Treffer: Transfer of Task-Probability-Induced Biases in Parallel Dual-Task Processing Occurs in Similar, but Is Constraint in Distinct Task Sets
Postsecondary Education
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Although humans often multitask, little is known about how the processing of concurrent tasks is managed. The present study investigated whether adjustments in parallel processing during multitasking are local (task-specific) or global (task-unspecific). In three experiments, participants performed one of three tasks: a primary task or, if this task did not require a response, one of two background tasks (i.e., prioritized processing paradigm). To manipulate the degree of parallel processing, we presented blocks consisting mainly of primary or background task trials. In Experiment 1, the frequency manipulation was distributed equally across the two background tasks. In Experiments 2 and 3, only one background task was frequency-biased (inducer task). The other background task was presented equally often in all blocks (diagnostic task) and served to test whether processing adjustments transferred. In all experiments, blocks with frequent background tasks yielded stronger interference between primary and background tasks (primary task performance) and improved background task performance. Thus, resource sharing appeared to increase with high background task probabilities even under triple task requirements. Importantly, these adjustments generalized across the background tasks when they were conceptually and visually similar (Experiment 2). Implementing more distinct background tasks limited the transfer: Adjustments were restricted to the inducer task in background task performance and only small transfer was observed in primary task performance (Experiment 3). Overall, the results indicate that the transfer of adjustments in parallel processing is unrestricted for similar, but limited for distinct tasks, suggesting that task similarity affects the generality of resource allocation in multitasking.
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Transfer of Task-Probability-Induced Biases in Parallel Dual-Task Processing Occurs in Similar, but Is Constraint in Distinct Task Sets
<cn> <bold>By: Inga Lück</bold>>
> <bold>Victor Mittelstädt</bold>
>
> <bold>Ian G. Mackenzie</bold>
>
> <bold>Rico Fischer</bold>
>
<bold>Review of: </bold>xlm0001259-open-practices-disclosure-form.pdf
<bold>Acknowledgement: </bold>All procedures were carried out in accordance with the Declaration of Helsinki and the ethical guidelines of the German Psychological Society. Portions of these findings were presented at the 2022 Tagung experimentell arbeitender Psycholog:innen (Conference of Experimental Psychologists) at University of Cologne, Germany. We have no conflicts of interest to disclose.All data as well as the code behind the analyses have been made publicly available at PsychArchives (for analysis code, see http://dx.doi.org/10.23668/psycharchives.8260; for data, see http://dx.doi.org/10.23668/psycharchives.8261). The study’s material is available at https://github.com/igmmgi/jsPsychExperiments/tree/master/Experiments/PP_2BT. The design, hypotheses, and analysis plans of Experiment 2 (https://aspredicted.org/6GT_QC1) and Experiment 3 (https://aspredicted.org/V9C_MZ5) were preregistered.
The study of human performance in situations involving the simultaneous performance of two or more tasks is of particular interest, as such demands not only increasingly occur in everyday private and professional life but are often associated with performance costs (for reviews, see, e.g., Fischer & Janczyk, 2022; Koch et al., 2018). Processing two tasks simultaneously (dual tasking) typically results in longer and less accurate responses than working on the same tasks separately (single tasking). Studying such performance costs has been of particular interest in basic and applied research because understanding the nature of these costs can help to optimize dual tasking and to identify situations in which dual-task costs are absent (e.g., Shaffer, 1975), can be eliminated (e.g., extensive practice; Schumacher et al., 2001), or identify which task combinations (e.g., Göthe et al., 2016) or individual dual-task processing strategies can increase dual-task efficiency (e.g., Brüning et al., 2020).
Typical performance costs which are observed when combining two simple cognitive choice reaction time tasks have been related to resource limitations and many models have tried to describe and explain how the competition for limited attentional resources is resolved under multiple task requirements. While most models agree that interference arises at central stages of processing (i.e., where there is competition for limited resources), they largely differ in whether the assumed resource limitation is of structural or strategic nature. The prominent response selection bottleneck (RSB) model (Pashler, 1994), for example, assumes a structural resource limitation (i.e., bottleneck), which limits processing at a central response selection stage to one task at a time. Central processing occurs in a strict serial order, in that processing of another task has to wait until the central processing of the first task is completed. Consequently, resource allocation is structurally determined in a first-come, first-served fashion and thus denies the possibility of flexible resource allocation and parallel processing at the bottleneck.
Others argue that a processing bottleneck represents a strategic choice: Resource capacities can, in principle, be shared and flexibly allocated between tasks so that parallel processing is possible (Meyer & Kieras, 1997; Mittelstädt, Mackenzie, & Miller, 2022; Navon & Miller, 2002; Tombu & Jolicoeur, 2003). Following the assumption of resource sharing models (Tombu & Jolicoeur, 2003), the ratio of resources between the tasks can be flexibly adjusted in a graded fashion. In a more extreme 100–0 resource allocation, Task 1 receives all resources, thus mimicking a central bottleneck and enforcing serial task processing. Therefore, serial processing can result independently of the assumed reason for the bottleneck (i.e., all-or-none allocation in resource sharing accounts or structural limitation in the RSB model). Under strict assumptions, parallel processing, on the other hand, is only possible in resource sharing accounts but not in structural bottleneck models.
One essential point of criticism of resource sharing models, however, is the lack of a clear explanation regarding
Therefore, ECTVA offers an explanation of how processing is prioritized within dual tasks. It predicts the degree of parallel versus serial task processing, suggesting a more distributed or focused allocation of attentional resources. It has been argued that serial processing is adopted because it facilitates the correct stimulus–response translation in each task by reducing the number of response reversals and, in most cases, reflects the more efficient dual-task strategy compared to parallel processing (Miller et al., 2009).
Parallel processing, on the other hand, is a consequence of a more equal prioritization and shared resources, which increases the risk of processing interactions between the two tasks when performed simultaneously. Parallel processing, however, has been characterized as less effortful (Lehle et al., 2009), may be favored by some individuals (e.g., Brüning et al., 2022), and has been shown to be adopted with ongoing task duration (Fischer et al., 2018), when resources are sparse (Plessow et al., 2012), or when high temporal task overlap between tasks is more frequent than conditions of low temporal task overlap (Miller et al., 2009).
