Inhibition of cued but not executed task sets depends on cue-task compatibility and practice

Berger, Alexander; Koch, Iring; Kiefer, Markus

doi:10.1007/s00426-024-02013-z

Inhibition of cued but not executed task sets depends on cue-task compatibility and practice

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Published: 30 July 2024

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Inhibition of cued but not executed task sets depends on cue-task compatibility and practice

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Abstract

In task switching, processing a task cue is thought to activate the corresponding task representation (“task set”), thereby allowing for advance task preparation. However, the contribution of preparatory processes to the emergence of n−2 repetition costs as index of task set inhibition processes is debated. The present study investigated whether merely preparing for a task activates a corresponding task set, which needs to be inhibited in order to switch to a different task. To this end, we presented so-called task cue-only trials in trial n−2 and assessed subsequent n−2 repetition costs. The results revealed n−2 repetition costs following a task cue-only, but only for compatible cues with a transparent cue-task relation and only at the beginning of the experiment. In contrast, n−2 repetition costs following task execution in trial n−2 were absent. In a second experiment, we sought to rule out that the presence of n−2 repetition costs following a task cue-only and the corresponding absence following task execution were the consequence of a decay of task sets. This second experiment replicated the result pattern of the first experiment, with n−2 repetition costs following a task cue-only being present only at the beginning of the experiment and only for compatible cues. Hence, cue-induced task set inhibition effects depended on cue-task compatibility and practice. Furthermore, merely prepared task sets were more likely inhibited than executed task sets.

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Introduction

The flexibility of the human cognitive system is often studied within the context of the task switching paradigm (Monsell, 2003). In this paradigm, participants have to perform at least two tasks and performance is usually impaired if the task switches compared to when it repeats, termed switch costs (Kiesel et al., 2010; Koch et al., 2018; Koch & Kiesel, 2022). In a widely used variant of this experimental procedure, the cued task switching paradigm, a task cue indicating the to-be-performed task is presented before the stimulus, therefore allowing in advance task preparation (Jost et al., 2013). Whether and how such preparatory processes contribute to task switching effects is a matter of debate (Jost et al., 2008, 2013; Logan & Bundesen, 2003; Schneider & Logan, 2005; Vandierendonck et al., 2010). The present study therefore elucidates such preparatory processes in task switching in more detail by investigating the involvement of cue-related processing on task set inhibition effects.

Measuring task set inhibition in task switching

In the context of task switching research, a task set can be defined as the cognitive configuration required for performing a particular task and includes, for example, relevant stimulus dimensions and response categories (Monsell, 2003; Rogers & Monsell, 1995). A common theory of task switching processes, termed task set reconfiguration, postulates that when switching tasks, the cognitive configuration needs to be endogenously changed in order to implement the new task set required in the current trial (Kiesel et al., 2010; Monsell, 2003; Vandierendonck et al., 2010). Following this view, the activation of the newly required task set must overcome the activation of the previous task set (when tasks switch) in order to be able to appropriately perform the new task. To this end, an inhibition of the task set (of the previous trial) is commonly assumed (Koch et al., 2010). Often, such inhibition mechanisms are studied using so-called n−2 repetition costs (Koch et al., 2010; Mayr & Keele, 2000).^{Footnote 1} n−2 repetition costs are investigated in task switching paradigms using three tasks and are defined as a worse performance in the last task (trial n) in task sequences of the ABA type (i.e. when the task repeats from trial n−2 to trial n) compared to CBA sequences (i.e. when the task switches from trial n−2 to trial n). This performance impairment in ABA sequences compared to CBA sequences is thought to reflect the inhibition of task set A during the transition from task A to B. As task set A was more recently inhibited in sequences ABA compared to CBA (in CBA sequences, the most recent execution of task A can be in trial n−3), it is more demanding to overcome this persisting inhibition in trial n, resulting in the above described performance decrements (Koch et al., 2010).

However, there is a debate regarding the processes contributing to n−2 repetition costs (reviewed in Koch et al., 2010; Vandierendonck et al., 2010). Among these processes, an inhibition of task sets, and episodic interference effects were discussed. A recent study directly tested the contribution of these processes on n−2 repetition costs (Schuch & Keppler, 2022), and found evidence for both top-down driven influences acting on the level of task sets (task set inhibition; see also Mayr, 2002) and more bottom-up, task- or stimulus-related influences (episodic interference; see also Grange, 2018; Grange et al., 2017). Continuing this debate, the present study tried to identify whether the sole activation of a task set is sufficient to produce n−2 repetition costs. Task set activation was realized in the present study by presenting task cue-only trials, i.e. task sets are only cued, but not executed as no task stimulus is presented, thereby ruling out any possible influences of task- or stimulus-related processes. Using this procedure, the present work aims to elucidate whether merely cued, but not executed task sets are similarly inhibited in preparation for a new task, as it is assumed for executed task sets. This question is relevant because previous evidence on the role of cue-related and response-related processes in task inhibition revealed inconsistent findings. We review these findings below.

