Processes of task-set reconfiguration: switching operations and implementation operations

Acta Psychologica 111 (2002) 1–28 www.elsevier.com/locate/actpsy

Processes of task-set reconfiguration: switching operations and implementation operations Thomas Kleinsorge *, Herbert Heuer, Volker Schmidtke Institut f € ur Arbeitsphysiologie, Universit€at Dortmund, Ardeystraße 67, D-44139 Dortmund, Germany Received 29 January 2001; received in revised form 1 October 2001

Abstract When participants are asked to shift between four dimensionally organized tasks which differ in the type of judgment (numerical vs. spatial) and/or the judgment-to-response mapping (compatible vs. incompatible), a characteristic profile of shift costs can be observed. It can be accounted for in terms of two different types of operations: generalizing switching operations on a dimensionally organized set of task representations and implementation operations [T. Kleinsorge, H. Heuer, Psycholog. Res. 62 (1999) 300]. In a first experiment we corroborated our previous findings by way of a new procedure that makes it possible to estimate shift costs unconfounded by a number of factors that are likely to affect estimates of shift costs based on more conventional procedures. In a second experiment we investigated the endogenous and exogenous nature of the postulated types of operations. The characteristic profile of shift costs disappeared when long precue intervals (PCIs) were used. Augmented by a formal analysis, this finding suggests that both switching and implementation operations are endogenously controlled. In addition, there remained some residual shift costs which were essentially insensitive to the nature of the task shift but depended on the difficulty of the new task. Most likely they reflect a process of consolidation of an already configured task set. Ó 2002 Elsevier Science B.V. All rights reserved. PsycINFO classification: 2340 Keywords: Shift costs; Endogenous control; Exogenous control

*

Corresponding author. Tel.: +49-231-1084-321; fax: +49-231-1084-340. E-mail address: [email protected] (T. Kleinsorge).

0001-6918/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 1 - 6 9 1 8 ( 0 1 ) 0 0 0 7 6 - 2

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1. Introduction In contrast to cognitive psychology’s progress in understanding the processes and structures that underlie the performance of a wide range of individual tasks, the processes by which humans configure themselves to perform a certain task (task-set configuration), and thus to deal with the stimuli they are confronted with in a certain way and not in other ways, have been widely neglected. Consequently, Monsell (1996, p. 93) characterized this area as a ‘‘somewhat embarrassing zone of almost total ignorance’’. However, in recent years research on task-set configuration has been intensified, and there seems to be a dramatic increase in both empirical and theoretical efforts to overcome the ignorance Monsell complained about. The present paper is one of these efforts. It is concerned with the identification and characterization of different processes involved in task-set configuration and with the eventual convergence of different proposals which have been based on different methodological approaches. Task shifting has become the main paradigm for the study of task-set configuration. It involves the speeded and frequent alternation between individual tasks. Inferences are based primarily on reaction times, in particular on the reaction-time difference between trials which involve a task shift (shift trials) and trials which involve a task repetition (non-shift trials). Typically, this difference is positive and called the shift cost. Several sources have been suggested to contribute to shift costs. On a rather general level a distinction can be drawn between accounts of shift costs in terms of active (re-)configuration processes (e.g., Rogers & Monsell, 1995) and accounts in terms of episodic carry-over (e.g., Wylie & Allport, 2000). Although proposing different kinds of mechanisms, both lines of theorizing are certainly not mutually exclusive, and there seems to be a tendency in the recent literature to end up with an integration of both accounts (e.g., Goschke, 2000; Meiran, 2000). While not denying the role of episodic carry-over as a determinant of shift costs (the mere existence of which indicates at least some unspecific carry-over effect), the account presented in the present paper is focused on the analysis of shift costs in terms of the duration of active reconfiguration processes. One reason for this is that the methodological approach we have chosen largely abstracts from specific transitions between individual tasks and in doing so neglects important information needed to account for shift costs in terms of specific episodic carry-over effects. Nevertheless, some of the critical findings we interpret as supporting our account in terms of active reconfiguration alternatively could be explained as episodic carryover effects, therefore we shall discuss such alternative accounts in Section 4. Beyond this the reader should keep in mind that not mentioning the contribution of processes of episodic carry-over does not imply the claim that these processes do not exist, but is a result of our specific methodological approach and theoretical emphasis. Our efforts to gain insight into the processes that underlie task-set configuration started with the consideration that, although task-shifting experiments typically involve sets of only two tasks in each experimental condition, the use of larger sets

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might have the potential of providing additional insights into the processes of taskset reconfiguration (cf. Mayr & Keele, 2000, for a similar point of view). This led us to explore shift costs with a set of four dimensionally organized tasks (Kleinsorge & Heuer, 1999), with the two task dimensions being the type of judgment (numerical vs. spatial) and the judgment-to-response mapping (compatible vs. incompatible). Our general hypothesis, which was based on some analogies between task-set configuration and motor programming (cf. Kleinsorge, 2000, for details), was that shift costs should reflect the dimensional organization of the four tasks, which indeed they did, though in a somewhat complicated manner. Shift costs were not simply a monotonic function of the number of dimensions on which the task changed from one trial to the next, but the effect of a change on one dimension depended on whether or not certain other dimensions were changed as well. The first observation of such a phenomenon dates back at least to Rogers and Monsell (1995): they found that the classical response–repetition benefits (e.g., Kirby, 1980), which showed up in non-shift trials in their experiments too, turned into response–repetition costs in terms of reaction time and/or error rate in shift trials. In fact, response–repetition costs have also been observed with more subtle changes of stimulus category (Kleinsorge, 1999). In our previous study (Kleinsorge & Heuer, 1999) we found in addition that the reaction-time benefits of a repeated judgmentto-response mapping over an alternated mapping turned into reaction-time costs when only the mapping was repeated, but the type of judgment was changed. When the type of judgment was repeated, however, there were always reaction-time benefits as compared to trials in which the type of judgment was changed, no matter whether the mapping was repeated or changed. These observations suggest that switches on certain dimensions imply (or prime) switches on certain other dimensions, while the reverse is not necessarily true. More specifically, we accounted for the observed profile of shift costs as a function of the relation between successive tasks in terms of two types of operations which serve, first, to select the appropriate task representation and, second, to transform the selected task representation into the appropriate task-control structure (implementation). Each of these processes is characterized by its duration. The selection of the appropriate task representation we assumed to be composed of a number of switching operations in a dimensionally organized memory representation which we called the ‘‘task space’’, with each single switching operation having a constant duration. The number of switching operations depends on the relation between successive tasks according to the following rules: 1. In addition to the type of judgment and the judgment-to-response mapping, the responses constitute a third task dimension. These three dimensions form a hierarchy, with the type of judgment on top and the responses at the bottom of the hierarchy. Primary switches on a higher-level dimension generalize to all lower-level dimensions, resulting in concurrent switches on these lower-level dimensions. 2. Corrective re-switches are required when generalized switches are inappropriate; they occur serially and do not generalize to lower-level dimensions.