As a marker of parallel processing, the so-called backward crosstalk effect (BCE) has often been used. It indicates to which degree processing in Task 1 is affected by simultaneous processing of Task 2 (e.g., Hommel, 1998; Lien & Proctor, 2002; Logan & Schulkind, 2000).<anchor name="b-fn1"></anchor><sups>1</sups> This backward crosstalk typically occurs at the central processing stages (Janczyk, 2016; Mittelstädt et al., 2022), which conflicts with assumptions of an all-or-none RSB that does not allow for any additional central processing. As a consequence, it has been suggested that the original response selection stage might be divided into an automatic response activation stage, which allows for crosstalk, and a subsequent capacity-limited response identification stage that needs to be performed sequentially (Hommel, 1998; Lien & Proctor, 2002; Schubert et al., 2008). Alternatively, the bottleneck might be conceptualized as a capacity sharing bottleneck in which the sharing of processing capacity between tasks also allows for crosstalk to occur (Mittelstädt et al., 2022).
Hommel (1998), for example, examined backward crosstalk by implementing stimuli with two dimensions (i.e., stimulus color [red/green] and identity [H/S]). First, the stimulus color had to be indicated by a left (red) or right (green) key press. The second task required verbal responses depending on stimulus identity (e.g., saying
Parallel task processing should give rise to stronger processing interactions between tasks, thus increasing the size of the BCE. Serial task processing, on the other hand, should reduce the impact of concurrent Task 2 processing and thus decrease the BCE. In fact, many studies have utilized the size of the BCE to assess the degree of parallel versus serial task processing depending on individual factors and situational contexts. These include, for example, top-down instructions (Lehle et al., 2009; Lehle & Hübner, 2009; Plessow et al., 2017), the prospect of reward (Fischer et al., 2018), the probability of experienced conflict (Fischer et al., 2014), the relative importance of tasks (Miller & Tang, 2021; Mittelstädt & Miller, 2017), the level of acute stress experience (Plessow et al., 2011, 2012), or different mood states (Zwosta et al., 2013).
Miller and Tang (2021), for example, assessed resource allocation (indicated by increased parallel versus serial processing) in dual tasks by manipulating the frequency of individual tasks (see also Mittelstädt et al., 2022). To do so, they used a recently introduced dual-task paradigm, the prioritized processing paradigm (PP; e.g., Miller & Durst, 2014, 2015). In this paradigm, participants responded to one of two tasks: a primary (prioritized) task or a background task. The primary task was executed if this task required a response (i.e., go primary task). However, if the primary task demanded no response (i.e., no-go primary task), participants had to respond to the background task instead. Miller and Tang now manipulated how often the primary and background task had to be responded to by creating blocks with many primary or background task trials. Despite the fact that participants performed only one task in each trial, the background task nevertheless interfered with primary task processing as reflected in BCEs, suggesting parallel processing (for similarities to classical dual-task paradigms and effects, see Miller & Durst, 2015). Critically, by increasing the relative probability of responding to the background versus primary task, participants were encouraged to allocate more resources to the high-frequency task (Miller & Tang, 2021; Mittelstädt et al., 2022). Indeed, primary task processing was generally faster and showed smaller BCE in blocks with many primary tasks (i.e., high primary [HiPri] blocks) compared to blocks with many background tasks (i.e., high background [HiBac] blocks). Conversely, background task processing was generally faster and produced larger BCE in blocks with many background tasks compared to blocks with many primary tasks. These results indicate that manipulating the relative frequency of individual tasks reinforced resource allocation to the more frequently experienced task and determined the degree of parallel versus serial processing in dual tasks (Miller & Tang, 2021).
Critically, it remains unclear to which extent these resource allocation effects induced by the task frequency manipulation are bound to the individual tasks or the overall task-frequency context (e.g., background tasks in general). In the present study, we aimed to assess the task specificity of biased parallel processing against the background of a resource allocation framework. For this purpose, we used the PP paradigm as implemented by Miller and Tang (2021) and extended it with a second background task. More precisely, participants were required to respond to one of two background tasks (e.g., letter or number task) if the primary task (e.g., color task) required no response. In the first experiment, we wanted to see whether the global changes in task performance as a function of the task frequency manipulation persist in this triple task environment since it is unclear if people adjust their dual task processing if they cannot anticipate which of two background tasks will appear in a given trial. In the second and third preregistered experiments, only one of two background tasks conveyed the probability manipulation (i.e., inducer versus diagnostic background tasks). Here, only one of the background tasks was presented more or less often to create blocks with many primary or background tasks. Critically, the background tasks were conceptually and visually similar in Experiment 2, but not in Experiment 3. This allowed us to see whether (background) task similarity is an important boundary condition in modulating potential transfer effects from inducer-based to diagnostic-based trials.
If resource allocation, triggered by the frequency of a specific background task, extends to the general task context (i.e., all background tasks), performance for all background tasks (inducer and diagnostic) should be improved in conditions of a frequent (inducer) background task compared to conditions with a frequent primary task. In addition, increased parallel processing, in terms of increased between-tasks interference, might not only be obtained for the frequent (inducer) background task but also for the unbiased (diagnostic) background task. By contrast, if processing adjustments are only found in trials with the frequency-biased inducer task set, the task probability manipulation seems to be task-specific and applied locally.
Experiment 1
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The goal of Experiment 1 was to investigate whether participants proactively adjust their task processing to global changes in task frequencies even if they do not know which specific background task will appear. Extending the PP paradigm, we included two possible background tasks of which only one appeared in each trial. The relative frequency of primary versus background task trials was manipulated across blocks by changing the probability of primary task no-go trials. The two different background task sets were presented equally often so that both were frequency manipulated. We expected to replicate previous findings by Miller and Tang (2021) and assumed that a triple task environment would result in the same effects of the task-frequency manipulation. Firstly, stronger between-tasks interference, and thus a larger BCE, should arise in blocks with frequent background task trials (i.e., HiBac blocks) compared to frequent primary task trials (i.e., HiPri blocks). Secondly, background task performance should improve (shorter response times [RTs] and/or lower error rates [ERs]) when background tasks are executed more often than primary tasks.
<h31 id="xlm-50-5-775-d43e293">Method</h31><bold>Participants</bold>
The reported data were collected from 34 volunteer participants (29 female, aged 18–35 years,
<bold>Apparatus and Stimuli</bold>
Stimulus presentation and recording of responses were controlled by jsPsych (de Leeuw, 2015). All visual stimuli were presented on a grey background. The stimulus of the primary task consisted of a centrally presented square (100 × 100 px with 10 px linewidth<anchor name="b-fn2"></anchor><sups>2</sups>) in the colors red, green, and blue. Stimuli of the two background tasks were presented in white (bold 80 px monospaced font) within the square and consisted of the numbers 1, 2, 8, and 9 for the number task and the uppercase letters A, B, Y, and Z for the letter task, respectively. Responses were key presses with the left and right index fingers on the “Q” and “P” keys of a QWERTZ computer keyboard.