Influence of preparatory processes on task set inhibition

Several lines of research have addressed the contribution of preparatory processes to n−2 repetition costs, using different approaches to estimate such an influence. As it is unlikely that n−2 repetition costs can be reduced to an inhibition of the cue representation itself (Gade & Koch, 2008), influences of preparatory processes on n−2 repetition costs probably act upon the ease or difficulty of reconfiguring task sets, not simply an encoding of cues. Regarding the detection of such an involvement of task preparation to n−2 repetition costs, studies first varied the cue-target interval (CTI), i.e. the time interval available for cue processing. In task switching with two tasks, switch costs are usually reduced with longer CTIs, indicating that participants use the additional time for cue processing to prepare for a task switch (Jost et al., 2013; Kiesel et al., 2010). For the influence of CTI on n−2 repetition costs, there is less consistency regarding the direction of this influence in the literature. For example, Gade and Koch (2014) provided an overview of published studies reporting the influence of a CTI manipulation on n−2 repetition cots, which showed a diverse pattern with increases and decreases of n−2 repetition costs with longer CTI. This inhomogeneity might be explained by additional factors modulating the influence of CTI on n−2 repetition costs like cue type (Gade & Koch, 2014) and the CTI in trials n−2 and n−1 (Scheil & Kleinsorge, 2014a).

Second, a go/no-go methodology was implemented (Philipp et al., 2007; Scheil & Kleinsorge, 2022; Schuch & Koch, 2003). The rationale was that stimulus processing (or at least response selection and execution) is terminated by the presentation of a no-go signal (the go-/no-go signal was presented either with or after stimulus onset), therefore elucidating to what degree task preparation processes are involved in n−2 repetition costs. In short, these studies showed that response selection and execution processes are relevant for the occurrence of n−2 repetition costs (Philipp et al., 2007; Schuch & Koch, 2003), suggesting that sole task preparation may not be sufficient for inducing task set inhibition (but see Scheil & Kleinsorge, 2022, for conflicting evidence, when no-go trials are bound to only one task).

Third, the influence of task preparation processes on n−2 repetition costs was also investigated by varying the cue itself. By manipulating task cue transparency / cue-task compatibility, i.e. how straightforward the relation of the task cue and associated decision categories is (Jost et al., 2013), it was investigated whether n−2 repetition costs depend on the supposed ease of task set activation in the cue interval. Similar to findings for switch costs (Gade & Steinhauser, 2020; Jost et al., 2013), n−2 repetition costs were reduced with more transparent / compatible cues (Gade & Koch, 2014; Houghton et al., 2009), suggesting a more efficient reconfiguration of task sets if the cue activates the task set more directly and thus activation of the new task is facilitated.

Taken together, these studies showed a rather inconsistent picture regarding the contribution of preparatory processes to task set inhibition indexed by n−2 repetition costs. However, they demonstrated a susceptibility of n−2 repetition costs to manipulations of preparatory stages in the task switching procedure (for a more general overview for the susceptibility of task switching effects to variations of the experimental procedure, see Koch et al., 2018). Moreover, these findings do not unequivocally support the preparatory-related account of n−2 repetition costs, as in all these studies, task cues were always followed by a stimulus. Hence, it is conceivable that stimulus- or task set execution-related processes have affected the above-described effects. To isolate the influence of cue-related processes from stimulus-related or task set execution-related processes, a promising approach is to present so called task cue-only trials, that is, task cues that are not followed by a task stimulus and thus also not by an executed task.

In task cue-only trials, only the task cue is shown unpredictably without the presence of a following stimulus, and after a certain interval the next trial follows. Hence, only the task cue can be processed in task cue-only trials. The presence of switch costs in studies using two tasks could be already demonstrated after task cue-only trials (Lenartowicz et al., 2011; Swainson et al., 2021, 2023), indicating that sole task cue-induced task preparation is sufficient to induce a performance deficit in the following trial if the task set switches (see also Kleinsorge et al., 2005; Kleinsorge & Gajewski, 2004).

While the presentation of task cue-only trials hence appears to be a promising method to address the preparatory account of n−2 repetition costs, we are only aware of one study utilizing task cue-only trials in the context of n−2 repetition costs. Prosser et al. (2022) investigated whether the presentation of a task cue-only in trial n−1 is sufficient to trigger an inhibition of the task set performed in trial n−2 (i.e. only trial triplets including a task presented in trial n−2 were analyzed). The results showed a lack of reliable n−2 repetition costs in task responses, similar to studies presenting a no-go signal in trial n−1 (Gade & Koch, 2007; Schuch & Koch, 2003), suggesting that a task cue-only might not be sufficient to trigger an inhibition of a previously performed task set (Prosser et al., 2022). However, to the best of our knowledge, no previous study directly tested whether cue-induced task set activation itself is the target of inhibitory processes in preparation of an upcoming task, i.e. whether task set reconfiguration (and an accordingly assumed inhibition of the previous task set) occurs after task cue-only presentation. To this end, unlike presenting cue-only trials in trial n−1, as Prosser et al. (2022) did, the present study presented task cue-only trials in trial n−2.

