Beyond stimulus-response rules: Task sets incorporate information about performance difficulty

Abstract

The capacity for goal-directed behavior relies on the generation and implementation of task sets. While task sets are traditionally defined as mnemonic ensembles linking task goals to stimulus-response mappings, we here asked the question whether they may also entail information about task difficulty: does the level of focus required for performing a task become incorporated within the task set? We addressed this question by employing a cued task-switching protocol, wherein participants engaged in two intermixed tasks with trial-unique stimuli. Both tasks were equally challenging during a baseline and a transfer phase, while their difficulty was manipulated during an intermediate learning phase by varying the proportion of trials with congruent vs. incongruent response mappings between the two tasks. Comparing congruency effects between the baseline and transfer phases, Experiment 1 showed that the task with a low (high) proportion of congruent trials in the learning phase displayed reduced (increased) cross-task interference effects in the transfer phase, indicating that the level of task focus required in the learning phase had become associated with each task set. Experiment 2 indicated that strengthening of task focus level in the task with a low proportion of congruent trials was the primary driver of this effect. Experiment 3 ruled out the possibility of cue-control associations mediating this effect. Taken together, our results show that task-sets can become associated with the focus-level required to successfully implement them, thus significantly expanding our concept of the type of information that makes up a task set.

Introduction

“Cognitive control” refers to our ability to employ an internal goal to guide behavior (e.g. Miller & Cohen, 2001). This capacity allows for highly flexible behavior, but many of its constituent mechanisms are poorly understood. A core construct mediating cognitive control is the notion of a “task set”, conceived of as a mnemonic ensemble of a task goal and its associated rules for linking stimuli to actions (e.g., Kiesel et al., 2010; Monsell, 2003). For instance, the task set involved in peeling potatoes would link the task goal and its associated rules for holding the potato and pulling the peeler across its skin. Task sets are crucial for goal-directed behavior because they specify the contextually appropriate action to perform on stimuli that in principle can afford many different acts; for instance, the potato also lends itself to being washed or diced, but imposing the “peeling task set” overrides these rival stimulus-response associations. Notably, different tasks do not only differ in the particulars of their goals and stimulus-response links, but also in terms of the level of attentional focus required for performing them successfully. For instance, peeling potatoes arguably requires a less strongly imposed task set than deboning a fish filet, and even the same task can require different levels of attentional investment at different times (for instance, as a function of changing levels of concurrent distractions). The present study’s overarching goal was to gain a better understanding of how task sets and task difficulty relate to each other.

Influential definitions of the essential components of a task set include a task rule (typically, a stimulus categorization rule) and the associated mapping of stimulus categories to responses (e.g., Rogers & Monsell, 1995). To illustrate, successfully modeling performance on the classic color-naming Stroop task requires specifying the current task rule (e.g., “categorize the font colors of the color-word stimuli”), and how task-relevant stimulus features map onto responses (e.g., “press the left button for red and the right button for green”) (e.g., Botvinick et al., 2001; Cohen et al., 1990). Moreover, the implementation of a task rule is conventionally conceptualized as a top-down attentional biasing process (e.g., Cohen et al., 1990; Gilbert & Shallice, 2002; Meiran, 2000). With reference to the above example, performing the color-naming task requires paying attention to the task-relevant stimulus features (font color) and ignoring their task-irrelevant stimulus features (word meaning). While the notion of paying attention to task-relevant stimulus features is therefore inherent in traditional definitions of task set, these definitions do not entail that a task set also contains information about just how much attention needs to be invested to carry out the task successfully. We here refer to this as “task focus level”, a putative control parameter that governs how strongly the current task set is being implemented or, equivalently, the level of top-down attentional biasing on task-relevant over task-irrelevant stimulus features (cf. Botvinick et al., 2001; Cohen et al., 1990).