<bold>Procedure</bold>
At the beginning of each trial in the experimental blocks, a black plus sign (+) served as a fixation cross and appeared in the middle of the screen for 500 ms. Next, the primary task stimulus (colored square frame) was presented. The background task stimulus (i.e., either a number or a letter) appeared with a constant stimulus onset asynchrony (SOA) of 50 ms in the middle of the colored frame. The stimuli remained on the screen until a response was provided or up to a maximum of 3,000 ms. After each trial, feedback indicated whether the response was (a) “correct!” (b) “error—wrong key!” or (c) “error—too slow!” (RTs larger than 3,000 ms). In the case of an error, the correct stimulus–response mappings were displayed as a reminder. Feedback was always displayed in black font with the duration depending on the accuracy: correct feedback stayed on screen for 500 ms, whereas incorrect feedback lasted for 2,000 ms. Before the next trial started, a blank screen was presented for 300–700 ms (uniformly distributed in steps of 100 ms).
For the primary task, two colors were randomly selected and assigned to the left and right index fingers. The remaining color indicated to withhold the primary task response (no-go trial) and to respond to the background task stimulus (number or letter) instead. For the background tasks, participants were instructed to categorize number stimuli as smaller or larger than 5 and the letter stimuli as before or after the letter M in the alphabet. For both background tasks, the finger mappings were consistent across participants so that the mappings represented the intuitive spatial left-to-right alignment of these stimuli. Specifically, numbers smaller than 5 and letters before M were responded to with the left index finger, while numbers larger than 5 and letters appearing after M in the alphabet were responded to with the right index finger. The specific identities of the two presented stimuli for the primary and background task were selected randomly in each trial. Although stimuli were randomly drawn, the number and letter categorization task appeared equally often as the background task, independent of which task had to be performed (primary or background task).
All participants first practiced each of the three tasks in a single task setting with 12 trials each (e.g., only the background number task). The primary task was always practiced first, followed by two practice blocks for each background task in a random sequence. The experimental part consisted of eight blocks in total, four per probability condition (HiPri and HiBac). Half of the participants were tested in four blocks in the HiPri condition followed by four blocks in the HiBac condition, whereas this order was reversed for the other half of the participants. The first block of each condition part (48 trials) was treated as an additional practice block to ensure that participants could get used to the applied task probability. The next three blocks comprised 96 trials each. In HiPri blocks, two-thirds (i.e., 66.7%) of trials called for primary task responses and one-third for background task reactions, whereas HiBac blocks required primary task responses in only one-third (i.e., 33.3%) of trials and background task responses in the rest of trials.
<bold>Design</bold>
In this experiment, we used a 2 (Proportion condition: HiPri, HiBac) × 2 (Backward compatibility: compatible, incompatible) repeated-measures design to analyze primary task performance, while we used a 2 (Proportion condition: HiPri, HiBac) design when analyzing the background task performance. RTs (in ms) and ERs (in %) served as dependent variables.
<bold>Data Analysis</bold>
Data were analyzed using R, Version 4.2.1 (R Core Team, 2021) and the packages dplyr, Version 1.0.9 (Wickham et al., 2023), ggplot2, Version 3.3.6 (Wickham, 2016), and cowplot, Version 1.1.1 (Wilke, 2020). For analyses, data sets were considered if they consisted of a minimum of 10 valid observations in each condition cell of the 2 × 2 design and reached at least 80% overall accuracy. This was done to ensure fairly precise measurements of our variables of interest. In Experiment 1, no data set needed to be replaced on the basis of these criteria.
All practice blocks and trials without any response were excluded from any analyses. Erroneous trials were omitted prior to RT analyses. Following Miller and Tang (2021), RTs below 200 ms or above 2,000 ms were also excluded (0.4% primary and 0.3% background task trials). For primary task performance, analysis of variance (ANOVA) on RTs and ERs included the factors Probability condition (HiPri vs. HiBac) and Backward compatibility (compatible vs. incompatible) as repeated measures. For background task performance, the comparison between the within-subjects factor Probability condition (HiPri vs. HiBac) was comprised as separate paired
<bold>Transparency and Openness</bold>
We report how we determined our sample size, all data exclusions (if any), all manipulations, and all measures in the study. All data and analysis code are available at PsychArchives (for analysis code, see Lück et al. 2022a,
Results for primary and background tasks are displayed in Figure 1.
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><anchor name="fig1"></anchor>
<bold>Primary Task</bold>
RT
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The ANOVA revealed a significant main effect of Probability condition,
Errors
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The main effect Probability condition was significant,
<bold>Exploratory Analyses: Effects of Task Sequence</bold>
A potential reason that task probability manipulation determined the size of the BCE in primary task RTs and ERs might be found in sequential effects of task order (primary vs. background task).<anchor name="b-fn4"></anchor><sups>4</sups> For example, the task set of a background task might be much more active, revealing a greater impact on primary task processing when a background task was executed in the previous trial. Especially in blocks with many background task trials, a primary task trial was quite often preceded by a background task trial. Thus, it could be that the increased BCE in these blocks only accumulated across these trials. Analogously, less influence of a background task and, thus, a smaller BCE would be expected with a high repetition of primary task trials as in blocks with many primary task trials. Therefore, it is possible that the observed effects of different task probabilities are attributable, at least partially, to local adaptation rather than global adaptation. To explore this possibility, we added the factor Previous task (primary vs. background task) to the ANOVA.
RT
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The BCE in the current primary task trial was larger when preceded by a background task trial (92 ms) than when it was preceded by a primary task trial (43 ms),
Errors
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As in RTs, the Previous task significantly affected the size of the BCE,
<bold>Background Tasks</bold>
RT
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Responses to the background tasks were significantly faster when background tasks were frequent (HiBac blocks, 620 ms), than when they were infrequent (HiPri block, 700 ms),
Errors
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ER closely mirrored RT, with fewer background task errors in blocks with a high probability of background tasks (HiBac blocks, 4.57%) compared to a low probability (HiPri blocks, 8.23%),
Experiment 1 replicated and extended previous findings of resource adjustments based on task frequency manipulations in dual tasks (Miller & Tang, 2021). Specifically, we tested whether manipulating the task probability in the PP paradigm also evokes processing differences if the upcoming task combination is uncertain. The results clearly indicate that participants were sensitive to the frequency manipulation. Performance critically depended on the task frequency of primary versus background tasks, even though the background task of a trial randomly varied between two task sets. The main findings of this experiment are, firstly, that the BCE in primary task performance was larger in conditions of frequent background tasks compared to blocks of frequent primary tasks.