Task set inhibition following task cue-only presentation

Regarding the question whether task sets become inhibited following a task cue-only, previous studies were conducted in our lab in the context of a modulation of masked semantic priming (Berger et al., 2022; Kiefer et al., 2019). These studies were motivated by the attentional sensitization model of unconscious cognition (Kiefer & Martens, 2010), which postulates that activated task sets sensitize subsequent unconscious processing. In line with predictions of this model, it was previously shown that masked semantic priming is enhanced after the execution of a semantic task, indicating that performing the semantic task sensitizes processing pathways also later involved in semantic prime processing (Kiefer, 2019; Kiefer & Martens, 2010; Martens et al., 2011; Ulrich et al., 2014). Following this line of research, in those studies we assessed masked semantic priming in a masked primed lexical decision task subsequent to task cue-only trials associated with a semantic and a perceptual task, to infer from the modulation of priming the preceding activation of task sets following task cue-only presentation. However, in contrast to executed tasks, following the presentation of a task cue-only, semantic priming was mostly larger for perceptual than semantic task sets (Berger et al., 2022; Kiefer et al., 2019). This effect was interpreted in terms of an inhibition of task sets subsequent to task cue-only trials: only prepared, but not executed task sets were assumed to be inhibited (presumably to facilitate performance of the conflicting task set of the masked primed lexical decision task), resulting in the reversed modulation of masked priming compared to that following task set execution.

Influence of cue-task compatibility on task set inhibition effects

Kiefer et al. (2019) found inhibition of task sets following a task cue-only only if the task cue and associated decision categories matched, suggesting that it depended on properties of the task cue. This manipulation was later called cue-task compatibility (Berger et al., 2022), with task cues matching the decision categories of the task termed compatible cues and non-matching task cues termed incompatible cues. The cue-task compatibility manipulation in Kiefer et al. (2019) was motivated by a previous task switching study (Jost et al., 2017), which showed that a dominant task (strong stimulus-response bindings based on spatially compatible S-R mapping rules) received more inhibition than other, less dominant, tasks. Following this line of reasoning, Kiefer et al. (2019) reasoned that the presence of inhibition effects only following compatible task cues suggests that task sets triggered by compatible task cues are more dominantly represented according to the straightforward cue-task relation. Accordingly, they should be more in conflict with other tasks and receive more inhibition when a different task than the cued task has to be performed. However, a recent study found a comparable level of task set inhibition effects following task cue-only trials for compatible and incompatible task cues (Berger et al., 2022), which may be due to a greater engagement in task preparation for incompatible cues as suggested by electrophysiological recordings (Berger & Kiefer, 2024). This suggests that task sets triggered by both compatible and incompatible task cues might need to be inhibited when switching to another task (at least in the context of a modulation of masked priming). In contrast, studies in task switching with always executed tasks showed a different influence of cue-task compatibility. In these studies, n−2 repetition costs were smaller for compatible than incompatible cues, suggesting stronger task set inhibition effects for incompatible cues (Gade & Koch, 2014; Houghton et al., 2009).^{Footnote 2}

However, these two lines of research differed on a conceptual level. n−2 repetition costs measure the after-effects of task set inhibition in terms of the influence of a previously inhibited task set on performance in trial n. In contrast, our previous studies assessed the influence of a presumably inhibited task set following a task cue-only on masked semantic priming in an immediately following primed lexical decision task. Hence, direct and persisting influences of task set inhibition may dissociate, especially because in task switching studies a new task cue is presented in trial n, and task set activation in task switching was shown to be facilitated with compatible task cues (Jost et al., 2013). In light of the above-outlined influence of cue-task compatibility on task set inhibition effects, the present study was aimed to investigate how task set inhibition effects following a task cue-only observed in the context of a modulation of priming can be extended to task switching and whether this task set inhibition depends on cue-task compatibility.

Influence of task practice on task set inhibition effects

Besides the influence of cue-task compatibility, our previous work also revealed an influence of task practice upon task cue effects on masked priming (Berger et al., 2022, 2024), indicating that task set activation (and likewise a subsequent inhibition) following a task cue may change with practice. Probably, there is a reduced need for distinct advance task preparation with practice, as task sets can be more easily retrieved with stimulus onset, i.e. when the need for task execution is evident (Berger et al., 2024). An accordingly less pronounced task preparation process following a task cue-only with practice should result in lower demands to inhibit cued task sets. This would be in line with results in task switching, showing a reduction of n−2 repetition costs following task set execution with practice (Grange & Juvina, 2015; Scheil, 2016). This practice effect on n−2 repetition costs was (partially) driven by a reduced influence of task set inhibition processes (Grange et al., 2019). Accordingly, the amount of task practice is a further relevant factor for the investigation of task set inhibition effects, especially following a task cue-only.