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The resulting number of switches which, when multiplied with the duration of a single switch, determines the duration of the selection process, is given in the second column of Table 1 for each relation between successive tasks. For example, when only the type of judgment has to be changed from one trial to the next (fifth row in Table 1), this results in three switching operations. First, there is a switch on the judgment level that generalizes to the mapping level and the response level. Second, because the features on these two levels actually are repeated, two corrective reswitches are needed in addition. For the second kind of process involved in task-set reconfiguration we assumed that its duration is different when only a new mapping has to be implemented and when a new type of judgment has to be implemented; in addition we assumed that implementation of a new type of judgment implies implementation of a new mapping of the outcomes of the judgment to the responses. With our previous data it even appeared that implementation of a new type of judgment together with a new mapping required twice the time needed by the implementation of a new mapping only. The assumption of a hierarchical ordering of the three task dimensions is based on the fact that it is logically necessary to know the possible outcomes of a judgment process before they can be mapped on their corresponding responses, with this mapping in turn having logical priority over the activation of a response. Correspondingly, it is plausible that task-set reconfiguration starts with specifying the required type of judgment before selecting the particular judgment-to-response mapping (cf. Kleinsorge & Heuer, 1999, for details). The assumption that primary but not corrective switches generalize downstream the hierarchy is plausible on the basis of functional considerations. A generalizing switch should be an efficient means of cognitive reconfiguration under conditions in which a change on a superordinate level of action representation (for example, the level of goals) normally goes along with the requirement to establish another repertoire of subordinate actions. However, when also corrective re-switches would generalize, this would endanger the stability

Table 1 Hypothetical durations of selection and implementation, observed and predicted mean reaction times, and error rates for the different relations between successive tasks (previous type of Judgment same or different, previous Mapping same or different, previous Response same or different) Relation

Hypothetical duration

Mean reaction time

J

M

R

Selection

Implementation

Observed

Predicteda

¼ ¼ ¼ ¼ 6 ¼ 6 ¼ 6 ¼ 6 ¼

¼ ¼ ¼ 6¼ 6¼ ¼ 6¼ 6¼

¼ ¼ 6¼ ¼ 6¼ 6¼ ¼ 6¼

0 TS 2TS TS 3TS 2TS 2TS TS

0 0 TM TM TJ TJ TJ TJ

453 478 802 783 923 926 882 875

454 477 804 781 925 902 902 878

Error percentage 1.4 1.67 8.02 4.13 4.22 3.09 2.43 1.09

a With parameter estimates RT0 ¼ 454 ms, duration of switching operation TS ¼ 23:3 ms, duration of mapping implementation TM ¼ 304 ms, duration of judgment plus mapping implementation TJ ¼ 401 ms.

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of the system because with action representations that cover a wider range of intermediate levels a whole sequence of generalizing re-switches might be required. Our account of the profile of shift costs among a set of dimensionally organized tasks leads to a simple additive model which can be fitted to the observed data. Independent of any goodness-of-fit measure, it suggests that certain qualitative differences in shift costs should exist between certain sets of relations between successive tasks. In addition, the formalism is derived from more general theoretical assumptions. Perhaps the most important of these assumptions is that primary switches generalize across all lower-level task dimensions. This assumption seems to imply certain organizational characteristics of the task space, the organized set of memory representations of all tasks that are possible in a certain situation. The present experiments are intended to bolster and elaborate our account of shifting within a set of dimensionally organized tasks. In the first experiment we address a number of methodological criticisms that can be raised against our previous findings. In the second experiment we relate our hypothesized processes of task-set reconfiguration, namely selection – characterized by the number of switching operations – and implementation to the distinction of endogenously and exogenously controlled processes (Rogers & Monsell, 1995).

2. Experiment 1 Our account of shifting among a set of dimensionally organized tasks thus far is largely post hoc and based on a pattern of experimental results that was not really predicted. Thus, of course, the findings need replication, which also allows data analyses guided by specific a priori hypotheses. Second, and this is perhaps a more serious concern, our results were obtained with a particular variant of the task-shifting paradigm which, as we know now, is not necessarily appropriate for the kind of account we have suggested. Thus, our first step here is to exclude potential artefacts which could have affected the switch-cost profile and thus the basis for our tentative conclusions. Variants of the task-shifting paradigm differ in how the sequences of tasks are arranged. For example, in some experiments performance in pure (only one task) and mixed (alternating tasks) blocks of trials is compared (e.g. Allport, Styles, & Hsieh, 1994; Rubinstein, Meyer, & Evans, 2001). In other experiments shift trials and nonshift trials from same blocks are compared, as in the alternating-runs procedure (Rogers & Monsell, 1995) or with random sequences of tasks (Meiran, 1996). In our previous study tasks varied unpredictably within long sequences of trials. This procedure embodies the risk of at least two types of artefacts when the purpose is to assess the durations of processes of task-set reconfiguration. The first type of artefact is related to the baseline measures, that is, to the assessment of performance in non-shift trials. Although Rogers and Monsell (1995, Exp. 6) found essentially no differences between non-shift trials which were first, second, or third task repetitions, such a finding seems not to be universal, but lagged effects of task shifts have also been observed (e.g., Kleinsorge, 1997; Meiran, Chorev, & Sapir,

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2000). In fact, they were also present in our previous study (Kleinsorge & Heuer, 1999). Whenever this is the case, there is some uncertainty with respect to which trials to use as baseline. In particular artefacts can accrue from this rather arbitrary choice as soon as lagged effects of a task-shift depend on the nature of this shift. The second type of artefact is related to the recent observation that shift costs do not only depend on the current task shift, but also on the preceding one (Mayr & Keele, 2000). Specifically, the costs of shifting from task B to task A have been shown to be higher when B was preceded by task A than when B was preceded by a third task C, presumably because of the requirement to overcome some residual inhibition of task A in trial n that has been built up when it has been abandoned in trial n  1. The more general conclusion one can draw from this finding is similar to the conclusion that reaction time in non-shift trials is likely to depend on whether earlier trials were also non-shift trials or not: reaction time in shift trials does not only depend on the current shift but also on preceding ones. With dimensionally organized tasks higher-order sequential effects, as they have been identified by Mayr and Keele (2000), can become quite complicated and opaque. According to such considerations, strict control of context is required when the purpose is to study shift costs unconfounded by different kinds of sequential effects, especially when conclusions are to be drawn on quantitative estimates of the durations of certain configuration processes. As mentioned in Section 1, our account of shifting within a set of dimensionally organized tasks is concerned only with processes of task-set reconfiguration and neglects additional processes which are now known to affect shift costs. Thus, it is crucial that the data are not confounded by at least those additional components of task-shifting like the overcoming of residual backward inhibition that can readily be supposed on a priori grounds. For the present experiments we chose a procedure similar to the one used by Gopher, Armony, and Greenshpan (2000). Basically, the sequence of trials was split into blocks of five trials each with breaks between blocks. Within each block a single task shift occurred randomly in the third or fourth trial or not at all. This design allows strict control over all sequential dependencies at least on the time scale of a single block and, among other things, has the advantage that shift and non-shift trials occur in strictly identical contexts, which is not the case, for example, when pure and mixed blocks are compared or with the alternating-runs procedure. 2.1. Method 2.1.1. Participants Twelve female and four male participants took part in the experiment. Their mean age was 24.9 years (range: 18–31 years). They were paid for their participation. 2.1.2. Apparatus Stimuli were displayed on a 1400 VGA monitor, placed at about 60 cm distance from the participants’ eyes. The response device consisted of a small box (width: 11.5 cm, length: 15 cm) which was slightly tilted toward the participant with a height of 1.5 cm at the near end and a height of 3 cm at the far end. Two rows of ‘upper’

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and ‘lower’ keys (1:5  1:5 cm) were let in this box. The lateral distance between the two keys of each row was 6.5 cm, and the distance between the two rows was 6 cm. Only the two lower keys were used as response keys. The experiment was controlled by a 486 microcomputer. 2.1.3. Tasks and stimuli The experimental tasks were created by a factorial combination of the type of judgment (numerical vs. spatial) and the judgment-to-response mapping (compatible vs. incompatible). In each trial, the imperative stimulus consisted of one central and one peripheral digit. Digits were of height 1.2 cm and of width 1.0 cm. The central digit was presented above or below a central fixation star with a vertical separation of about 3 mm. The peripheral digit appeared to the left or to the right of the central digit with a horizontal separation of about 3 mm. Participants were instructed to judge the numerical value of the central digit whenever the digits appeared above the center of the screen. This numerical judgment required a decision whether the central digit was of the set f1; 2; 3; 4g or of the set f6; 7; 8; 9g. Participants were instructed to judge the spatial position of the peripheral digit relative to the central one whenever the digits appeared below the center of the screen. The judgment-to-response mapping was cued by color. When the digits were green, participants were required to apply the compatible mapping. When the digits were red, they were to apply the incompatible mapping. Both digits were always presented in the same color. Based on the fact that smaller numbers tend to elicit a leftward response and larger numbers a rightward response (Dehaene, Bossini, & Giraux, 1993), for the numerical task the compatible mapping was defined according to these tendencies. 1 For the incompatible mapping this assignment was reversed. The compatible mapping was reinforced by displaying the digits 1, 2, 3, 4 at the bottom left side and the digits 6, 7, 8, 9 at the bottom right side of the monitor throughout a block of trials. When the central digit was ‘small’, that is, from the range 1 to 4, the left key of the lower row of keys had to be pressed with a compatible mapping (green digits), whereas the right key of the lower row of keys had to be pressed with an incompatible mapping (red digits). Correspondingly, when the central digit was ‘large’, that is, from the range 6 to 9, the right key had to be pressed with a compatible mapping, whereas the left key had to be pressed with an incompatible mapping. For the spatial task, a compatible mapping required a ‘left’ response to a left peripheral digit and a ‘right’ response to a right peripheral digit. With an incompatible mapping, this assignment was reversed. The keys were pressed with the index fingers of the left and right hands. 2.1.4. Design and procedure Each participant took part in two sessions on two consecutive days. Each session was subdivided into a training phase and a test phase. The training phase of the first 1 Meanwhile we have learned that these response tendencies cannot always be observed. However, this issue is not crucial for the present topic.