Secondly, background task performance was better when background tasks were frequent compared to infrequent. This suggests that the amount of resources and attention deployed to a specific task type (primary vs. background task) was adjusted according to the frequency of this task type. Participants proactively gave priority to the more often executed task. This did not only ameliorate the performance in the more frequently presented task (background task performance) but also affected the between-tasks interference (BCE in primary task performance). In other words, the findings of Experiment 1 are in line with the idea that processing resources can be divided in a general manner when multitasking with unpredictable task combinations.
Finally, it should be noted that differences in the BCE between blocks of frequent primary and frequent background tasks seem not to be based on pure sequential effects. Background tasks might reveal a stronger impact on primary task processing when the background task was attended in the previous trial, which occurred more often in blocks of frequent than in blocks of infrequent background tasks. Exploratory sequential analyses confirmed that the influence of a previous background task on the BCE of a subsequent primary task was of the same extent for both block types, that is, frequent background task and frequent primary task. These findings show that the previous task type does not account for the different size of the BCE in blocks with many background tasks and blocks with many primary tasks.
Experiment 2
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Experiment 1 indicated that processing resources can be shared between tasks, and this allocation depends on the frequency of primary or background tasks. A larger BCE emerged, and background task performance improved when more background tasks required a response in a block. Thus, the resource allocation seemed to depend on the frequency of task type (i.e., background task) and less on the specific task set since one of two background tasks was displayed in each task (i.e., number or letter task).
Experiment 2 was dedicated to test the generalizability versus specificity of adapting to task probabilities. We investigated whether the benefits of the increased resource allocation to a high-frequent background task (e.g., number task) that was obtained in blocks with many background task trials compared to blocks with many primary task trials would spill over to the other background task (e.g., letter task). This other background task, however, did not share the same frequency distribution but was presented equally often in the two frequency-manipulated blocks (see Figure 2). For this, only one of the two background tasks (inducer task) was presented more or less often in the different probability blocks. The other background task (diagnostic task) appeared equally often in blocks of HiPri task and background task frequency. We investigated to which extent potential adjustments seen in inducer task trials would also transfer to trials with the unbiased diagnostic background task. If the processing adapts globally, the background task performance (RT and ER) should significantly improve for both inducer and diagnostic trials in blocks of frequent background task trials compared to blocks with many primary task trials. In addition, the BCE should significantly decrease (primary task performance) in blocks with many primary task trials compared to blocks with many background task trials. This pattern should arise in inducer and diagnostic background tasks alike, which would speak for a transfer of the processing adjustments from the biased to the unbiased task set. On the other hand, if the before mentioned processing adjustments are restricted to the frequency-biased task, the BCE and background task performance differences across the probability conditions should only emerge in inducer trials, but not in diagnostic trials. Statistically, the BCE, as well as background task performance, would significantly differ between blocks with many primary versus many background tasks only for inducer trials, not for diagnostic trials.
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><anchor name="fig2"></anchor>
Method
> <h31 id="xlm-50-5-775-d43e544">Participants</h31>
Following our preregistration (
Apparatus, stimuli, procedure, and instructions were the same as in Experiment 1 except as otherwise described. The crucial difference to Experiment 1 was that the background task frequency manipulation was entirely built on only one background task (i.e., inducer background task). Blocks with frequent primary task trials included 224 primary task trials and 112 background task trials, the latter consisting of 28 inducer and 84 diagnostic background task trials. Blocks with frequent background task trials included only 112 primary task trials and 224 background task trials, the latter consisting of 140 inducer and 84 diagnostic background task trials. Thus, the unbiased diagnostic background task appeared equally often (in 25% of trials) in both probability conditions (see Figure 2). In trials that required a primary task response, inducer and diagnostic task stimuli appeared equally often to ensure that any possible effects did not represent simple habituation to a particular background task. The sequence of probability conditions and the assignment which specific background task (letter or number task) served as inducer and diagnostic task were counterbalanced across participants.
<h31 id="xlm-50-5-775-d43e568">Design</h31>To analyze the primary task performance, a 2 (Proportion condition: HiPri, HiBac) × 2 (Backward compatibility: compatible, incompatible) × 2 (Background task type: inducer, diagnostic) repeated-measures design was applied. For the background task performance, a 2 (Proportion condition: HiPri, HiBac) × 2 (Background task type: inducer, diagnostic) design was used. RTs (in ms) and ERs (in %) served as dependent variables.
<h31 id="xlm-50-5-775-d43e572">Data Analysis</h31>We followed the same (preregistered) data preparation procedure and used the same statistical analysis software as in Experiment 1. For analyses, data sets were considered if they consisted of a minimum of 10 valid observations in each condition cell of the 2 × 2 × 2 design and reached at least 80% overall accuracy. Based on these criteria, no data set of any participant had to be excluded. The data trimming procedure for RTs below 200 ms and above 2,000 ms excluded 0.4% of primary task trials and 0.6% of background task trials. The ANOVAs on primary task RT and ER were extended by the within-subject factor Background task type (inducer vs. diagnostic). This led to a 2 (Probability condition: HiPri vs. HiBac) × 2 (Backward compatibility: compatible vs. incompatible) × 2 (Background task type: inducer vs. diagnostic) repeated-measures design. The background task performance was examined with two ANOVAs with the factors Probability condition (HiPri vs. HiBac) and Background task type (inducer vs. diagnostic) as repeated measures. To assess the probability condition difference separately for inducer and diagnostic background tasks in primary and background task performance, separate ANOVAs were conducted for each Background task type.
<h31 id="xlm-50-5-775-d43e576">Transparency and Openness</h31>We report how we determined our sample size, all data exclusions (if any), all manipulations, and all measures in the study. All data and analysis code are available at PsychArchives (for analysis code, see Lück et al. 2022a,
Results for primary and background task performance are displayed in Figure 3.