The control parameter of task focus level has been investigated previously. For instance, how task focus level is adjusted to meet moment-by-moment changes in demand has been studied extensively (e.g.,Botvinick et al., 2001; Jiang & Egner, 2014). but it is not presently clear whether information about the focus level required for performing a given task becomes integrated in the task set itself. It has been known for a long time that the brain binds together concurrently processed information, such as different features of an object (e.g. Kahneman et al., 1992; Treisman & Gelade, 1980), as well as actions performed in relation to that object (e.g., Hommel, 1998). Such stimulus-response ensembles have been conceptualized as mnemonic “event files” (Hommel, 2004; Hommel et al., 2001), whereby subsequent encounters with some or all of the event features lead to the retrieval of the (most similar) previously encoded event file, which can serve as a shortcut for perceptual inference and response selection. Several more recent findings have suggested that event files also appear to incorporate internal mental states (reviewed in Abrahamse et al., 2016; Egner, 2014; Frings et al., 2020). For instance, an object that a particular semantic classification task is being performed on appears to become associated with that task, such that the object facilitates the execution of that task (compared to other tasks) on subsequent exposures (e.g., Moutsopoulou et al., 2015; Pfeuffer et al., 2017; Waszak et al., 2003). Of particular relevance to the current purpose, it has also been demonstrated that specific stimuli can become associated with the control parameter of task focus level: stimuli that are frequently paired with high attentional demands appear to reinstate a greater focus of attention on task-relevant stimulus features (e.g., Bugg et al., 2011; Bugg & Hutchison, 2013; Spinelli & Lupker, 2020)

In sum, the extant literature has documented that specific stimuli can become associated both with task sets and with particular task focus levels. However, it is not presently known whether the co-occurrence of particular task sets and demands on task focus levels become associated with each other, even in the absence of repeated stimuli. In other words, can people learn to associate an abstract task set (rather than concrete stimuli) with the task focus level required for executing that set? This is a conceptually important question, because an affirmative answer would significantly expand our idea of what a task set is, adding to the categorical attentional targets that are inherent in a task rule (e.g., “attend to color” versus “attend to words”) the notion that task set representations have, or can acquire, information about how much attention needs to be invested, or the task focus level required to perform the task successfully. Integrating this type of information with the basic task rules would seem highly useful, as it would allow task sets retrieved from long-term memory to be implemented with the level of task focus typically required for them already in place, rather than having to be newly titrated. While intuitive, this sort of learned association between task rules and task focus level has, to our knowledge, never been established empirically.

The current study therefore aimed to test the hypothesis that task set representations may entail task focus level settings. To achieve this goal, we employed a classic cued task-switching protocol in which we manipulated the level of focus required to successfully perform each task. During the experiments, participants were tasked with classifying trial-unique stimuli according to their size or animacy (Fig. 1a). Following an initial baseline phase where both tasks required a comparable level of focus, we varied the demand-levels between the tasks (rendering one task more difficult) during a subsequent learning phase, expecting participants to increase their level of focus on the more difficult relative to the easier task. This was followed by a final transfer phase, where both tasks were again equally demanding (Fig. 1b). By comparing the baseline and transfer phase performance between the two tasks, we aimed to investigate whether the change in demand levels introduced during the learning phase became bound to, or integrated with, the respective task sets, in which case the formerly more demanding task set would continue to be associated with a higher level of task focus during transfer.

Figure 1.

A) Trial structure: Example stimulus and cue display, and trial timing, for all experiments. B) Approximate percentage of congruent and incongruent trials for each experiment, as a function of task and phase.

Experiment 1a

The first experiment sought to test whether task sets can become associated with the level of focus required to successfully perform the task in question. To make participants associate a particular task with a specific required focus-level, we created a paradigm where participants switched between two tasks, and - during a learning phase - one of the two tasks was rendered more attentionally demanding than the other. Specifically, the required task focus level was manipulated indirectly by varying the proportion of congruent trials between the two task sets. Congruency here refers to whether a given stimulus would require the same response in both task sets (in which case it would be a congruent stimulus) or a different response in the two task sets (in which case it would be an incongruent stimulus). This type of response mapping manipulation is well-known to produce a cross-task congruency effect, whereby responses are slower and more error-prone on incongruent than congruent trials (e.g., Allport et al., 1994; Kiesel et al., 2010; Meiran, 1996; Rogers & Monsell, 1995; reviewed in Rubin & Koch, 2006; Vandierendonck et al., 2010).

