequence whereas the use of concurrent preparation did, cannot be explained by a resource model and supports the dual-processor model. This rejection of resource models in favor of structural process models is in line with several other studies (e.g., Navon, 1984; Pashler, 1994; van Gemmert & van Galen, 1997). However, there is a problem for the dual-processor model too. The ®nding in Experiment 1 that the reversal e€ect in the latency of the second sequence did not entirely disappear may be attributed to the limited time available during execution of the ®rst sequence (cf. Garcia-Colera & Semjen, 1988; Verwey, 1995). Yet, the remaining reversal e€ect in the latency of the second sequence was smaller with two

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reversed mappings than when only the mapping of the second sequence was reversed. Also, Experiment 2 showed that latencies of 2-key sequences in second position were shorter following another 2-key sequence than when following a 6-key sequence. This is at odds with the notion that the amount of concurrent preparation should increase as execution of the ®rst sequence takes longer. For now, a reasonable posthoc explanation seems that less preparation is required when successive sequences are equally long and when mapping remains the same. This is in line with earlier indications that parameter re-mapping shortens preparation time (Rosenbaum, Weber, Hazelett & Hindor€, 1986). 4.3. Deviating 2-key sequences It is noteworthy that 2-key sequences behaved di€erently from longer sequences in several situations: (a) The sequence length e€ect in the single-sequence condition of Experiment 1 was caused solely by faster execution of the 2-key sequence. It did not a€ect 3- and 4-key sequences. (b) The sequence length e€ect on execution rate disappeared for the ®rst sequences in the dual-sequence condition of Experiment 1 and was substantially reduced in Experiment 2 because 2-key sequences were slowed more than longer sequences. In fact, in an earlier study I also found elimination of the sequence length e€ect when familiar sequences were produced in succession (Verwey, 1996), but I paid little attention to this ®nding at the time. (c) It took considerable practice in the practice phase of Experiment 2 (reported in Verwey, 1999) before execution rate of 2-key sequences was no longer faster in simple than in choice RT tasks. This was not found for the 6-key sequence. d) Besides, it took considerable practice before the 2-key sequence was no longer executed much faster than longer sequences [Verwey, 1999; this was also found in the practice phase of Experiment 1 where the WSIKI advantage for 2-key sequences decreased from 138 ms in Session 1 and 87 ms in Session 2, to 26 ms in Sessions 7 and 8; F …7; 56† ˆ 12:7, P < 0.001]. (e) A reversal e€ect on execution rate was found only with 2-key sequences that were executed as ®rst sequence in Experiment 1. This was caused by the sequenceÕs own mapping and not by mapping of the second sequence. In short, 2-key sequences were executed relatively fast in single-sequence conditions, especially with limited practice and when the single-sequence condition was a simple RT condition, but this advantage of 2-key sequences reduced considerably in dual-sequence conditions (especially when produced ®rst) and when mapping was reversed. These ®ndings were not anticipated, but they can be explained better by the dualprocessor model than by a resource model. As stated in Section 1, the dual-processor model explains the execution rate e€ect of concurrent preparation by assuming that the cognitive processor may, sometimes, operate in parallel with the motor processor in executing familiar sequences. The ®nding that 2-key sequences are a€ected much more by concurrent preparation and by mapping reversal than longer sequences suggests that the cognitive processor mainly facilitated execution of 2-key sequences. Then, why would the cognitive processor speed up mainly 2-key sequences? Possibly, the cognitive processor is better at reproducing short sequences and, therefore, can only support execution of short sequences. A pilot study I recently