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><anchor name="fig3"></anchor>
<bold>Primary Task</bold>
RT
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The main effect of the factor Probability condition was significant,
Errors
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The main effect Probability condition was significant,
<bold>Exploratory Analyses: Effects of Task Sequence</bold>
Again, we investigated whether the task type (primary or background task) of the previous trials influenced the size of BCE and thus whether local adaptation might contribute to the differences between the probability conditions. We expanded the abovementioned ANOVAs with the factor Previous task (primary task vs. background task).
RT
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The BCE in the current primary task trial was larger when the previous trial was a background task trial (99 ms) than when it was a primary task trial (54 ms),
Errors
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As in RTs, the Previous task significantly affected the BCE, seen in a significant two-way interaction,
<bold>Background Tasks</bold>
RT
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Background task responses were faster in HiBac blocks (673 ms) compared to HiPri blocks (785 ms),
Errors
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ER closely mirrored the RT pattern. The main effect Probability condition was significant,
In Experiment 2, the probability conditions were conveyed by only one of the background tasks (inducer), while the other was unbiased (diagnostic). We found processing adaptations in primary and in background task performance for both background task types (inducer and diagnostic), speaking for global, task-unspecific adjustments. In more detail, the primary task performance revealed a larger BCE in blocks with frequent background task trials (HiBac) compared to blocks with many primary task trials (HiPri). This shows that the more frequent task type (background vs. primary) received more attentional resources. By shifting more capacity toward the background task, the background task interfered more with the processing of the infrequent primary task. Most importantly, these adaptations were found in the frequency-biased inducer background task as well as the frequency-unbiased diagnostic background task, implying that processing adjustments transferred from the biased inducer to the unbiased diagnostic task. Thus, such frequency-induced changes in resource allocation seem to be general, rather depending on the task context (many or few background tasks) instead of the specific background task set (inducer vs. diagnostic background task). Furthermore, the effect was found in RT and ER alike underlining its stability.
As in Experiment 1, exploratory sequential analyses did not support the assumption that the effect of probability condition on the size of the BCE may reflect a mere side product of trial-by-trial adjustments on the basis of previous task type (primary or background task).
In addition, the background task performance improved when background tasks had to be executed more often in a block. Since this pattern occurred in both background task types (inducer and diagnostic), again the processing adaptations were not restricted to the frequency-biased task set (inducer) but generalized to the unbiased diagnostic task. Interestingly, however, there was also evidence for task-specific background task processing adjustments as reflected in stronger probability effects for inducer as compared to diagnostic background tasks. This could stem from the experienced task frequencies and picking up their contingencies (De Houwer & Beckers, 2002). In blocks with many primary task trials, the diagnostic background task was executed more often than the inducer background task (25% vs. 8.33%). Thus, the diagnostic task might have received more processing resources than the inducer task, facilitating its responses. Hereby, the frequency effect could have turned out stronger for the inducer task. This result pattern suggests task-specific adjustments that can transfer between task sets if these task sets share central characteristics.
Experiment 3
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Experiment 2 demonstrated that the impact of background task probability on primary task processing was also observed for a background task that was not subject to the frequency bias. This finding suggests that resources allocated to the more frequent task type (i.e., background task in the HiBac blocks) seem to have spilled over to any background task even if that specific task did not share the same frequency bias.
It is tempting to take these transfer effects as evidence for global adjustments. Yet, it should be noted that the two background tasks were highly similar. Although the two background tasks in Experiment 2 required different semantic (number vs. letter) categorizations, they shared a high conceptual and visual similarity. Both tasks inherited a similar spatial left-to-right mental representation (Dehaene et al., 1993; Gevers et al., 2003) and were displayed at the same location (center), and in the same color, font, and size (white bold 80 px monospaced font). It is conceivable that any transfer may thus be restricted to tasks with a high resemblance.
Therefore, Experiment 3 was designed to test whether a transfer of processing adjustments can also be obtained in background tasks with reduced representational overlap. The letter discrimination now required a vowel/consonant categorization, reducing the spatial mental representation. In addition, the number and letter background tasks were presented in different colors (blue and red) to make them visually more distinct.
<h31 id="xlm-50-5-775-d43e850">Method</h31><bold>Participants</bold>
In line with our preregistration, 53 volunteer participants (44 female, one diverse, aged 18–34 years,
<bold>Apparatus and Stimuli</bold>
The apparatus and stimuli were identical to the previous experiment with the following changes: In the primary task, participants had to decide whether a shape was either a circle, a square, or a diamond. All shapes had a white border color. The letter background task was changed to a vowel/consonant categorization with the stimuli E, K, R, and U. The number background task did not change. Stimuli for each background task were displayed in different colors (red and blue).
<bold>Procedure</bold>
The procedure was the same as in Experiment 2 with the following adaptations. As there were three shapes in the primary task, two shapes were randomly selected from the set and assigned to the left (q-key) and right index fingers (p-key). The remaining shape represented the primary no-go response. For the background tasks, the specific color-to-task stimuli assignment (e.g., numbers in red and letters in blue) was randomly selected for each participant. In the letter background task, stimulus-response mappings were randomly selected for each participant. Half of the participants answered to a vowel with a left finger button press (q-key) and to a consonant with the right finger (p-key) and vice versa.
<bold>Design</bold>
As in Experiment 2, a 2 (Proportion condition: HiPri, HiBac) × 2 (Backward compatibility: compatible, incompatible) × 2 (Background task type: inducer, diagnostic) repeated-measures design was applied to analyze the primary task performance. For the background task performance, a 2 (Proportion condition: HiPri, HiBac) × 2 (Background task type: inducer, diagnostic) design was used. RTs (in ms) and ERs (in %) served as dependent variables.
<bold>Data Analysis</bold>
The same exclusion criteria, data cleaning processes, and data analyses were applied as in Experiment 2. Statistical analyses were conducted with the same software as in Experiments 1 and 2. The RT data trimming procedure excluded 0.4% of primary task trials and 1.2% of background task trials.
<bold>Transparency and Openness</bold>
We report how we determined our sample size, all data exclusions (if any), all manipulations, and all measures in the study. All data and analysis code are available at PsychArchives (for analysis code, see Lück et al. 2022a,
Results for primary and background task performance are displayed in Figure 4.