This effect has been attributed to “cross-talk” (interference) in processing due to the ambiguous nature of the stimulus, which can cue either task set, and - in the case of an incongruent mapping - cues opposing responses under the two sets (Koch & Allport, 2006; Rogers & Monsell, 1995; Steinhauser & Hübner, 2007). Based on the assumption that the degree of such cross-talk would be small when the irrelevant stimulus associations are successfully ignored, and high when they are not, many authors have taken the size of the cross-task congruency effect as an index of the relative degree of task focus on, or shielding of, the current task set (e.g., Braem, 2017; Dreisbach & Fröber, 2019; Geddert & Egner, 2022). In line with this literature, we consider congruent trials as requiring a low task focus level to be performed correctly, and incongruent trials as requiring a high task focus level to be performed correctly, and we interpret the size of the congruency effect as an inverse metric of task focus, such that a smaller congruency effect indicates greater task focus (because the participant was more successful at focusing on the task-relevant and ignoring the task-irrelevant stimulus features).

We expected the manipulation of the rate of (in)congruent trials in the learning phase to produce an adaptation in task focus level, whereby participants would impose a higher focus level on the task that was associated with more incongruent trials. This would be expressed in a “proportion cross-task congruent effect”, where the mean congruency effect is reduced in the task where incongruent trials are frequent compared to the task where incongruent trials are rare (e.g., Geddert & Egner, 2022). This data pattern is widely interpreted as reflecting adaptation of task focus level to contextual demands (Botvinick et al., 2001; for review, see Bugg & Crump, 2012). By comparing congruency effects between a pre-learning baseline phase and a post-learning transfer phase, in both of which congruency rates did not differ for the two task sets, we sought to determine whether learned task focus levels during the learning phase would “stick” to each task set during the transfer phase.

Participants

Given that we are not aware of any previous study probing associations between task sets and task focus, we simply aimed for a typical sample size in the fields of task-switching and conflict-control in Experiment 1a (N = 36 participants), with the intention to subsequently directly replicate any finding of interest in Experiment 1b. Data were collected from online Amazon Mechanical Turk (Mturk) participants located in the US with an approval rate of over 95%, who had completed more than 1000 HITs. We collected data until we reached our target sample size of 36 participants who achieved the accuracy criterion (> 75%). A total of 43 participants completed the experiment. Seven participants were rejected for not meeting the accuracy criterion, and we excluded data from three more participants due to having no correct trials in one or more of the experimental cells. As a result, our final sample consisted of 33 participants (mean age = 42, SD = 12; 12 females, 21 males). The study was approved by the Duke University Campus Institutional Review Board.

Stimuli

684 pictures of animals and objects were sourced from several databases (Hovhannisyan et al., 2021; Konkle & Caramazza, 2013; Moreno-Martínez & Montoro, 2012; Possidónio et al., 2019; Russo et al., 2018). The 684 stimuli were equally divided between four categories: natural and large (e.g., an elephant), natural and small (e.g., a mouse), human-made and large (e.g., a building) and human-made and small (e.g., a cigar). All pictures were re-sized to 300 by 300 pixels. Each stimulus was presented only once in the experiment.

Task and Procedure

Participants performed two categorization tasks, classifying stimuli either according to their origin (natural/human-made) or size (larger/smaller than a shoebox). For both tasks participants classified the stimuli with the “A” and “L” keys (e.g., “A” for stimuli representing small/natural objects and “L” for stimuli representing large/human-made objects). Across participants we maintained the key-to-condition constant for the size task (“A” for small and “L” for large), while we counter-balanced the button assignment for the two categories of the origin task (natural vs. human-made) over participants, in order to vary which stimulus categories were congruent/incongruent across participants. The task was programmed using JavaScript and jspsych (De Leeuw, 2015).