The present study

To study an assumed inhibition of task sets following task cue-only trials, we assessed n−2 repetition costs and tested whether such costs can be observed following a task cue-only, and how such costs are moderated by cue-task compatibility and task practice. To this end, we presented task cue-only trials in a paradigm in which participants had to switch between three tasks in order to assess n−2 repetition costs as an index of task set inhibition processes (Koch et al., 2010). In contrast to previous work (Prosser et al., 2022), task cue-only trials were presented in trial n−2 in order to estimate whether task sets are inhibited following task cue-only presentation, i.e. whether mere task cue presentation is sufficient to trigger a task set activation, which needs to be inhibited when switching to another task. This prediction is based on the assumption that task set inhibition is engaged in preparation of an upcoming task only if the earlier task set had been previously activated and has now to be abandoned.

The amount of task set inhibition triggered by task cue-only trials was compared to that one triggered by task execution, resulting in the following experimental design: In trial n−2, either a task cue followed by a semantic or perceptual classification task or a task cue-only was presented. The task cue-only cued the semantic/perceptual task, for which, however, the actual target stimulus was not presented, so that, accordingly, the task could not be performed. In trial n−1, a lexical decision task (LDT) was presented. Note that this LDT used different stimuli compared to the semantic and perceptual task and was not explicitly cued. This design was chosen to closely resemble our previous work investigating the modulation of masked priming (Berger et al., 2022; Kiefer et al., 2019), which indicated task sets following a task cue-only to be inhibited in order to perform a LDT (where masked priming was assessed). In trial n, a task cue followed by a semantic or perceptual classification task was presented. Accordingly, the (cued or executed) task set could repeat or switch from trial n−2 to trial n, comprising ABA and CBA sequences, which were used for determining n−2 repetition costs. For an overview of the experimental design, see Table 1.

Table 1 Overview of the experimental design of the present study

Full size table

Our design differed from the typical measurement of n−2 repetition costs in task switching in two aspects. First, the LDT in trial n−1 was not cued. Second, the LDT used different stimuli (i.e., letter strings) compared to the semantic/perceptual classification task (i.e., pictures). Accordingly, the pictures were “bivalent” stimuli (i.e., affording two different tasks), while the LDT targets were “univalent” and the semantic/perceptual task could not be applied on the LDT stimuli and vice versa. Following previous research, which showed a reduction or absence of n−2 repetition costs if trial n−1 differed in the stimulus format (Sdoia et al., 2022), the number of possible tasks (Scheil & Kleinsorge, 2023b), the response set (Scheil & Kleinsorge, 2023a), or was a task cue-only one (Prosser et al., 2022), the present design may constitute less than optimal conditions for the detection of n−2 repetition costs. However, the responses of all tasks were mapped onto the same two keys (see “Method” section) and the response sets therefore overlapped between tasks. Hence, there was between-task competition in the response set and according to accounts assuming conflict in the response set to be crucial for the occurrence of n−2 repetition costs (Gade & Koch, 2007; Schuch & Koch, 2003), the present design may therefore fulfill the necessary requirements for observing n−2 repetition costs. Moreover, the absence of a cue in trial n−1 may even be beneficial in terms of ruling out alternative explanations, as it is consequently unlikely that a possible detection of n−2 repetition costs following task cue-only trials is the consequence of an inhibition of the cue representation (according to two cues being presented in direct succession). To elaborate on this, if we would have presented a cue in trial n−1 (which was the LDT), a task cue-only trial would have always been followed immediately by another cue, reflecting a cue switch. According to accounts assuming cue switches to be a major determinant of task switching effects (Logan & Bundesen, 2003; Schneider & Logan, 2005), we consider omitting the task cue in trial n−1 increases the likelihood, that possibly observed n−2 repetition costs reflect an inhibition of (aspects of) the cued task set (see also Gade & Koch, 2008).

Aim of the present study

The aim of the present study was threefold, resulting in the following research questions:

(1)
Can n−2 repetition costs be observed following a task cue-only in trial n−2? We suppose task cue-only presentation to be sufficient to trigger an activation of task sets, which needs to be inhibited when switching to a new task. Accordingly, we expect to observe n−2 repetition costs following a task cue-only in trial n−2. In addition and in line with previous observations in task switching (for a review, see Koch et al., 2010), we also expect to find n−2 repetition costs following task execution in trial n−2. That is, we suppose both mere task preparation and task execution to trigger an inhibition of task sets reflected by n−2 repetition costs.
(2)
Does the inhibition of task sets following a task cue-only depend on properties of the task cue, namely cue-task compatibility? Our previous work and earlier observations in task switching suggested that the size of task set inhibition effects depends on properties of the task cue, with however inconsistent findings. Based on previous findings in the task switching literature (Gade & Koch, 2014; Houghton et al., 2009), we expect larger n−2 repetition costs, both following merely cued and executed task sets, for incompatible task cues.
(3)
Are there any practice-induced changes in n−2 repetition costs following a task cue-only? Previous work suggested a reduced engagement into task preparation following task cue-only trials with practice (Berger et al., 2024), which should result in lower demands for inhibiting only cued, but not executed task sets. Therefore, we would expect n−2 repetition costs following a task cue-only to decrease with experimental duration.^{Footnote 3}

Experiment 1

Method

Design and analysis of Experiment 1 was pre-registered (https://osf.io/37brv). Analysis scripts and data were uploaded to a public repository (https://osf.io/ady8t/).