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><anchor name="fig4"></anchor>
<bold>Primary Task</bold>
RT
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As in the previous two experiments, the main effect of Probability condition was significant,
Errors
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The main effect of Probability condition was significant,
Exploratory analyses: combined measure of speed and accuracy
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In contrast to Experiment 2, primary task performance in this experiment was difficult to interpret due to diverging result patterns in RTs and ERs. Specifically, primary RT analyses yielded the unexpected finding of stronger probability effects in the diagnostic than inducer background task trials, whereas the reverse was true in ERs. Thus, we reanalyzed the primary task data using the
The ANOVA over the BIS confirmed the significant main effects of the Probability condition,
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><anchor name="fig5"></anchor>
<bold>Exploratory Analyses: Effects of Task Sequence</bold>
To examine whether the task type of the previous trial (primary or background task) might have influenced the modulation of the BCE between the probability conditions, the factor Previous task (primary task vs. background task) was added to the ANOVA.
RT
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The BCE in the current primary task trial was larger when the previous trial was a background task trial (35 ms) than when it was a primary task trial (11 ms),
Errors
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ERs closely mirrored RT results. The factor Previous task significantly affected the BCE, seen in a significant two-way interaction,
<bold>Background Tasks</bold>
RT
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The main effect of the factor Probability condition was significant,
Errors
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A significant main effect of the Probability condition was obtained,
In Experiment 3, two rather distinct background tasks were implemented that did not share the mental left-to-right spatial representation as the background tasks of Experiment 2. In addition, stimuli for each task were displayed in different colors to make them further distinct.
As expected, a high probability of background task (HiBac blocks) increased the BCE in the primary task (ERs) and led to faster responses for the more frequent background inducer task. In contrast to the previous experiments, primary task ER suggested that the probability manipulation only modulated the size of BCE in the frequency-biased inducer task trials but not in the frequency-unbiased diagnostic task trials. Unexpectedly, however, this pattern reversed in primary task RTs (i.e., the unbiased diagnostic tasks but not the biased inducer task showed a larger BCE in blocks with frequent background tasks) compared to frequent primary tasks.
To consider this inconsistency, we reanalyzed the data using the BIS, a measure combining speed and accuracy (Liesefeld et al., 2015; Liesefeld & Janczyk, 2019). This score was chosen because it is said to have an advantage over other popular measures such as inverse efficiency scores, rate-correct scores, or linear-integrated speed-accuracy scores (Liesefeld & Janczyk, 2019). The BIS provided evidence that the probability effect generalized: The task probability affected the BCE size in trials with the biased inducer task and, to a lesser extent, in trials with the unbiased diagnostic task.
In sum, while the primary task results of Experiment 2 were clear-cut, some caution needs to be applied when interpreting the primary task performance in this experiment due to diverging result patterns in RTs and ERs. Specifically, consistent evidence in favor of transfer was only observed when transforming data into a combined speed–accuracy measure. Fortunately, there was a clear and strong pattern in background task performance, which allows a more meaningful conclusion: Only in the inducer background task, a big performance advantage emerged in both RT and ER in blocks with many background tasks. The performance in the diagnostic background task was completely unaffected by the task probability.
Thus, the combined results suggest that the processing resources were divided according to the probability of tasks. By differentiating the tasks, the transfer of these adjustments was limited, though. In background task performance the benefit of increased background task trials was restricted to the biased task set. When handling conceptually and visually distinct background tasks, their performance seemed to be adjusted in a task-specific fashion. Making the background tasks more distinct might have led to a more separate representation of the task sets. Using more distinct task sets might also play a role in why we observed the diverging primary task performance in this experiment (but not Experiment 2). The result pattern made an interpretation of primary task performance less straightforward than that of the background task performance.
The combined measure of speed and accuracy seems to suggest that shielding against interference was at least partially adjusted in a global fashion. Increased interference effects in blocks with many background task trials were seen in inducer as well as diagnostic task trials. It might be that a common source of processing conflict—here the identical motor responses—suffices to provoke a transfer of context induced processing adjustments. The results of Experiment 3 underline how important the presentation and internal representation of tasks can be for the benefit of resource allocation in dual tasks.
General Discussion
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When processing several tasks concurrently, humans can adapt the amount of processing resources allocated to each individual task to maximize efficiency. This study investigated how general processing adjustments induced by task frequencies are in multitasking environments. Specifically, we tested whether increased parallel processing is restricted to the task set inducing the frequency manipulation (task-specific processing adjustment) or whether processing adjustments can spread to another unbiased task (global processing adjustment).
For this, we adapted the prioritized PP (Miller & Durst, 2014, 2015), in which a background task had to be executed only when the primary task stimulus did not require a response (i.e., no-go trial). We included two background tasks so that a stimulus of either background task was presented with the go or no-go stimulus of the primary task. In three experiments, the frequency of primary versus background task was manipulated, resulting in blocks with a high frequency of primary or high frequency of background task trials, respectively. Task frequency-induced deployment of attentional resources were assessed via two markers of parallel processing, first, the BCE in primary task performance and second, the background task performance.
The results of primary task performance suggest that resource sharing between the primary and background task increased in blocks with a high proportion of background tasks (Experiments 1 and 2). In line with Miller and Tang (2021), the impact of the background tasks on performance in the primary task was stronger (e.g., larger BCE) when the background tasks were executed frequently compared to infrequently. Importantly, and as an extension to Miller and Tang (2021), this task frequency-induced bias of resource deployment was obtained when two background tasks were implemented, and participants were not able to prepare for the execution of a specific background task in advance. In Experiment 2, the bias of background task frequency was applied only to one of the two background tasks (inducer task), while the other occurred equally often in all blocks and served as the diagnostic task to test for a general adjustment of resource deployment. Importantly, in blocks with a HiBac task frequency, a larger BCE and, thus, more parallel processing was found for both the biased inducer and the unbiased diagnostic background task. Concluding, participants adapted their performance in an abstract and global fashion which did not depend on the specific task sets of an upcoming trial.
These findings were further substantiated by the obtained performance in the background tasks. The background task performance was considerably improved (i.e., faster responses and fewer errors) when either both background tasks (Experiment 1) or only one background task (Experiment 2) occurred with high probability. Importantly, in Experiment 2, this performance benefit was not only found for the frequency-biased inducer background task but was also observed in the frequency-unbiased diagnostic background task, even though to a somewhat lesser extent. This transfer to a frequency-unbiased task suggests a more global shift of resource deployment in favor of all background tasks. The general observation that background task performance improved in blocks with many background tasks compared to blocks with many primary tasks is a strong indicator of increased parallel processing. Considering that the no-go primary task processes should be particularly slow in blocks with many background tasks, strict serial processing should have prolonged background processing—not improve it (cf., Miller & Tang, 2021).