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day consisted of 128 blocks of five trials each, the training phase of the second day served as a warm-up and lasted about 10 min after which it was terminated by the experimenter. Each test phase consisted of 256 blocks of five trials each. Blocks in which an error occurred were repeated at the end of the session. In each block, either the third or the fourth trial was the potential shift trial. The term ‘potential shift trial’ refers to the fact that the possible shifts resulted from a factorial combination of the factors: previous type of judgment (same vs. different, relative to the trial before the shift) and previous mapping (same vs. different), leading to 25% of blocks in which no task shift was required. The 256 blocks of the test phase resulted from a factorial combination of the factors: type of judgment in the potential shift trial (numerical vs. spatial), mapping in the potential shift trial (compatible vs. incompatible), serial position of the potential shift trial (3 vs. 4), response in the potential shift trial (left vs. right), previous response (same vs. different), next response (same vs. different) and the already mentioned factors, previous type of judgment and previous mapping. In the training phases, a random subset of these blocks was presented. When the potential shift occurred in the third trial, responses in trials 1 and 5 of the block were determined randomly; when the potential shift occurred in trial 4, the responses of the first two trials were chosen randomly. Of the experimental factors, serial position, response and next response served only to balance conditions and were not included in the analyses. Blocks were separated from each other by 5-second intervals during which the monitor switched 10 times between the colors blue and gray at an irregular pace. A block was initiated by simultaneously pressing both upper keys with the two index fingers. This procedure served to segregate the individual blocks and to make higherorder sequential dependencies inoperative. The response–stimulus interval (RSI) was 500 ms.

2.2. Results 2.2.1. Reaction times Our analyses were restricted to the potential shift trials. Nevertheless, whenever an error occurred in any of the five trials which constituted a block, this block was discarded from the analysis of reaction times. We furthermore screened reaction times for outliers. First, all reaction times longer than 2.5 s were discarded. In a second step, for each participant and each factorial combination of the five experimental factors (see below) the means and standard deviations were computed and reaction times longer than three standard deviations above the mean were discarded; this procedure was repeated until no more reaction times fell above this criterion. In total, this resulted in an exclusion of 1.7% of trials. The statistical analyses were based on the means of the remaining trials. Individual mean reaction times were determined for each combination of the factors: judgment (numerical vs. spatial), mapping (compatible vs. incompatible), previous judgment (same vs. different), previous mapping (same vs. different), and previous response (same vs. different).

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In a first analysis we averaged for each participant and each relation between successive tasks the mean reaction times of the four tasks. The means across participants are given in Table 1 as a function of the relation between successive tasks. First, whenever the type of judgment was changed, reaction time was longer than when the type of judgment was repeated. Second, when the mapping was changed, this resulted in an increased reaction time when the type of judgment was repeated, but a reduced reaction time when the type of judgment was changed. Third, a response alternation resulted in reaction-time costs when only the response was changed, but in reaction-time benefits when any other task characteristic was changed as well, although these benefits were not fully consistent across the other changes. In terms of the relational factors, previous type of judgment (same vs. different), previous mapping (same vs. different), and previous response (same vs. different), the characteristic shift-cost profile of Table 1 results in a set of rather complex interactions. However, more straightforward analyses are suggested by theoretical considerations. In Table 1 are also given the theoretical durations of task selection and implementation according to our account of shifting among a set of dimensionally organized tasks. This account results in a simple additive model: RT ¼ RT0 þ DS þ DI , with RT0 as baseline for repetitions, DS as the duration of task selection (which is an integer multiple of the switch duration TS ), and DI as the duration of implementation (either 0; TM or TJ ). The simple additive model can be fitted to the observed mean reaction times, and the results as well as the parameter estimates are shown in Table 1. The fit is reasonably well (RMSE: 11.2 ms, r2 ¼ :996), and deviations occur mainly when either the response or the mapping changes in addition to the type of judgment. Of course, a reasonable fit of a set of eight data points with a four-parameter model is in no way surprising. Of more importance is that the formal representation of our account of shifting among a set of dimensionally organized tasks makes obvious the constraints which the theoretical considerations impose on the data (cf. Roberts & Pashler, 2000). Such constraints exist, first, with respect to the model parameters. Specifically, we assume that implementation of a new kind of judgment implies implementation of a new mapping of the outcomes of the judgments to the responses. Thus, the constraint is TJ > TM (or in a weaker version: TJ P TM ). In addition, the duration of switching operations should be larger than zero. For a statistical examination of the constraints on model parameters we fitted the model to the individual mean reaction times of each participant. (Mean RMSE of the fit was 18.4 ms, range from 8.7 to 34.9 ms for the 16 participants.) The mean of the estimated switching duration, TS , was 23 ms, with the 95-% confidence interval ranging from 14 to 33 ms. The mean of the estimated duration of implementing a new type of judgment, TJ , was longer than the mean of the estimated duration of implementing a new mapping, TM , 401 vs. 304 ms, the difference being significant, tð15Þ ¼ 6:3, p < :01. Given the constraints on the parameters, the simple model also predicts particular reaction-time differences between sub-sets of the eight relations between successive tasks. We examined these predictions by means of a series of contrasts. First, from Table 1 it is apparent that a change of the mapping with a repeated type of judgment should be associated with a longer reaction time than a repetition of the mapping

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(theoretically the reaction-time difference is TM þ TS ). The corresponding contrast was highly significant, F ð1; 15Þ ¼ 285:0, p < :01. Second, a change of the type of judgment together with a change of the mapping should be associated with a longer reaction time than a repetition of the type of judgment when the mapping changes (theoretically the reaction-time difference is TJ  TM ). Again the corresponding contrast was highly significant, F ð1; 15Þ ¼ 26:6, p < :01. Third, and perhaps most important, a change of the mapping with an alternated type of judgment should be associated with a shorter reaction time than a repetition of the mapping (theoretically the reaction-time difference is TS ). In this case again the contrast reached statistical significance, F ð1; 15Þ ¼ 43:0, p < :01. A final set of four contrasts was computed for trials with repeated and alternated responses, separately for the four relations between type of judgment and mapping. (According to Table 1 the theoretical differences are TS .) The response–alternation costs when both the type of judgment and the mapping were repeated were significantly different from zero, F ð1; 15Þ ¼ 20:5, p < :01, as were the response–alternation benefits when only the mapping was changed, F ð1; 15Þ ¼ 4:6, p < :05. However, the expected response–alternation benefits when the type of judgment was changed were absent (with repeated mapping) or present, but non-significant (with alternated mapping). 2 The present analysis is focused on the shift costs as a function of the relation between successive tasks. Thus it is appropriate to abstract from the specific tasks by way of averaging. For example, average shift costs for shifts from A to B and from B to A can be attributed to the relation between A and B, while the separate costs of shifting from B to A and from A to B do not only reflect relational effects, but also task-specific ones like differences in implementation durations for tasks A and B or differences between switching durations. Nevertheless, we wanted to ascertain that the characteristic shift-cost profile of Table 1 does not only accrue from a subset of the four tasks. Of course, for each individual task it can be somewhat distorted by task-specific effects; in addition, the profile for each individual task is noisier than the mean profile. The shift-cost profiles for the four tasks as a function of the relation to the preceding task are shown in Fig. 1. For each task we ran the same set of contrasts as for the mean shift-cost profile. The results are shown in Table 2. While both the reaction-time costs of a change of the mapping with repeated type of judgment (contrast 1) and of the change of the type of judgment with alternated mapping (contrast 2) were consistently significant or almost so across the four tasks, the reaction-time benefits of a change of the mapping with alternated type of judgment (contrast 3) were significant in only three of the four tasks. Of the contrasts between repeated and alternated responses only a minority were significant. However, all significant contrasts were associated with the expected differences between the mean reaction times. Whenever there were differ2 In a general ANOVA, the crucial interaction of previous judgment and previous mapping was significant too, F ð1; 15Þ ¼ 327:27, p < :01, as were the interactions of previous judgment, previous mapping, and previous response, F ð1; 15Þ ¼ 8:81, p < :05, and of previous mapping and previous response, F ð1; 15Þ ¼ 7:07, p < :05.