Participants

N = 55 participants were recruited for Experiment 1. We excluded n = 2 participants for their mean RT exceeding the sample mean RT in the semantic / perceptual classification tasks or the LDT by 2 SDs. The final sample consisted of N = 53 participants. Mean age was 22.58 years (SD = 2.7) and 43 participants were female (81.1%). Of the final sample, n = 26 participants received compatible cues and n = 27 incompatible cues (for a description of compatible and incompatible cues, see the next section).

As pre-registered, the sample size was chosen to achieve a balanced assignment of the stimulus lists to the cue-task compatibility groups (see next section). It was also chosen to be in line with our former study observing an inhibition of task sets following task cue-only trials in the context of masked semantic priming (Berger et al., 2022) due to a lack of previous task switching studies including a presentation of task cue-only trials in trial n−2. Nevertheless, we performed a post-hoc power analysis using the effect size observed for the interaction of task set sequence and n−2 trial type (see the Results of Experiment 1), which revealed a high power for detecting such an effect for Experiment 1 (1 – β = 0.98).

Tasks and stimuli

Stimuli for the semantic and perceptual classification task as well as the LDT were taken from previous studies (Berger et al., 2022; Kiefer et al., 2019). Stimuli for the semantic and perceptual classification task were 360 grey-scale pictures, depicting animate and inanimate objects. For the semantic classification task, these pictures had to be classified as depicting a living (e.g. tiger) or a non-living (e.g. knife) object, while pictures had to be classified as a round (e.g. ball) vs. elongated (e.g. pencil) object for the perceptual classification task. The pictures were evenly distributed across the semantic and perceptual classification task (each n = 180). It was ensured that the distribution of the other decision category (e.g. round and elongated objects across the living and non-living objects) was approximately balanced, χ²(1) = 1.52, p = .218. In the LDT, letter strings had to be classified as meaningful German word or as pronounceable, but meaningless pseudoword. There were n = 120 words and n = 120 pseudowords. Length of pseudowords (on average 5.13 letters) and words (on average 5.05 letters) did not differ significantly, t(232) = 0.60, p = .552.

Participants responded with the left and right button of a response box. The living, round and word decisions were mapped to one button, which participants were instructed to press with their index finger. The non-living, elongated and pseudoword decisions were mapped to the other button, which participants had to press with their middle finger. Right-handers and left-handers responded with the index and middle finger of their dominant hand and the mapping of response buttons was accordingly reversed for left- and right-handers (right-handers: living, round and word decision mapped to the left button; left-handers: living, round and word decision mapped to the right button).

We created 24 different stimulus lists, in which the assignment of pictures and LDT stimuli to the different conditions (see the “Design” section) was counterbalanced. All conditions and response categories were balanced. Furthermore, for each participant, we pseudo-randomized the stimulus list to ensure that all type of trial triplets / conditions were about equally often followed by all trial triplets / conditions, so that participants could not predict which condition would follow (corresponding chi-squared tests did not indicate a significant imbalance between the sequence of conditions, χ²(49) < 10, p > .99, for each stimulus list). Stimulus lists were repeated across participants (each at least 2 times), as we collected more than 24 participants.

Task cues to indicate the semantic and perceptual classification task were the capital letters “R” and “B” as in previous work (Berger et al., 2022). Task cues could either be compatible or incompatible with the cued decision categories by a match or mismatch with the first letter of the first alternative of the decision category. For compatible task cues, the letter “R” indicated the perceptual decision (“rund / länglich”, engl. “round / elongated” decision) and the letter “B” the semantic decision (“belebt / unbelebt”, engl. “living / non-living”). For incompatible cues, this assignment was reversed, i.e. the task cue “R” indicated the semantic decision, while the task cue “B” indicated the perceptual decision.

LDT targets, task cues (both in white font), and pictures were presented against a black background at the center of the screen. Pictures had a subtended 3.2 × 3.8 degrees visual angle, and the height of all text stimuli (task cues, LDT targets, feedback) was set to 0.88 degrees visual angle. Participants were seated in frontal of a computer screen at a distance of 70cm. The screen was an LCD device and had a resolution of 1280 × 1024 pixels and a screen refresh rate of 60Hz.

Procedure

The experiment was programmed and run in PsychoPy (Peirce et al., 2019), version v.2021.2.3. A schematic overview of the experimental procedure is depicted in Fig. 1. The experiment consisted of 720 trials (task cue and task, task cue-only or LDT), which were divided into 240 trial triplets. In the first trial (trial n−2), either a task cue (750ms) and task picture or a task cue-only was presented. The picture immediately followed the task cue and was presented until a response was given or a response deadline of 2500 ms passed. Presentation duration of task cue-only trials was 750 ms as well. After a 300 ms blank, the LDT target was presented in trial n−1, which remained on the screen until a response was made or 2500 ms (response deadline) passed. In trial n, at the end of each trial triplet, after a 300 ms blank a task cue and task followed with the same stimulation properties as in trial n−2. After an additional 300 ms blank, the next trial triplet started, i.e. there was no pause between trial triplets to achieve a continuous flow for the participants. When a response deadline elapsed, feedback (“Zu langsam!”, engl. “Too slow!”) was provided in red for 500ms. The experiment was divided into 8 blocks, and participants could take a break between blocks.