These findings demonstrate that task frequency-induced resource allocation and respective processing consequences (i.e., the extent of parallel processing) can, in principle, generalize to frequency-unbiased tasks. Thus, to our knowledge, this is the first study which provides empirical evidence for a global deployment of attentional resources. Importantly, the results of Experiment 3 help to further constrain under which conditions such transfer effects occur. Against the background of Experiment 2, the results of Experiment 3 suggest that global parallel processing seems to be limited when rather distinct (background) tasks are implemented. Specifically, the study found no indication of transfer effects in background task performance, and only a limited transfer of adjustments was observed for between-tasks interference processing when considering a combined measure of speed and accuracy.
Importantly, the results of the background task performance provide an overall coherent picture favoring local adjustments that were restricted to the frequency-biased task. This shows that adjusting processing resources not only highly depends on the context (i.e., task frequency manipulation) but also on the characteristics of the included task sets and their similarity. The finding, that the frequency-induced resource allocation remained within the frequency-biased task but did not transfer to conceptually dissimilar tasks, suggests that people are able to reactively (on-the-fly) adjust their parallel task processing to specific background tasks from trial to trial as long as some features make these tasks more distinct.
The ambiguous result patterns in Experiment 3 suggests that the distinctness of the two background tasks might have affected the between-tasks interference. A combined measure of speed and accuracy (BIS) showed that the adjustments to task probability, which emerged in trials with an inducer background task stimulus, were also observed in trials with an unbiased diagnostic background task stimulus. The smaller transfer effect in Experiment 3 compared to Experiment 2 highlights the role of task similarity. However, it also suggests that the degree of task shielding may partially operate in a global fashion, even when facing more distinct tasks. One possibility is that the inducer and diagnostic background tasks impose a common source of conflict on responding in the primary task, so it may not matter which task is more frequent in the HiBac than HiPri condition.
In sum, these findings help to further constrain theorizing within multitasking models that allow parallel processing and stimulate future research. For example, from both a theoretical and practical point of view, it seems useful to further elaborate on the exact features that determine the potential of resource deployment, such as dimensional overlap, overlap of representational codes, as well as input and output modality.
<h31 id="xlm-50-5-775-d43e1253">Implications for Task-General or Task-Specific Adjustments in Multitasking</h31>It could be argued that the probability of the primary and background task only affected the degree of between-tasks interference because the blocks featured different sequential contingencies. This is, interference should be higher if the background task was activated and executed in the previous trial (i.e., background task trial). How often such a trial sequence appeared in a block systematically varied with the task probability: In blocks with many background task trials, it was more likely that a background task preceded a primary task trial than primary tasks followed one another. Thus, these sequence effects could have accumulated in blocks with many background task trials and caused the found increased interference. However, exploratory analyses did not support this idea. The identity of the previous task did not determine whether the task probability affected the size of interference. This again highlights that manipulating the task probability triggered rather contextual and general adjustments. However, these sequential analyses revealed a novel finding that participants appeared to adapt the degree of parallel processing based on recent experience, as evidenced by a higher BCE in a current trial when the previous trial required a background task response compared to a primary task response. Notably, this adaptation effect was observed independently of the task probabilities manipulation.
In addition, task-specific adjustments are supported by recent findings that each task combination in a dual task is internally represented as its own entity (Hirsch et al., 2017, 2018, 2021). Implementing two varying secondary tasks (T2 and T3) alongside a constant first task (T1) in a PRP paradigm, switch costs were found when the secondary task changed between trials. This was taken as evidence for the existence of two individual dual-task sets for each secondary task, so-called task-pair sets (i.e., T1–T2 set and T1–T3 set). The similarities between the PRP and PP paradigms (Miller & Durst, 2015) suggest that the division of tasks into task-pair sets may also apply to the PP paradigm. Then, individual task-pair sets might have been formed for each background task (i.e., primary task and inducer background task vs. primary task and diagnostic background task). As task-pair sets also include cognitive parameters to identify the subtasks and perform them in the proper order (Hirsch et al., 2018), it is plausible to assume that the extent of resource sharing between the specific tasks may have also been integrated in the corresponding higher-order task-pair sets.
Following this logic, manipulating the frequency of the tasks induced task-specific adjustments in resource allocation. That the degree of resource sharing transferred between similar tasks in Experiment 2 gives rise to the idea that the background tasks might have been integrated to a larger extent compared to when the tasks were distinct (Experiment 3). Then, they might have been represented as two subdivisions of the category background task instead of being seen as two separate entities, that is, number versus letter background task. Exploratory analyses seem to support this argumentation.<anchor name="b-fn7"></anchor><sups>7</sups> Switching between the inducer and the diagnostic background tasks seemed easier between similar rather than between more distinct background tasks. Specifically, the switch costs in Experiment 2 with similar background tasks were half the size of those in Experiment 3 that implemented distinct background tasks. Consequently, reduced switch costs when similar task sets were implemented suggests that the representations of the background tasks overlapped more strongly in Experiment 2, while they were represented more separately in Experiment 3. Notably, the background tasks were not fully integrated, even when the inducer and diagnostic tasks were similar, because switch costs were not eliminated.
Furthermore, the differences between the background task sets of Experiments 2 and 3 allow speculation about possible features that might determine whether processing adjustments transfer between tasks: the degree of visual and conceptual overlap. In order to create more distinct task sets for the two background tasks in Experiment 3, the stimuli for each background task were displayed in a different color. This visual distinction might suffice to prevent transfer of resource deployment according to ECTVA. Within this theory, how stimuli are processed depends on the value of certain parameters. One set of these parameters adjusts the visual attention that is directed towards a certain stimulus within the frame of the theory of visual attention (Bundesen, 1990). One of these is the priority parameter that determines the extent of attention that is addressed to a stimulus. Displaying tasks in different colors is a highly salient feature difference which could have triggered different priorities and thus attentional scopes to be addressed to the tasks. Following this implementation of control, manipulation effects in the frequency of one task should transfer to other tasks as long as they are visually similar because they received the same priority parameter irrespective of the degree of conceptual overlap.
In addition, the conceptual overlap between the background tasks was reduced. In Experiment 2, both the number and the letter background tasks shared a spatial left-to-right mental representation. In Experiment 3, this spatial representation was removed in the letter background task by implementing a vowel–consonant categorization. Such categorization rules are known to facilitate task-set separation and to protect processing from unrelated information (Dreisbach & Haider, 2009; Dreisbach & Wenke, 2011). When tasks share an abstract conception in their categorization rule, a communality between the tasks could have formed that enabled them to interfere with one another. In our case, an interference between the background tasks might have led to an exchange of the processing adjustment that was initially only associated with one task. Consequently, the processing adjustment in the inducer background task could have transferred to the diagnostic background task.