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Fig. 1. Experiment 1: Mean reaction times as a function of previous type of judgment (J), previous mapping (M), and previous response (R), shown separately for the four tasks.

ences between reaction times that did not conform to the expectations based on the model, these differences did not only fail to approach statistical significance, but they were numerically small in addition. 2.2.2. Errors Error frequencies in the potential shift trials were referred to 256 blocks of trials in each session, while the blocks of trials which were appended because in the original blocks errors occurred in one of the serial positions were neglected. In addition, those blocks of trials were neglected in which the potential shift trials were preceded by an error.

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Table 2 Results of reaction-time contrasts computed separately for the four dimensionally organized tasks (type of judgment/mapping) Task

1

2

3

4a

Numerical/compatible Numerical/incompatible Spatial/compatible Spatial/incompatible

xx xx xx xx

(x) xx xx xx

xx

xx xx

xx xx

4b

x

4c

4d

x

(1) Repeated vs. alternated mapping with repeated type of judgment; (2) Repeated vs. alternated type of judgment with alternated mapping; (3) Repeated vs. alternated mapping with alternated type of judgment; (4) Repeated vs. alternated response with repeated type of judgment and mapping (a), repeated type of judgment and alternated mapping (b), alternated type of judgment and repeated mapping (c), and alternated type of judgment and mapping (d). xx p < :01; x p < :05; ðxÞ p < :10.

While the model of Table 1 provides a guidance for the analysis of reaction times, it does not so for the analysis of error rates. However, regarding the costs and benefits of response repetitions and alternations, these seem to be reflected in reaction times and/or error rates (Rogers & Monsell, 1995). The same could hold for the costs and benefits of repetitions and alternations of other task characteristics. Thus, we analyzed error percentages by means of the same set of contrasts as reaction times. As is apparent from Table 1, with a repeated type of judgment a change of the mapping was associated with a higher error rate than a repeated mapping, F ð1; 15Þ ¼ 10:8, p < :01. Second, a change of the type of judgment together with a change of mapping was associated with a smaller rather than a higher error percentage than a change of only the mapping, F ð1; 15Þ ¼ 8:9, p < :01. Third, a change of the mapping with an alternated type of judgment was also associated with a smaller error percentage than a repeated mapping, F ð1; 15Þ ¼ 5:8, p < :05. The differences between repeated and alternated responses closely matched the corresponding reaction-time differences. However, none of the four contrasts reached statistical significance. Statistical significance was approached when both the judgment and the mapping alternated, F ð1; 15Þ ¼ 3:8, p < :10, and when only one of these task characteristics was alternated the probability of wrong acceptance of the hypothesis of mean error rates being different was less than .15.

2.3. Discussion The purpose of the first experiment was to explore the robustness of the pattern of shift costs which can be observed when shifts are among a set of dimensionally organized tasks. In particular the procedure was designed to exclude a number of potential artefacts that can arise when there is no strict control over the context of shift and non-shift trials and/or the context for these two types of trials is not strictly equated. The advantage of the present procedure is that shift and non-shift trials occur after exactly identical series of preceding trials; shift and non-shift trials are

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taken from identical serial positions, and there is no reason to suspect that expectations of shifts may differ when shift and non-shift trials are presented (as, for example, is the case with the alternating-runs procedure). The fact that with the improved methodology the shift-cost profile, which we have observed earlier with a procedure subject to potential artefacts (Kleinsorge & Heuer, 1999), showed up again, lends credibility to the hypothesis that it indeed reflects the durations of processes of taskset reconfiguration rather than, for example, lagged effects of preceding task shifts. The shift-cost profile can be accounted for by a simple kind of model which is additive in its component times, although it produces a rather complex interactive pattern of effects of the experimental variables. The model embodies a distinction between two different processes. The first process serves to select the appropriate task representation. This process is hypothesized to consist of a number of switching operations among the dimensionally organized task representations. These switching operations are likely to be of two kinds. Primary switching operations occur at the highest level of the hierarchy of task dimensions where an alternation occurs, and they generalize to all lower levels. Corrective switching operations follow when the primary switching operations have induced inappropriate generalized switches at lower-level task dimensions. The second process serves to make the selected task representation operative. However, the estimated durations of these implementation operations may reflect additional processes. For example, differences in the times needed to identify task cues may contribute to them. Thus, at present the category of implementation operations covers a range of processes the nature of which has to be determined yet. Importantly, not everything we subsume under the label of implementation operations has to run off after the switching operations have taken place, although we think that the largest portion of what we call implementation is indeed a consequence of having selected an appropriate task set. Formally it is important to note that the implementation operations account for most of the variability in the shift-cost profile. However, they do not account for the small variations superposed on the large differences between repeated tasks, alternated mappings, and alternated types of judgment. These small variations reflect the switching operations in the dimensionally organized task space. It is apparent that our formal account of shifting among dimensionally organized tasks is a simplified approximation to reality. For example, there is no reason to claim that the assumption of identical durations of all sorts of switches is correct in any strict sense, but the differences may be rather small and thus negligible. After all, the purpose of the formal representation is not to reach an excellent quantitative fit, but to capture the major ideas of a distinction between switching operations and implementation operations and of a distinction between generalizing primary switching operations and non-generalizing corrective ones. Thus, the formalism is not a purpose in itself, but it serves to clarify the observable consequences of the theoretical claims and to guide the data analysis accordingly. The error profile turned out to be essentially parallel to the reaction-time profile, so that the latter cannot be attributed to a speed–accuracy tradeoff. However, a major difference between the reaction-time profile and the error profile was that error

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rates were not increased when the judgment was changed as compared to a change of the mapping. For this there is a simple methodological reason. When participants respond according to the wrong mapping, all responses will be errors (as long as they are correct according to the wrong mapping). But when they respond according to the wrong type of judgment, only 50% of the responses will be errors, because the irrelevant stimulus attribute varied randomly, so that in about 50% of the trials responses to the irrelevant attribute were identical to the (correct) responses to the relevant attribute.

3. Experiment 2 The purpose of the second experiment is to relate our distinction between switching operations and implementation operations as components of task-set reconfiguration to other process distinctions. Specifically we ask whether our distinction is identical to the distinction between endogenous and exogenous processes of taskset reconfiguration (Rogers & Monsell, 1995). Although the distinction between endogenously and exogenously controlled processes of task-set reconfiguration is quite clear operationally, namely their independence versus dependence on the presentation of the imperative stimulus, the functional difference between these types of processes is largely unknown. Rogers and Monsell (1995, p. 229) proposed that the endogenous and exogenous components of shift costs basically reflect parts of the total duration of the same ‘‘stagelike process of reconfiguration’’ whose ‘‘completion can be triggered only exogenously by the arrival of a stimulus suitably associated with the task’’. Contrary to that, Meiran (1996, p. 1439) interpreted the (sometimes very small) residual costs for task shifts he observed ‘‘as reflecting retroactive adjustment’’, a process that – at least as we interpret it – should be functionally distinct from advance configuration. Finally, in the model of Rubinstein et al. (2001), the endogenous component of shift costs is attributed to a process – goal shifting – which is clearly distinct from the process of rule activation which should result in the exogenous component of shift costs. On a descriptive level there is an obvious similarity of our distinction between switching operations, which serve to select an appropriate task representation, and implementation operations on the one hand and the distinction of Rubinstein et al. (2001) between goal shifting and rule activation on the other hand. However, the databases for the two distinctions are grossly different. While our distinction is based on a characteristic profile of shift costs for a set of dimensionally organized tasks, or on a certain pattern of interactive effects of different kinds of relations between successive tasks, the distinction of Rubinstein et al. is based largely on additive effects of task precues and complexity of rules on shift costs. This led them to relate their functionally defined hypothesized processes to the operationally defined classes of endogenously and exogenously controlled processes. The present experiment is designed to answer the question whether our distinction can be mapped on the distinction between endogenously and exogenously controlled processes in the same way. The procedure to answer this question is rather straightforward. In one condition