Before the main experiment started, participants practiced the experimental procedure. First, they practiced the LDT, as well as the semantic and perceptual classification tasks in separate blocks. Afterwards, they practiced the semantic and perceptual classification task conjointly in a block. Finally, they practiced the procedure as presented in the main experiment. During practice, participants received feedback about the correctness of their response.

Design

For the analysis of n−2 repetition costs, there were three factors of interest: Task set sequence, n−2 trial type and cue-task compatibility. Task set sequence and n−2 trial type were manipulated within-subjects, while cue-task compatibility was manipulated between-subjects. Task set sequence had two levels, ABA and CBA, i.e. whether the (merely cued or executed) task set repeated (ABA) or switched (CBA) from trial n−2 to trial n.^{Footnote 4} n−2 trial type had two levels as well, trial n−2 being a task or being a task cue-only one. Finally, one group of participants received compatible, while the other group received incompatible task cues (see “Tasks and stimuli” section), resulting in a 2 × 2 × 2 mixed design. For each combination of the within-subjects factors, i.e. task set sequences depending on n−2 trial type, 60 trial triplets were presented (240 / 4 = 60).

Furthermore, the experimental procedure allowed us to also analyze task switches and task repetitions, i.e. whether the task from trial n to trial n−2 of the next task triplet switched or was repeated (when trial n−2 of the next trial triplet was a task). Accordingly assessed switch costs could serve as a kind of treatment check, as they constitute a quite stable effect in task switching (Kiesel et al., 2010; Monsell, 2003). For the analysis of switch costs, there were two factors of interest; task sequence (task switch vs. task repetition) and cue-task compatibility, resulting in a 2 × 2 mixed design.

Statistical analysis

Conventional analysis of mean response times and error rates

Single-trial data were pre-processed using the statistical software R (R Core Team, 2020). RT outliers were specified separately per trials (task in trial n−2, LDT in trial n−1, task in trial n), but collapsed across task sets as RTs exceeding ± 2 SDs of the individuals mean RT in that task (Berger & Kiefer, 2021, 2023). RT outliers and trials, where no response occurred until the RT deadline, were excluded from all analyses (8.0% of all trials). For the analysis of RTs, we also excluded incorrect responses. Furthermore, for the analysis of n−2 repetition costs, trial triplets with an error, a RT outlier or no response until the deadline in trial n−2 or trial n−1 were excluded as well. After pre-processing, there was an average number of 50.9 (SD = 3.5) per-condition trials available for the analysis of n−2 repetition costs for RTs, and 52.4 (SD = 3.1) trials for ERs.

For conventional analysis of n−2 repetition costs, mean RTs and ERs in trial n were calculated and analyzed using a repeated measures ANOVA with the within-subjects factors task set sequence and n−2 trial type as well as the between-subjects factor cue-task compatibility. For the analysis of task switch costs, a repeated measures ANOVA on mean RTs and ERs in trial n−2 (trial n−2 being a task) was calculated with the within-subject factor task sequence and the between-subjects factor cue-task compatibility. ANOVA analyses were performed using JASP (JASP Team, 2020). We report in the “Results” section only summarized results covering the theoretical relevant effects, but the corresponding tables displaying all tested effects can be found in Supplementary Material E.

Effect course analysis

To investigate how n−2 repetition costs following a task cue-only in trial n−2 develop over the course of the experiment, we calculated effect course analyses. We will only shortly summarize this method, for more detailed information we refer the reader to Berger et al. (2024). Performance (RT and correctness of the response) of trial n in trial triplets with a task cue-only in trial n−2 were extracted for each participant and stored into two separate vectors depending on the task set sequence (ABA vs. CBA). Within these vectors, performance measures were sorted according to their temporal occurrence in the experiment. These vectors were smoothed using moving averages to account for the large variability in single-trial RTs / responses (for further details, see below). Afterwards, the vectors were contrasted to display how the difference between ABA vs. CBA conditions (n−2 repetition costs) develops throughout the course of the experiment. That is, the first occurrence of condition ABA was contrasted against the first occurrence of condition CBA, and so on. To test whether the effect is significant at any time point within the experiment, cluster based permutation testing was applied (CBPT, cf. Maris & Oostenveld, 2007). At each time point / trial (called sample in the context of CBPTs), a dependent t-test was conducted and adjacent samples, in which the t-test crossed an a-priori specified threshold, were grouped together into clusters. Clusters were described by a cluster T value, that is the sum of all t-values of the significant tests at the sample level included in this cluster. Significance of clusters was assessed by a permutation procedure, that is in each iteration, separately per participant, the condition assignment was randomly shuffled. In these random permutations of the data, clusters were built as described above. The p-value of an observed cluster was defined as the proportion of permutations with a cluster T-value exceeding the T-value of the observed cluster. For the present analysis, the window size for the calculation of moving averages was set to 13 (60 / 5 + 1), alpha at the sample level was set to α = 0.1 and 5000 permutations were ran comparable to previous work (Berger et al., 2024).