Each trial consisted of a 2 s presentation (or until response) of an item inside a red or blue rectangular frame. The color of the frame cued the task that the participants needed to perform on that item. The frame color assigned to each task was counter-balanced over participants. After the response or the end of the 2 s stimulus presentation, a feedback screen (“correct”/”incorrect”) was shown for 0.5 s. The trial ended with a fixation cross randomly jittered over a uniform distribution of 0.45, 0.6 and 0.75 s intervals. An example trial is presented in Figure 1A. The two tasks were presented equally often and pseudo-randomly inter-mixed, with the constraint of no more than 3 consecutive presentations of the same task.

The level of task focus required to classify stimuli was manipulated via the potential for cross-task interference, that is, the congruency of the mapping between the stimuli and response keys across the two tasks. For congruent trials, the stimulus required the same response in both tasks. For incongruent trials, the stimulus required a different response between the tasks. For example, a picture of an ant would be congruent if participants were instructed to respond with the same key for small items and for natural items, while a picture of a matchbox would be incongruent under this response mapping.

The experiment began with instructions, followed by 12 practice trials. After completing the practice trials, participants performed 100 trials in a “baseline phase”, 300 trials in a “learning phase”, and 100 trials in a “transfer phase”. Each phase was immediately followed by the next, and the participants were not informed about any differences between these phases. As illustrated in Figure 1B, the baseline and transfer phases had approximately 50% of congruent and incongruent items presented in each task. By contrast, during the learning phase, we manipulated the level of attentional focus that participants needed to perform each task. One task was assigned to be the low proportion congruent task, while the other task was assigned to be the high proportion congruent task. The low proportion congruent task contained approximately 75% incongruent stimuli, thus requiring a higher average task focus level, while the high proportion congruent task contained approximately 75% congruent stimuli, thus requiring a lower average task focus level. The assignment of tasks (origin or size) to the high/low proportion congruent conditions was counterbalanced across participants.

Trial sequences were generated randomly for each participant, with some constraints. Our main objective in the randomization was to maintain the target proportion of congruent and incongruent trials per task and phase depicted in Figure 1B. Other objectives were to limit the repetitions of each task to no more than three consecutive trials and ensure a balanced distribution of task switch probabilities. This approach produced some variability in congruency and switch proportions across participants. While on average the proportion of congruent and incongruent trials reached the targeted values, it had a standard deviation of 2% from those values. Proportion of congruent and incongruent trials and switch/stay trials for all experiment proportions can be found in Table A1 and A2 of the Appendix. The mean switch probability across participants was 54% with a standard deviation of 2%.

Several aspects of this design are particularly important to note; namely, that the overall level of congruency in the learning phase was ~50%, that all trials involved unique, never-repeated stimuli, and that each task involved the same number of stimuli from each of the four stimulus categories (natural/large, natural/small, human-made/large, human-made/small). This means that any effects of the proportion congruent manipulation on behavior in the learning and transfer phases can only be attributed to task-set specific learning processes, and not to learning about block-level demands (as in traditional “listwide” proportion congruent manipulations; for reviews, see Braem et al., 2019; Bugg & Crump, 2012), stimulus-level demands (thus preempting item-specific switch proportion effects and stimulus-response contingency learning effects; for reviews, see Braem et al., 2019; Bugg & Crump, 2012), or stimulus category-level demands.

Data analysis

The primary dependent measure of interest was response time (RT) on correctly performed trials, but we also analyzed and reported performance accuracy. We expected RT to vary with the difficulty of the experimental conditions, in that it should take participants longer to switch than to repeat a task, and longer to respond to incongruent than to congruent stimuli. The latter effect was furthermore expected to be modulated by the proportion congruency manipulation. The data pre-processing and analysis were conducted in R Studio (RStudio Team, 2020). To visualize the results, we used the ggplot2 package (Wickham, 2011).

For reaction time (RT) analysis, we removed the first trial of each block, incorrect trials, and trials following incorrect ones. For analyzing accuracy, only the first trial of each block was removed.