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we determined the shift-cost profile when the participants were informed about the required kind of judgment and mapping concurrently with the imperative stimulus, while in the second condition the information about the next task was provided by precues. An affirmative answer to our question requires that the precues serve to modify the shift-cost profile in a particular way. Specifically, switching operations related to the selection of the type of judgment and the mapping should be absent, while only switching operations related to the selection of responses (which were not precued) and implementation operations should remain. In terms of the simple additive model this amounts to the expectations that, first, the duration of task selection is reduced to 0 or TS , and second, that the implementation durations TM and TJ remain unchanged when task precues are presented. Unfortunately the apparently straightforward procedure requires that all participants exploit the opportunity for advance task-set configuration that is provided by the precues in all trials. However, this requirement is unlikely to be satisfied. For example, Rogers and Monsell (1995) found a reduction of shift costs with long preparation intervals only when their duration was constant during a block of trials, but not when short and long preparation intervals were mixed. This suggests that advance preparation is strategic, but not mandatory. More recently, De Jong (2000) argued that residual shift costs, which remain even after long preparation intervals, result more or less completely from failures to prepare for a forthcoming task. This argument was based on the observation that the reaction-time distribution in shifttrials with long preparation intervals could be represented as a mixture of reactiontime distributions in shift-trials with short preparation intervals (duration of task-set configuration included in reaction times) and reaction time distributions in non-shift trials (duration of task-set configuration not included in reaction times). Thus, in shift trials with long preparation intervals residual shift costs are clearly present when the longest reaction times only are compared with those in non-shift trials, but more or less absent when only the shortest reaction times are compared; mean reaction times, of course, represent a kind of intermediate. As a consequence of the strategic nature of advance task-set configuration, mean reaction times observed for precued trials should be intermediate between those expected and those observed without precues. However, the analysis of De Jong (2000) does also suggest a procedure which at least ameliorates the problem: in precued trials it is mainly the right tail of the reaction-time distribution which is affected by failures to make use of the precues, while the left part of the distribution should mainly comprise reaction times of trials with advance task-set configuration. Therefore we supplemented the analysis of individual mean reaction times of each condition by an analysis of individual first quartiles, which should be less affected by failures of advance configuration. 3.1. Method 3.1.1. Participants Eleven female and 13 male participants took part in the experiment. Their mean age was 23.0 years (range: 19–27 years). They were paid for their participation.

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3.1.2. Tasks and stimuli Apparatus, tasks, and stimuli were the same as in Experiment 1 (Section 2), except that the RSI was 1500 rather than 500 ms. When precues were presented at the beginning of the precue interval (PCI) of 1200 ms, the fixation star was replaced by a red or green arrow (length: 4 mm) which pointed up or down. The direction of the arrow cued the location of the imperative stimuli and thus the type of judgment required; its color cued the color of the imperative stimuli and thus the judgment-toresponse mapping. 3.1.3. Design and procedure Each participant took part in two sessions on two consecutive days. Each session consisted of a training phase and two test phases of 128 blocks each. In the test phases, blocks in which an error occurred were repeated at the end of the phase. Sequences of blocks were constructed as for Experiment 1 (Section 2), except that the serial position of the potential shift trial (third or fourth) was determined randomly for each block within a sequence of 128 blocks with the constraint of equal frequencies and not fully crossed with the other factors that were used for the construction of blocks of trials. Trials were separated by an RSI of 1500 ms which included a precueing interval (PCI) of 1200 (condition with precues) or 0ms (condition without precues). In the latter condition the colored arrow appeared simultaneously with the imperative stimulus. PCI was varied between sessions, with order counterbalanced across participants. 3.2. Results 3.2.1. Reaction times As in Experiment 1 (Section 2), we restricted our analysis to the potential shift trials and screened the data for errors and outliers (3.8% of trials). For each participant and each of the 32 combinations of four tasks and eight relations to the preceding task we determined the mean reaction time and in addition the first quartile of the reaction-time distribution, separately for the trials with 0 ms and 1200 ms PCIs. For the following analyses the means and the first quartiles for the four tasks were averaged because only these averages capture the effects of the relation between successive tasks unconfounded by task-specific effects. The means across participants are shown in Table 3 together with the expected values based on the simple additive model. We shall report the results in detail first for the individual means and thereafter for the individual first quartiles. 3.2.2. Reaction times: individual means As shown in Fig. 2(a), without precues (PCI of 0 ms) the characteristic profile of shift costs showed up again, although the RSI (1500 ms) was considerably longer than in Experiment 1 (500 ms) (Section 2). The simple additive model again provided a reasonable fit (RMSE: 10.7 ms, r2 ¼ :998). When fitted to the individual data of the 24 participants (mean RMSE: 43.9 ms, range: 15.1–98.5 ms), the mean estimate of the switching duration, TS , was 39 ms, with the 95-% confidence interval ranging

Relation J

Mean RT M

R

First RT quartile

PCI ¼ 0

PCI ¼ 1200 a

PCI ¼ 0 b

Error percentage PCI ¼ 1200

c

PCI ¼ 0

PCI ¼ 1200

d

Obs.

Pred.

Obs.

Pred.

Obs.

Pred.

Obs.

Pred.

¼ ¼ ¼ ¼

¼ ¼ 6¼ 6¼

¼ 6¼ ¼ 6¼

608 622 1110 1060

595 634 1105 1066

547 548 734 713

540 555 731 716

463 487 892 864

459 491 894 862

407 418 511 492

409 417 506 498

2.02 1.32 7.79 2.56

1.12 2.20 5.55 4.15

6¼ 6 ¼ 6 ¼ 6¼

¼ ¼ 6¼ 6¼

¼ 6¼ ¼ 6¼

1287 1224 1219 1201

1272 1233 1233 1193

811 798 759 777

801 786 786 771

1042 1017 1010 971

1042 1010 1010 978

519 520 495 511

519 511 511 503

3.01 2.35 1.87 1.67

2.95 2.18 4.04 1.20

a

Parameters: RT0 ¼ 595 ms, TS ¼ 39:4 ms, TM ¼ 431 ms, TJ ¼ 559 ms. Parameters: RT0 ¼ 540 ms, TS ¼ 14:9 ms, TM ¼ 161 ms, TJ ¼ 216 ms. c Parameters: RT0 ¼ 459 ms, TS ¼ 32:3 ms, TM ¼ 371 ms, TJ ¼ 487 ms. d Parameters: RT0 ¼ 409 ms, TS ¼ 7:8 ms, TM ¼ 81 ms, TJ ¼ 87 ms. b

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Table 3 Observed and predicted mean reaction times and first quartiles as well as error rates for the different relations between successive tasks without (PCI ¼ 0 ms) and with (PCI ¼ 1200 ms) task precues

17

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Fig. 2. Experiment 2: Mean reaction times and first reaction time quartiles as a function of previous type of judgment (J), previous mapping (M), and previous response (R), (a) without precue, (b) with precue.

from 18 to 61 ms (cf. Table 3). The mean estimates of the implementation durations TM and TJ were 431 and 559 ms, respectively, the difference being highly significant, tð23Þ ¼ 5:8, p < :01. With precues (PCI of 1200 ms) the shift-cost profile was flatter (cf. Fig. 2(b)). We fitted the additive model again, though – depending on the particular assumptions about advance task-set configuration – it is not fully adequate. However, the inadequateness should not necessarily reduce the goodness of fit considerably, but should be reflected mainly in the parameter estimates. In particular, when with the long PCI