Supplementary analyses

Besides the above-mentioned analyses, we performed additional analyses as pre-registered. First, we analyzed whether the performance in the LDT in trial n−1 depended on n−2 trial type, i.e. how switching from a task or a task cue-only to the LDT influenced LDT performance (Supplementary Material B). Furthermore, for this and all other analyses described above, we also performed drift-diffusion model (DDM) analyses (Ratcliff & McKoon, 2008; Voss et al., 2013; Wiecki et al., 2013), which are reported in Supplementary Material A, C, D.

Results

Switch costs in trial n−2

For the analysis of RTs in executed tasks in trial n−2 depending on whether the task switched or repeated from the previous trial triplet, we observed a significant effect of task sequence, F(1, 51) = 10.73, p = .002, task switches were significantly slower than task repetitions (mean switch costs = 27 ms). Furthermore, the main effect of cue-task compatibility was significant with on average 103ms slower responses for incompatible task cues, F(1, 51) = 11.15, p = .002. There was also a significant interaction of task sequence × cue-task compatibility (F(1, 51) = 10.61, p = .002), indicating larger switch costs for incompatible (55 ms) than compatible cues (0 ms), for which switch costs were numerically absent.

Concerning the analysis of ERs, there were numerical switch costs of 0.7%, which however were not statistically significant, F(1, 51) = 2.91, p = .094. Neither the effect of cue-task compatibility nor the interaction of cue-task compatibility and task sequence reached significance (all Fs < 1.94. all ps > .170).

n−2 repetition costs

Mean RTs of task performance in trial n are depicted in Fig. 2. As can been seen in this figure, there was a large main effect of cue-task compatibility, F(1, 51) = 12.44, p < .001, RTs for trials with incompatible task cues were about 124ms slower compared to compatible task cues. Both the main effect of task set sequence (F(1, 51) = 2.36, p = .130) and n−2 trial type (F(1, 51) = 1.20, p = .279) were not significant, but there was a significant interaction, F(1, 51) = 4.09, p = .048, indicating that the effect of task set sequence was modulated by n−2 trial type. Specifically, we observed n−2 repetition costs (18 ms) only following a task cue-only in trial n−2, whereas no n−2 repetition costs were observed following task set execution in trial n−2 (−2 ms). All other interactions did not reach significance, all Fs < 0.69, all ps > 0.41.

A corresponding analysis of ERs in trial n revealed no significant effects, all Fs < 2.59, all ps > .113. Mean ERs as well as mean RTs in trial n depending on task set sequence, n−2 trial type and cue-task compatibility are reported in Table 2.

Table 2 Mean RTs and ERs in trial n in Experiment 1

Full size table

Effect course analysis of n−2 repetition costs

We performed effect course analyses on RTs to assess how the observed n−2 repetition costs following a task cue-only in trial n−2 developed throughout the experiment, i.e. how inhibition effects of only cued, but not executed task sets, changed with practice. The time courses of n−2 repetition costs following a task cue-only, separately for the two cue-task compatibility groups, are depicted in Fig. 3. For both cue types, n−2 repetition costs were maximal at the beginning of the experiment and decreased with increasing experimental duration. For compatible cues, the effect course analysis revealed a significant cluster, ranging from trial 1–10, cluster T = 23.06, p = .036. Hence, presentation of a task cue-only elicited significant n−2 repetition costs, but only at the beginning of the experiment and only for compatible cues. In contrast, for incompatible cues, while the descriptive pattern was comparable, no significant cluster was observed.

Discussion

First, as kind of a treatment check, we observed significant switch costs in RTs, i.e. slower responses if trial n of the previous trial triplet was the same task as in trial n−2. These switch costs were only observed for incompatible cues, being in line with previous observations of larger switch costs for incompatible / less transparent cues (Arbuthnott & Woodward, 2002; Gade & Steinhauser, 2020; Grange & Houghton, 2010; Jost et al., 2013). Accordingly, switching tasks produced a cost, predominantly for incompatible cues, which would be typically expected in a task switching experiment (Kiesel et al., 2010; Monsell, 2003). Note that while there was no RT difference between task switches and task repetitions for compatible cues, additional drift-diffusion model analyses indicated numerically a switch cost on drift rate, i.e. processing speed for both cue types (see the Supplementary Material A).

Regarding our research questions, we observed n−2 repetition costs, but only following a task cue-only and not following task execution in trial n−2. Effect course analysis showed n−2 repetition costs following a task cue-only to decrease during the course of the experiment and only for compatible cues, a significant cluster was observed. However, analyses on averaged RTs did not reveal a significant modulation of the n−2 trial type × task set sequence interaction by cue-task compatibility, F(1, 51) = 0.68, p = .415. Hence, mean n−2 repetition costs following a task cue-only did not differ significantly between compatible and incompatible cues. In contrast, the effect course analysis incorporating a fine-grained resolution of the effect’s development failed to detect a significant cluster for incompatible cues, despite of a similar shape of the effect course compared to compatible cues, probably due to an overall increased variability for incompatible cues. For a more detailed discussion of how n−2 repetition costs developed throughout the experiment and the influence of cue-task compatibility on n−2 repetition costs, see the “General discussion” section.