There were two sets of analyses; the first assessed whether the learning phase manipulation was successful in producing task-level proportion congruent effects (smaller mean congruency effects in the low proportion congruent task compared to the high proportion congruent task), and the second probed whether any task set-focus associations acquired in the learning phase would generalize to the subsequent unbiased transfer phase. To test the former, a 2 x 2 x 2 repeated measures analysis of variance (rmANOVA) was conducted on the learning phase data, with task (low proportion congruent /high proportion congruent), congruency (congruent/incongruent), and task transition (stay/switch) included as factors. Note that while the factor of task transition was included in all analyses, switch costs were not of primary interest in this study.

After confirming a proportion congruent effect in the learning phase, we asked the main question of interest: If participants associated the focus level needed to successfully perform a task with a specific task-set, we would expect to observe the proportion congruent effect from the learning phase to extend to the transfer phase, even though here both tasks involved never-before-seen stimuli with an unbiased 50% congruency rate. To test this, we compared the RT patterns of participants between the pre-learning baseline block and the post-learning transfer block via a 2 x 2 x 2 x 2 rmANOVA with task (low proportion congruent /high proportion congruent), congruency (congruent/incongruent), task transition (stay/switch), and phase (baseline/transfer) included as factors. A successful association between task set and task focus level would be expressed in a 3-way interaction between task, congruency, and phase, reflecting relatively smaller/larger congruency effects in the transfer than baseline phase for the low proportion congruent task/high proportion congruent task, respectively. The same analysis scheme was used for analyzing accuracy data. All data, analysis code and task script can be found at: https://osf.io/duy9c/

Results

Reaction Time

Descriptive statistics are presented in Table 1 and visualized in Figure 2A, and the ANOVA results are shown in Tables A4 and A5. We began by probing whether the learning phase manipulation was successful. Critically, the learning phase data indeed displayed a proportion congruent effect, as reflected in a significant interaction between task and congruency (F(1,32) = 65.85, p < .001). As can be seen in the middle panel of Figure 2A, the difference between congruent and incongruent items in the high proportion congruent task ($M_{diff}=133$; t(32) = 9.07, p < .001) was larger than in the low proportion congruent task ($M_{diff}=7$; t(32) = 0.44, p = .66). Thus, the learning phase was successful in inducing adaptation to varying task difficulty. The interaction between congruency and transition was also significant F(1,32) = 17.31, p < .001), driven by higher switch cost for incongruent items ($M_{diff}=121$; t(32) = 8.84, p < .001), compared to congruent items ($M_{diff}=78$; t(32) = 5.68, p < .001). Other effects in this phase included expected main effects of congruency (i.e., the classic cross-task congruency effect, F(1,32) = 24.95, p < .001), task transition (i.e., classic switch costs, F(1,32) = 62.14, p < .001) and task (F(1,32) = 4.61, p = .03).

Table 1.

Mean RT values and standard deviations for experiments 1.a and 1.b.

		Baseline		Learning		Transfer
Experiment 1a		Low Proportion Congruent	High Proportion Congruent	Low Proportion Congruent	High Proportion Congruent	Low Proportion Congruent	High Proportion Congruent
Incongruent	Switch	1224 (213)	1239 (215)	1123 (177)	1203 (179)	1097 (157)	1157 (188)
	Stay	1069 (238)	1091 (182)	996 (174)	1087 (160)	1006 (197)	1055 (169)
Congruent	Switch	1179 (216)	1162 (199)	1104 (201)	1051 (180)	1083 (190)	1040 (169)
	Stay	1043 (230)	1082 (230)	1029 (195)	972 (175)	1022 (214)	950 (177)
Experiment 1b
Incongruent	Switch	1247 (169)	1287 (159)	1157 (155)	1239 (156)	1115 (161)	1218 (164)
	Stay	1133 (171)	1228 (176)	1088 (159)	1192 (159)	1069 (195)	1154 (186)
Congruent	Switch	1148 (184)	1212 (150)	1154 (166)	1107 (147)	1119 (170)	1093 (156)
	Stay	1131 (173)	1131 (150)	1074 (153)	1053 (177)	1066 (148)	1009 (183)

Figure 2.

Mean RT (standard mean error) values are displayed as a function of task (High Proportion Congruent vs Low Proportion Congruent), cross-task congruency (Congruent vs. Incongruent), and experimental phase (Baseline, Learning, and Transfer), for Experiments 1a (A) and 1b (B).