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the number of switching operations is indeed reduced, this should result in a smaller estimate of the switching duration, and when implementation operations are indeed exogenous in nature, the estimated durations with the long PCI should not differ from the estimated durations with the zero PCI. As shown in Table 3, the fit of the model to the mean reaction times was still reasonable (RMSE: 12.0, r2 ¼ :985), but the parameters did not fully conform to expectations. From the fits to individual data (mean RMSE: 51.9 ms, range: 19.7–116.1 ms), the mean estimate of the switching duration, TS , was 15 ms. This was not significantly different from zero, the 95% confidence interval ranging from )7 to 37 ms, but also not significantly smaller than the 39 ms observed without task precues. The mean estimates of the implementation durations TM and TJ were 161 and 216 ms, respectively, again the difference being significant, tð23Þ ¼ 3:7, p < :01. Contrary to expectations both these estimates were significantly smaller than without precues, tð23Þ ¼ 7:8, p < :01, and tð23Þ ¼ 8:7, p < :01, respectively. In addition, the difference between the two kinds of implementation costs was significantly smaller with (55 ms) than without (128 ms) precues, tð23Þ ¼ 2:6, p < :05. Thus, the durations of implementation operations were reduced and became more similar when advance taskset configuration was possible. We computed the same series of contrasts as in Experiment 1 (Section 2) . In addition we compared the contrasts in the no-precue and precue conditions. First, when the type of judgment is repeated, a change of the mapping should be associated with reaction-time costs. This was the case both without, F ð1; 23Þ ¼ 121:4, p < :01, and with precues, F ð1; 23Þ ¼ 103:3, p < :01. In addition, the costs were higher without than with precues, F ð1; 23Þ ¼ 70:1, p < :01. Second, when the mapping is changed, a change of the type of judgment should be associated with a longer reaction time than a repetition of the type of judgment because of the difference in implementation durations (TJ > TM ). This difference should be unaffected by the presence of precues, provided that only switching operations are endogenously controlled. The respective contrast was highly significant without precues, F ð1; 23Þ ¼ 37:2, p < :01, as well as with precues, F ð1; 23Þ ¼ 9:2, p < :01. Nevertheless, as is apparent from Table 3, the reaction-time difference was larger without than with precues, F ð1; 23Þ ¼ 7:3, p < :05. Third, when the type of judgment is changed, a change of the mapping should be associated with shorter reaction times than a repetition of the mapping. This difference should be due to a difference in the number of switching operations and not be observed in precue conditions. The respective contrast was highly significant without precues, F ð1; 23Þ ¼ 13:0, p < :01, and just failed to reach statistical significance with precues, F ð1; 23Þ ¼ 4:0, p < :10. The interaction was non-significant, F < 1. The reaction-time differences between response repetitions and alternations conformed to expectations without precues, although they did not always reach statistical significance. Only the reaction-time costs of response repetitions when the mapping was changed, but not the type of judgment, F ð1; 23Þ ¼ 4:8, p < :05, and when the type of judgment was changed, but not the mapping, F ð1; 23Þ ¼ 10:7, p < :01, were significant. With precues the response–repetition benefits and costs did not always conform to expectations and in no case even approached statistical

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significance. The same was true for the four interaction contrasts to compare the response–repetition benefits and costs in conditions without and with precues.

3.2.3. Reaction times: individual first quartiles The analysis of the individual reaction-time means revealed a flattening of the shift-cost profile in conditions with task precues that was not only due to a reduced number of switching operations, but also to shorter durations of implementation operations. While individual mean reaction times are affected by trials in which the information provided by the precues is not exploited for advance task-set configuration, for the individual first quartiles of the reaction-time distributions in the various experimental conditions this confound is absent or at least weaker. Thus, the tendency of the shift-cost profile to flatten out should be intensified provided that it is indeed due to advance task-set configuration. Without precues (PCI of 0 ms) the mean first quartiles exhibited the characteristic shift-cost profile (cf. Fig. 2(a)), and – as is evident from Table 3 – the simple additive model provided an excellent fit (RMSE: 4.2 ms, r2 ¼ :9996). When fitted to the individual data of the 24 participants (mean RMSE: 29.2 ms, range: 11.5–58.4 ms), the mean of the estimated switching duration, TS , was 32 ms, with the 95-% confidence interval ranging from 19 to 46 ms. The mean estimates of the implementation durations TM and TJ were 371 and 487 ms, respectively, the difference being highly significant, tð23Þ ¼ 9:0, p < :01. With precues (PCI of 1200 ms) the simple additive model still provided a reasonable fit, as can be seen in Table 3 (RMSE: 7.7 ms, r2 ¼ :983), though the shift-cost profile was rather flat (Fig. 2(b)). From the fits to individual data (mean RMSE: 29.7 ms, range: 10.7–62.3 ms) the mean estimate of switching duration, TS , was 8 ms, with the 95-% confidence interval ranging from )8 to 24 ms. This estimate was thus not significantly different from zero, and it was significantly smaller than the 32 ms observed without precues, tð23Þ ¼ 2:5, p < :05. The mean estimates of implementation durations TM and TJ were 81 and 87 ms. The difference between implementation durations was not significant, tð23Þ ¼ 0:7, and both kinds of implementation durations were significantly smaller than in conditions without precues, tð23Þ ¼ 8:2, p < :01, and tð23Þ ¼ 12:3, p < :01, respectively. In addition, the difference between the two kinds of implementation costs was significantly smaller with (5 ms) than without (116 ms) precues, tð23Þ ¼ 8:8, p < :01. We computed the same set of contrasts as for the individual mean reaction times. First, with a repeated type of judgment the reaction-time costs associated with a change of the mapping were significant both without, F ð1; 23Þ ¼ 108:0, p < :01, and with precues, F ð1; 23Þ ¼ 53:9, p < :01, but without precues the costs were significantly higher than with precues, F ð1; 23Þ ¼ 75:8, p < :01. Second, with an alternated mapping there were reliable costs of a change of the type of judgment without precues, F ð1; 23Þ ¼ 73:5, p < :01, but not with precues, F ð1; 23Þ < 1; without precues the costs were significantly larger than with precues, F ð1; 23Þ ¼ 52:2, p < :01. Third, with an alternated type of judgment there were reliable benefits of a change of the mapping without precues, F ð1; 23Þ ¼ 15:6, p < :01, but not with precues, F ð1;

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23Þ ¼ 2:4, p > :10; however, the interaction failed to reach statistical significance, F ð1; 23Þ ¼ 2:3, p > :10. The reaction-time differences between response repetitions and alternations conformed to expectations without precues, but did not always reach statistical significance. Only the response–repetition benefits with repeated type of judgment and repeated mapping, F ð1; 23Þ ¼ 5:3, p < :05, as well as the response–repetition costs with alternated type of judgment and alternated mapping, F ð1; 23Þ ¼ 8:4, p < :01, were significant. With precues the reaction-time differences between response repetitions and alternations did not consistently conform to expectations, and the corresponding contrasts did in no case even approach statistical significance. Comparing conditions without and with precues, there was a single significant interaction contrast: with alternated type of judgment and alternated mapping the response– repetition costs observed without precues were significantly different from the response–repetition benefits observed with precues F ð1; 23Þ ¼ 7:0, p < :05. The mean first quartiles of the individual reaction-time distributions, as shown in Fig. 2, together with the analysis of the model parameters and the series of contrasts, do strongly suggest that the characteristic reaction-time profile as a function of the relation between successive tasks is essentially absent when precues are presented and the data are only little confounded by trials without advance configuration of task sets. The only effect of the relation between successive tasks which remained in the presence of task precues was an increase of reaction time of the order of 100 ms whenever the type of judgment and/or the mapping was changed. In fact, post hoc analyses of the data obtained with the PCI of 1200 ms revealed that there were two sets of relations in terms of reaction times, those with repeated type of judgment and mapping, and those with at least one of these task characteristics being changed. Reaction times of each of the first set of relations were significantly different from reaction times of each of the second set of relations between successive tasks, while there were no significant differences between the reaction times for the relations within each of the two sets.