However, the results of Experiment 1 revealed an unexpected finding that made the interpretation of n−2 repetition costs somewhat difficult. While we observed n−2 repetition costs following a task cue-only, no n−2 repetition costs were present following task (set) execution in trial n−2 (additional drift-diffusion model analyses even indicated an n−2 repetition benefit following task execution, see Supplementary Material D). That is, in contrast to usually observed effects in task switching (Koch et al., 2010), we did not observe a cost of repeating the execution of the same task set from trial n−2 to trial n. Task preparation is commonly assumed to only constitute one aspect of multiple processes contributing to the occurrence of n−2 repetition costs (Vandierendonck et al., 2010). Hence, this lack of n−2 repetition costs following executed tasks is especially surprising as in task execution the additional influence of response-related processes and episodic interference should add to preparatory influences on n−2 repetition costs (Philipp et al., 2007; Schuch & Keppler, 2022; Schuch & Koch, 2003).

Moreover, the interpretation of n−2 repetition costs following a task cue-only and the absence of such costs following task execution is additionally challenged by a different total duration of both n−2 trial types. In Experiment 1, we equated the blank interval following both trial types, that is following the response to a task and following a task cue-only. For both trial types, there was a blank interval of 300 ms until trial n−1 (the LDT) started. Consequently, the interval from trial onset, i.e. task cue onset, to the next trial was drastically shorter if the n−2 trial type was a task cue-only one. For task cue-only trials, the duration from trial n−2 onset to trial n−1 onset was fixed and lasted 1050 ms (750 ms task cue-only + 300 ms blank interval = 1050 ms), while the corresponding duration for a task in trial n−2 varied from trial to trial and was remarkably longer according to the varying RT of task executions in trial n−2. The mean RT of tasks in trial n−2 was 674 ms, i.e. the average duration of this trial type was approximately 674 ms longer compared to that of task cue-only trials (750 ms task cue + 674 ms response + 300 ms = 1724 ms), while furthermore changing every trial. According to accounts assuming a decay of task sets with time (Altmann, 2002; Altmann & Gray, 2002; Vandierendonck et al., 2010), task set activation following an executed task could have vanished until the onset of the LDT (if one assumes task set activation to start to decay before the response is given), therefore reducing the need for inhibiting that task set (cf. Gade & Koch, 2005). In contrast, as the onset of the LDT followed more shortly after a task cue-only, the strength of the prepared task set may have been stronger, thereby increasing the conflict with the following lexical task set of the LDT, finally resulting in strong demands to inhibit only cued task sets.

However, there could be an alternative explanation for the presence of n−2 repetition costs following a task cue-only and the absence of such costs following task execution: Only cued, but not executed task sets could simply require a larger demand for inhibition, as they interfere to a stronger degree with conflicting task sets. Regarding this aspect, note that previous studies found larger switch costs following task cue-only trials compared to task execution when the preparation interval was short (Lenartowicz et al., 2011; Swainson et al., 2017, 2021). Especially in situations where the lack of task execution following a task cue-only may be surprising, cued but not executed task sets may interfere strongly with conflicting task sets of upcoming tasks and accordingly need to be inhibited. Note that in our experiment, although there was an equal number of task and task cue-only n−2 trial types, 75% of all presented task cues were followed by a task because task cues were always followed by a task in trial n. Hence, if greater inhibition requirements for task cue-only trials compared to task trials is the relevant factor for the differential n−2 repetition costs for these n−2 trial types, we should also expect a similar pattern of n−2 repetition costs when the total duration of both trial types is comparable. To this end, we conducted Experiment 2, in which we aimed to equate the duration of task cue-only and task n−2 trial types to examine whether a different temporal length of these two trial types may have caused the presence of n−2 repetition costs following a task cue-only and the corresponding absence of these costs following executed tasks in Experiment 1.

Experiment 2

In contrast to Experiment 1, where the blank interval following the response to the task and the offset of the task cue-only in trial n−2 was equated, Experiment 2 equated the total duration of both trial types. That is, for both task execution and mere task preparation (task cue-only), the duration varied from trial to trial and was comparable across trial types. Hence, Experiment 2 tested whether the lack of n−2 repetition costs following task execution in Experiment 1 was the consequence of a decay of task sets. Due to a comparable total duration of task and task cue-only n−2 trial types in Experiment 2, a decay of task sets should similarly affect both trial types, and we would consequently expect to observe a lack of n−2 repetition costs in both n−2 trial types. However, in contrast, if only cued, but not executed task sets require a larger amount of inhibition compared to executed task sets, n−2 repetition costs should remain larger following a task cue-only compared to an executed task. We hypothesized to observe n−2 repetition costs following a task cue-only and a corresponding lack of n−2 repetition costs following task execution, which is a comparable result pattern as in Experiment 1.