Finally, there is another approach that could account for why the background tasks were represented less distinctively in Experiment 2 than Experiment 3, that is, the information reduction hypothesis (Haider et al., 2005; Haider & Frensch, 1996, 1999b). This theoretical framework is often used in learning and skill acquisition to describe how task processing accelerates by practice. It assumes that over time people learn to distinguish between task-relevant and task-irrelevant dimensions (Goldstone & Styvers, 2001). Any redundant information can then be ignored to ease and speed up processing. This strategy also reduced eye movements towards irrelevant stimuli (Haider & Frensch, 1999a). Following this logic, it is possible that the letter and number background tasks were integrated to some extent in Experiment 2, making switching between these tasks easier. The observation that switch costs between the two background tasks were reduced in Experiment 2 compared to Experiment 3 supports this notion. However, the presence of switch costs in both experiments (see footnote 7) indicates that the tasks were at least partially represented distinctively.
In general, the considerations about potential features which determine task-general versus task-specific resource allocation rest on experimental changes between Experiments 2 and 3. So far, we identified the visual (dis)similarity and possibly shared mental representations between the two background tasks to guide the generality of adjustments. Further studies are certainly required to describe in more detail which task features and conditions determine when and how resource allocation is generalized and thus a transfer of resource-induced processing.
<h31 id="xlm-50-5-775-d43e1311">Extension to Other Situations With Frequency-Based Control Adjustments</h31>As elaborated, our results indicate that the manipulation of task frequencies determined the degree of parallel processing adjustments in dual tasking. Moreover, our findings suggest that the similarity between two tasks defines whether these frequency-induced changes generalize to an unbiased task.
The question to which extent frequency manipulations in one task (or context) transfer to other unbiased items/tasks is a notorious one in the field of cognitive psychology. In conflict tasks, for example, the context of (in)frequent conflict was shown to bias processing, both in the frequency-biased trials and in the frequency-unbiased trials (Bugg & Chanani, 2011; Bugg & Crump, 2012; Crump & Milliken, 2009). Here, however, frequency-unbiased trials consist of unique stimuli that belong to the same task set, and therefore, the same categorization rule can be used. Such control states induced by conflict frequencies have been shown to transfer even to newly introduced stimuli or conceptually similar task sets as long as the context of conflict frequency remains unaltered (Surrey et al., 2017).
Limited task-specific transfer was reported for frequency manipulations in the task switching domain. Manipulating the proportion of task switches versus repetitions within blocks, for example, evoked alterations in switch costs that were restricted to the task level (Siqi-Liu & Egner, 2020). Blocks consisting of predominantly task switch trials facilitated performance in task switch trials, replicating the typical finding of reduced switch costs when switching a lot (Dreisbach & Haider, 2006; Monsell & Mizon, 2006; Schneider & Logan, 2006; for a review, see Dreisbach & Fröber, 2019). Importantly, conveying the switch frequency by only one item of a task set, the adaptation spreads to the whole task set (Siqi-Liu & Egner, 2020; cf. Experiment 4). However, when only one of two tasks induced the switch frequencies, only the switch costs in the biased inducer task depended on the proportion of switches in a block (Siqi-Liu & Egner, 2020; cf., Experiments 3a and 3b). The processing of an unbiased task set did not change. These results therefore suggest task-specific processing adjustments.
Our findings imply that the similarity between the
Conclusion
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In conclusion, the presented results of this article suggest that altering the task frequencies can modify the degree of parallel processing in the affected tasks. These processing adjustments can then generalize to unbiased tasks. We found that tasks that shared many features (visually and conceptually) were underlying the same processing adaptations. When facing rather distinct task sets, the transfer was limited: Adjustments in background task performance were confined to the inducer task. Some evidence of transfer in the primary task was only observed in a combined speed-accuracy measure. Future studies are needed to investigate which task features allow processing adjustments to transfer from the inducing task to an unbiased task set and whether a common source of conflict might enable global changes when adjusting the degree of between-tasks interference.
Footnotes
<anchor name="fn1"></anchor><sups> 1 </sups> Note, in this context, parallel processing refers to Task 2 central processing that takes place while Task 1 is processed and typically causes interference between these tasks. In the literature, the term parallel processing has also been taken to reflect the ability to perform two tasks concurrently without interference and performance costs (see Fischer & Janczyk, 2022).
<anchor name="fn2"></anchor><sups> 2 </sups> The actual physical size of stimuli could have varied across participants because each participant scaled the size of their monitor in the beginning of the experiment by setting a displayed rectangle to the size of an actual credit card.
<anchor name="fn3"></anchor><sups> 3 </sups> The results did not change when a factor Background task set (letter task vs. number task) was included in the analyses.
<anchor name="fn4"></anchor><sups> 4 </sups> We thank Iring Koch for raising this possibility. It should be noted that our design was originally not planned for sequential analyses. This leaves us with a limited number of observations per participant and condition cell, ranging from nine to 72 in Experiments 1 and 2 and from one to 73 in Experiment 3. Thus, inferences have to be handled with caution.
<anchor name="fn5"></anchor><sups> 5 </sups> Results of the power analysis suggested 44 data sets for detecting an effect size of η<sups>2</sups>p =.18 in a three-way interaction with a power level of 0.8 (and a significance level of 0.05). The effect size analysis was based on RT results of the two-way interaction between the factors Probability Condition and Backward compatibility in Experiment 1.
<anchor name="fn6"></anchor>
<sups>
6
</sups> Exploratory analyses examined whether this might have been induced by the different Background task set (letter task vs. number task). Including the Background task set (letter task vs. number task) in the ANOVA revealed a tendency towards stronger BCE in the number (33 ms) than the letter task (14 ms),
<sups>
7
</sups> Exploratory analyses examined whether the background tasks were integrated in Experiment 2 and 3. For this, we looked at whether there were switch costs between direct sequences of inducer and diagnostic background tasks. If the tasks were integrated, switch costs should be reduced. Note that these results had only limited power. As we did not plan for sequential analyses, the number of observations per condition cell were limited and participants had to be excluded from analyses because of missing values. Specifically, nine participants were excluded in Experiment 2, and 10 participants in Experiment 3. When only considering background task trials and including the factor Background task transition (repetition trial vs. switch trial), the main effect of Background task transition was significant in Experiment 2,
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