3.2.4. Errors Error percentages are shown in Table 3. As in Experiment 1 (Section 2), we analyzed them by means of the same set of contrasts as the reaction times. It is apparent from Table 3 that, when the kind of judgment was repeated, a change of the mapping was associated with a higher error rate than a mapping repetition both without, F ð1; 23Þ ¼ 11:9, p < :01, and with precues, F ð1; 23Þ ¼ 12:2, p < :01. The interaction failed to reach statistical significance, F ð1; 23Þ < 1. When the mapping was alternated, a change of the kind of judgment was associated with a smaller error rate than a repetition, again both without, F ð1; 23Þ ¼ 11:5, p < :01, and with precues, F ð1; 23Þ ¼ 10:6, p < :01. Although numerically this difference appeared smaller with the long PCI, the interaction was far from approaching significance, F ð1; 23Þ < 1. Finally, the difference between same and different mappings with an alternated type of judgment, which was significant in Experiment 1 (Section 2), failed to reach significance in both conditions with different PCIs.

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As in Experiment 1 (Section 2), the differences between repeated and alternated responses were somewhat inconsistent as far as their statistical significance was concerned. Without precues only one of the four contrasts reached significance, namely the response–repetition costs when only the mapping was changed, F ð1; 23Þ ¼ 13:8, p < :01. These response–repetition costs in addition were reliably larger than those observed with precues, F ð1; 23Þ ¼ 5:0, p < :05. With precues again only one of the four contrasts reached significance; this time it was the response–repetition costs when both the kind of judgment and the mapping were changed, F ð1; 23Þ ¼ 8:2, p < :01. They were reliably larger than those observed without precues, as indicated by a significant interaction, F ð1; 23Þ ¼ 4:5, p < :05. 3.3. Discussion The present experiment was designed to answer the question whether the distinction between switching operations and implementation operations, which is based on a characteristic profile of reaction-time costs for shifts among a set of dimensionally organized tasks, coincides with the distinction between endogenously and exogenously controlled processes of task-set reconfiguration, which is based on the effects of task precues on shift costs. The hypothesis of such a coincidence has been suggested by a model of Rubinstein et al. (2001) which claims that a process called goal shifting is endogenously controlled, but a process called rule activation exogenously. In terms of the functions subserved by these processes there is an apparent parallel between switching operations and goal selection as well as between implementation operations and rule activation. The data do not conform to this hypothesis. Without precues we again observed the characteristic profile of reaction times as a function of the relation between successive tasks both for individual means and first quartiles of reaction-time distributions. With precues the intricate modulations of the reaction times were reduced for the means and essentially absent for the first quartiles, which are less affected by trials in which the precues are not exploited for advance configuration of task sets. All what remained was a residual shift cost of the order of 100 ms whenever the type of judgment and/or the mapping were changed, independent of the particular relation between successive tasks. Thus, on the one hand both switching operations and implementation operations turned out to be largely endogenously controlled. On the other hand, the characteristic pattern of response–repetition benefits and costs which should have survived the introduction of task precues because responses were not precued was not clearly present. While implementation operations turned out to be largely endogenously controlled, this was not fully the case, but there remained residual shift costs. There are at least three possible explanations of this finding, and at present it is impossible to decide between them with a sufficient degree of certainty. First, according to De Jong’s claim, these residual shift costs could reflect failures of advance preparation (cf. De Jong, 2000). From the results obtained with the individual mean reaction times it is clear that such failures were present in this experiment. Although the use of first quartiles reduces the effects of failures of advance preparation on the

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data, it does not necessarily eliminate them. In fact, the unreliable variations of reaction times across the six relations between successive tasks with type of judgment and/or mapping being changed appear not fully random. For example, across the six relations the means observed with precues are still correlated with the means observed without precues (r ¼ 0:53). Thus, while there is no clear-cut evidence in favor of a role of failures of advance preparation, there is also no clear-cut evidence against it. Although De Jong (2000) found that residual shift costs could be fully accounted for in terms of failures of advance preparation, he also suggested that ‘‘true’’ residual shift costs might arise with other populations than young healthy adults or with more complex tasks than the ones he studied. From the perspective of ‘‘true’’ residual shift costs, our findings could simply imply that implementation operations are basically a homogeneous set of operations which, however, cannot be completed endogenously (cf. Rogers & Monsell, 1995). Alternatively, and perhaps more likely, what we have called ‘‘implementation operations’’ could be a set of heterogeneous processes, some of which are endogenously controlled, while others are exogenously controlled. If this view is correct, questions regarding the nature of the two kinds of processes arise. Thus far not many facts are known on which answers could be based. The analysis of individual first quartiles does strongly suggest that the two kinds of processes do differ in that the durations of the endogenously controlled processes depend on the relation between successive tasks, while the durations of the exogenously controlled processes exhibit no (reliable) dependence of this kind. Although the present experiments were focused on the relations between successive tasks rather than on shift costs associated with shifts between particular tasks, we examined task-specific effects in an exploratory manner. In particular we determined shift costs as a function of the new task. For each of the four combinations of the two types of judgments and the two judgment-to-response mappings we computed the overall residual shift costs. These were the differences between the mean first quartiles observed for all six relations to the preceding task with the type of judgment and/or the mapping being changed (the six rightmost quartile bars in Fig. 2(b)) on the one hand and the mean first quartiles observed for the two relations to the preceding task with the type of judgment and the mapping being repeated (the two leftmost quartile bars in Fig. 2(b)) on the other hand. The overall residual shift costs were 81, 205, 44 and 50 ms for numerical judgments with compatible and incompatible mappings and spatial judgments with compatible and incompatible mappings, respectively. A one-way ANOVA of these residual shift costs, which mainly reflect the durations of exogenously controlled processes, revealed that the differences between tasks were statistically significant, F ð3; 69Þ ¼ 33:9, p < :01. We performed the same computations for the conditions without task precues and found overall shift costs of 515, 597, 429, and 423 ms for the four tasks. The differences between the two conditions without and with precues give estimates of the components of shift costs which reflect the durations of (potentially) endogenously controlled operations (434, 392, 385, and 373 ms for the four tasks), and a

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one-way ANOVA revealed that these were not significantly different between tasks, F ð3; 69Þ < 1. Thus, we tentatively conclude that while the endogenous but not the exogenous components of the shift costs depend on the relation between successive tasks, the exogenous but not the endogenous components depend on the nature of the new task. Their order across tasks does roughly correspond to task complexity as indicated by the reaction times in repetition trials (cf. Fig. 1), with the numerical/incompatible task being of highest complexity and the spatial-judgment tasks of lowest complexity. Note that this pattern of results contrasts with the one usually interpreted as evidence for task-set inertia, where costs are higher for shifts to an easier task (e.g., Allport et al., 1994). However, this finding seems to be restricted to a rather narrow class of situations (cf. Monsell, Yeung, & Azuma, 2000), so it is not too surprising not to observe this finding in the present experiments. We repeated the same kind of analysis with the individual mean reaction times. If indeed the durations of exogenously controlled processes depend on the nature of the current task, while the durations of endogenously controlled processes do not, this should also be evident from the individual mean reaction times; the finding should be robust against confounds of the estimates of the durations of exogenously controlled processes by (potentially) endogenously controlled processes. In fact, the residual shift costs estimated from the individual means were 257, 319, 166, and 129 ms for numerical judgments with compatible and incompatible mapping and spatial judgments with compatible and incompatible mapping, respectively. The differences between tasks were highly significant, F ð3; 69Þ ¼ 14:2, p < :01. Without task precues the overall shift costs were 621, 685, 480, and 489 ms for the four tasks, and the differences between conditions without and with precues were 365, 366, 314, and 361ms. These estimates of the durations of endogenously controlled processes were not significantly different, F ð3; 69Þ < 1. Of course, these estimates are too short overall, because in a number of trials (potentially) endogenously controlled processes were not performed in advance of the imperative signal, so that their durations were included in the residual shift costs and added to the estimates of the durations of exogenously controlled processes. The observation that the exogenous components of shift costs were largely dependent on the current task is inconsistent with the assumption that residual shift costs depend mainly on the characteristics of the previous task (e.g., Allport et al., 1994; Wylie & Allport, 2000). Although the reasons for this discrepancy are not entirely clear, perhaps one important factor in this respect is task complexity. Although at present this is a speculation, episodic carry-over effects may be especially pronounced with very simple tasks while active reconfiguration processes become more important with more complex tasks, with our tasks being relatively complex compared to other tasks usually employed in task-shifting research. The present data do only weakly constrain functional interpretations of endogenously and exogenously controlled implementation operations. However, one of the apparent possibilities is that the endogenously controlled operations serve to implement the basic task-control structure, that is, the neural network which is required for successful performance of the forthcoming task, while the exogenously controlled operations provide some consolidation or retroactive adjustment (Meiran, 1996) of