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carried out supports this in that participants had much more diculty verbally reproducing 6-key than 3-key sequences, even though they had just keyed both sequences a substantial number of times and had exhibited a considerable increase in execution rate. Obviously, this explanation requires further empirical support. 4.4. Re-allocating the cognitive processor There is yet another diculty for the dual-processor model. This pertains to the ®nding that in the dual-sequence condition, second sequences were also slowed (though less than when produced as ®rst sequence). This is not predicted by the dual-processor model and held especially for 2-key sequences in Experiments 1 and 2 and the ®rst part of the 6-key sequences in Experiment 2. Given the assumption that the cognitive processor is involved mostly in the execution of 2key sequences, these results suggest that slowing of the second sequence is caused by a relatively slow allocation of the cognitive processor from preparing to executing the second sequence. Support for slow allocation of the cognitive processor comes from many studies on task switching (e.g., Allport, Styles & Hsieh, 1994; Rogers & Monsell, 1995). The present data also provide evidence for this notion in that only the ®rst WSIKIs of the 6-key sequence were slowed in the dual-sequence condition [i.e., …F2 †S62 ; …F2 †S63 ; and …F2 †S64 , see Fig. 4]. The last two key presses of the 6-key sequence [i.e., …F2 †S65 and …F2 †S66 ] seem to have pro®ted again from the cognitive processor supporting the motor processor in sequence execution. 4.5. The dual-processor model Experiments 1 and 2 yield a large number of results that might potentially be explained by several models. The present data con®rm that resource models can be rejected as explanatory construct because they do not predict that concurrent preparation slows ongoing sequence execution whereas increased selection load, as caused by mapping reversal, has not e€ect on ongoing execution. In my view, the dual-processor model (e.g., Allport, 1980; MacKay, 1982; Pew, 1966; Schmidt, 1988; Sha€er, 1991) provides the most parsimonious explanation for the present results. However, as discussed before, the data suggest that this dual-processor model requires three additional assumptions for explaining all aspects of the data: (a) Preparation of a sequence is faster when it has the same length and mapping as the preceding sequence. (b) The cognitive processor is better at executing short than long sequences. (c) Allocating the cognitive processor from preparation to execution takes some time. Even though some evidence for these assumptions has been discussed, future research should provide evidence for the validity of these assumptions in the dual-sequence paradigm. It is important to note that the dual-processor model ®ts seamlessly with the parallel architecture of the brain that is assumed by neuropsychological models. According to these models, execution of unfamiliar sequences involves the dorsal prefrontal cortex, the anterior cingulate cortex, and the premotor cortex while with

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practice, control is taken over, perhaps only in part, by the supplementary motor area, the basal ganglia, and the lateral cerebellum (Gazzaniga, Ivry, & Mangun, 1998; Jenkins, Brooks, Nixon, Frackowiak & Passingham, 1994; Willingham, 1998). A recent positron emission tomography (PET) study con®rmed this shift in activation with practice and showed that when participants were asked to ``think of the next movement'' while executing familiar sequences, the dorsal prefrontal cortex and the anterior cingulate cortex were re-activated (Jueptner, Stephan, Frith, Brooks, Frackowiak & Passingham, 1997). Another recent study showed that the awareness of sequences in the serial reaction time task was associated with activation of, among others, the dorsal prefrontal cortex whereas implicit learning was associated with activity in the motor cortex, supplementary motor area, and basal ganglia (i.e., putamen; Grafton, Hazeltine and Ivry, 1995). Together, these ®ndings suggest that the neural substrates of the cognitive processor assumed by the dual-processor model, include the dorsal prefrontal cortex and the anterior cingulate cortex, whereas the motor processor comprises the supplementary motor area, the basal ganglia, and the lateral cerebellum. The dual-processor model is also related to the notion that implicit learning in the serial reaction time task is based on motor learning (Ho€mann & Koch, 1997; Nattkemper & Prinz, 1997), and to the category of hierarchical models of sequence control assuming that several systems, or processors, are simultaneously active (Broadbent, 1977; Sternberg et al., 1990). Conversely, the dual-processor model di€ers from hierarchical control models that assume that a single processing system traverses a hierarchical sequence representation and executes each element immediately upon retrieving it (e.g. Miller, Galanter & Pribram, 1960; Rosenbaum, Kenny & Derr, 1983). These hierarchical models do not assume concurrent processing and may be more appropriate when action sequences are coded by cognitive representations (cf. Sha€er, 1991). Even though the present study did not use additive factor methodology for distinguishing processes, it is tempting to assert that the cognitive and motor processors of the dual-processor model are in fact responsible for the response selection and motor processing stages that have been distinguished in 1980 and 1990 by Andries F. Sanders and, hence, that processing stages found with the additive factors logic do ``make sense beyond the realm of additive factor application''.

Acknowledgements I am grateful to Petra Wallmeyer for assistance in running and analyzing Experiment 1 and Martin Buist for running Experiment 2. Experiment 2 was analyzed and written in part while being on leave at the Human Factors Research Laboratory, University of Minnesota. The hospitality of Peter Hancock is acknowledged. Correspondence concerning this article should be addressed to Willem B. Verwey, Institut f ur Arbeitsphysiologie an der Universitat Dortmund, Ardeystraûe 67, 44139 Dortmund, Germany, email: [email protected].

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