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the implemented control structures. The benefits that arise from such a process, that is, the reduction of reaction time by performing a task repeatedly (at least once), should be related to the complexity of the control structure and thus likely to the complexity of the task, but not to the task in preceding trials. According to these considerations implementation operations can be subdivided into configuration of a task-control structure, which is an endogenously controlled process and does not depend on task complexity, and facilitation of the configured task-control structure, which is necessarily an exogenously controlled process because it requires that the control structure be put to use. While the residual shift costs turned out to be independent of the relation between successive tasks, this was not the case for the error rates in conditions with task precues. In fact, the error profiles observed in conditions without and with precues did not differ consistently, and even the few statistically significant differences appeared not particularly systematic. Given that error rates are often somewhat unreliable, it is not really justified to base any firm conclusion on these findings, except, of course, that the reaction-time profile cannot be attributed to a speed–accuracy tradeoff. In addition, the error data are confounded by failures of advance preparation. While for the reaction times it is possible to avoid such a confound at least to some degree by way of focusing the analysis on the faster reaction times, a similar procedure is not possible for the error data. Finally, with task precues the characteristic pattern of response–repetition benefits (when type of judgment and mapping are repeated) and response–repetition costs (when type of judgment and/or mapping are changed) was largely absent. Although this pattern tends to be somewhat unreliable across experiments, it was clearly present without precues, and with task precues there were exceptionally clear deviations. This finding was unexpected because responses were not precued. It can be taken to suggest that task precues are processed differently than task cues, perhaps without generalizing switches which account for the response–alternation benefits in taskshift trials. But the findings on response–repetitions costs and benefits are too unstable to allow any firm conclusion at present.

4. General discussion The present experiments had been designed to corroborate and extend previous experimental findings on shifting among a set of dimensionally organized tasks and to substantiate and differentiate the theoretical considerations which had been suggested by the original results (Kleinsorge & Heuer, 1999). Experiment 1 (Section 2) served to eliminate a number of methodological concerns and to test the expectations based on the theoretical considerations in a more specific way than had been possible before. Experiment 2 (Section 3) showed that our distinction of switching operations and implementation operations does not coincide with the operational distinction of endogenously and exogenously controlled processes of shifting between tasks. Instead, both kinds of operations turned out to be largely endogenously controlled, although this was not fully the case for implementation operations.

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Beyond the additional evidence for a hierarchical switching mechanism presented in this article we recently were able to bolster our account against a specific alternative explanation in terms of episodic carry-over. This alternative account is based on the event-file concept of Hommel (1998) that was recently extended to an explanation of shift costs by P€ osse and Hommel (1999). According to these authors, the elementary features of stimuli and responses of a certain trial become bound into one or several episodic memory traces. When on a subsequent trial any of the features of the preceding trial is repeated this results in a retrieval of the corresponding episodic memory trace. There will be a mismatch of the retrieved information and the features of the current trial whenever some feature is repeated whereas another feature is changed across trials, with this mismatch leading to shift costs. Applied to our experiments, such a mismatch would occur whenever a change of only one of the task dimensions type of judgment and mapping is required. Thus, for both these relations between successive tasks reaction times should be longer than when a change of both the type of judgment and the mapping is required. In fact, our observation of especially high shift costs for a change of the type of judgment only (with mapping repeated) can well be accounted for in terms of episodic carry-over. However, the same line of reasoning would predict especially high shift costs for a change of the mapping only (with type of judgment being repeated). For this relation between successive tasks, however, shift costs were consistently smaller than for changes on both dimensions rather than longer. To further strengthen our approach against an explanation in terms of episodic bindings we recently conducted an experiment in which we employed three instead of two kinds of judgments, three instead of two mapping rules, and three response alternatives (Kleinsorge, Heuer, & Schmidtke, 2001, Exp. 2). When the shift-cost profile we observed with binary task dimensions is indeed a result of episodic bindings, a similar profile should be observed with three-valued task dimensions because a partial feature mismatch across subsequent trials should occur regardless of whether only one or two alternatives are available on a certain task dimension. A generalizing switching mechanism, in contrast, should break down with three-valued task dimensions because no ‘other’ value is uniquely specified on hierarchically lower task dimensions to which a generalized switch could be directed to. In line with this reasoning, and supporting our notion of generalizing switches, we observed shift costs monotonously growing as a function of the number of task dimensions on which a change took place across subsequent trials. (For minor modifications of this statement see Kleinsorge et al. (2001)). The latter observations provide evidence against an alternative explanation of our findings in terms of a specific form of episodic carry-over. Of course, this does not preclude that other forms of episodic carry-over effects occurred in our experiments. However, these should not have resulted in serious distortions of our results. First, our main conclusions are based on data that are averaged across particular transitions between specific tasks. This way, asymmetric carry-over effects like those reported by Allport et al. (1994) in favor of their concept of task-set inertia should have become leveled. Second, as observed in Experiment 2 (Section 3), the characteristic shift-cost profile we interpret as evidence for generalized switches is part of the

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endogenous component of shift costs and not subject to passive dissipation like episodic carry-over effects are assumed to be (e.g. Meiran et al., 2000). The fact that generalized switching apparently breaks down with three-valued task dimensions might be interpreted as severely limiting the applicability of our model to real-life situations. However, choices between only two alternatives are quite common in everyday life, and it is not too hard to find examples for binary decisions on two hierarchically ordered ‘dimensions’. For instance, a choice situation like ‘Will I visit John or Mary, and will I travel by car or by train’ is structurally analogous to the situations realized in our experiments. When one has first decided to visit John using the car but then gets a call by Mary asking to visit her, a tendency to do so by taking the train would be in line with a generalized switch. We have no relevant data to substantiate the plausibility of such a tendency with respect to realworld problems, and it should be noted that even in our experiments participants actually do not behave according to the response tendencies released by generalized switches but in most cases perform the required shift with the help of corrective re-switches. Nevertheless, the demonstration that the structure of our experimental situation can easily be transferred to real-life situations argues against the claim that the restriction to binary choices makes the model ecologically irrelevant. To summarize, at present our account of shift costs with hierarchically ordered task dimensions involves three kinds of processes. First, there are generalizing switching operations which serve to select the appropriate task representation and have the key property that switches on a higher level of a task hierarchy generalize upon lower levels and necessitate corrective re-switches whenever the feature represented on a lower level remains unchanged across trials. These switching operations are indexed by the costs of feature repetitions. Second, there is one kind of implementation operation that is endogenously controlled. The duration of this kind of implementation operation depends on the relation between successive tasks but not on the specific task that has to be performed. The estimates of this component of shift costs cover also those processes that are associated with the encoding of task (pre-)cues. (As mentioned above, we do not assume that all the processes we subsume under the label of implementation operations run off after the switching operations.) Third, there is a class of implementation operations that is exogenously controlled. Their duration depends on the complexity of the task to be performed but not on the relation between successive trials. This feature makes them similar to the process of rule activation postulated by Rubinstein et al. (2001), though ‘‘activation’’ then has to be understood in the narrow sense of ‘‘using the rule at least once’’ and not in the broader sense of ‘‘making the rule operative’’.

Acknowledgements We thank Dana Lembke for assistance in analyzing the data and Matthias Manka and Petra Wallmeyer for conducting the experiments. The research reported in this paper was supported by grant Kl 1205/1-1 of the Deutsche Forschungsgemeinschaft to the first two authors.

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