We next assessed whether the associations between task set and demands on task focus acquired in the learning phase generalized to the transfer phase. Comparing the learning and baseline phases we found that the 3-way interaction of interest, between task, congruency, and phase, was significant (F(1,32) = 9.34, p = .004). As can be gleaned from comparing the left and right panels of Figure 2A, this interaction was driven by the fact that, while in the baseline block the congruency effect was similar for the low proportion congruent task ($M_{diff}=36$; t(32) = 1.97, p = .06) and the high proportion congruent task ($M_{diff}=43$; t(32) = 2.1, p = .05), during the transfer block there was a significant congruency effect obtained in the high proportion congruent ($M_{diff}=111$; t(32) = 5.9, p < .001) but not in the low proportion congruent task ($M_{diff}=1$; t(32) = 0.08, p = .93). The 2-way interaction between task and congruency was also significant F(1,32) = 13.12, p = .001), but qualified by the above 3-way interaction.

The interaction between phase and transition was significant F(1,32) = 8.48, p = .006) and was driven by switch cost being larger in the baseline phase ($M_{diff}=130$; t(32) = 8.9, p < .001), compared to the transfer phase ($M_{diff}=86$; t(32) = 5.51, p < .001).

Additional effects revealed in this analysis included expected main effects of congruency (F(1,32) = 15.49, p < .001), transition (F(1,32) = 80.55, p < .001), and phase (F(1,32) = 13.5, p = .001). All main effects were qualified by the previously reported interactions.

In sum, the results of Experiment 1a demonstrated that participants acquired associations between tasks sets and set-specific demands on task focus level in the learning phase, and subsequently maintained those associations during the unbiased transfer phase.

Accuracy

Descriptive statistics are presented in Table 2 and visualized in figure A1A, the ANOVA results are shown in Tables A16 and A17. For the learning phase, we found a proportion congruency effect, reflected by a significant interaction between task and congruency (F(1,32) = 37.38, p < .001). This interaction was driven by a larger difference in accuracy between congruent and incongruent trials in the high proportion congruent task ($M_{diff}=20\%$; t(32) = 6.17, p < .001), than in the low proportion congruent task ($M_{diff}=5\%$; t(32) = 3.87, p < .001).

Table 2.

Mean percentage accuracy values and standard deviations for experiments 1.a and 1.b.

		Baseline		Learning		Transfer
Experiment 1a		Low Proportion Congruent	High Proportion Congruent	Low Proportion Congruent	High Proportion Congruent	Low Proportion Congruent	High Proportion Congruent
Incongruent	Switch	72.2 (20.2)	71.3 (20.6)	85 (10.3)	73.4 (18.6)	87.4 (15.8)	76.1 (21.1)
	Stay	78.8 (18.9)	77.6 (19.9)	90.9 (7.4)	77.9 (20)	90.2 (12.7)	79.5 (17.3)
Congruent	Switch	84.6 (13.2)	87.6 (13.4)	91 (9.6)	94.3 (4.7)	92.8 (10.4)	94.8 (8.8)
	Stay	93.8 (9.3)	91.8 (9.1)	95.7 (5.3)	96 (2.9)	93 (9.8)	95.7 (9.4)
Experiment 1b
Incongruent	Switch	75 (17.5)	70.9 (22.1)	84.1 (8.7)	64.3 (23.8)	84.8 (11.8)	68.8 (26)
	Stay	83.2 (16.5)	73.1 (19.2)	87.2 (10.4)	68.2 (24.3)	89.2 (12)	70.8 (27.3)
Congruent	Switch	87.5 (12)	87.6 (11.9)	88.1 (9.9)	93.1 (5.8)	89.9 (11.6)	92.8 (9.1)
	Stay	91.7 (9.7)	91 (10.8)	89.9 (8.6)	94.1 (5.8)	93.2 (8.4)	94.4 (9.1)

Task (F(1,32) = 25.25, p < .001) and congruency (F(1,32) = 33.48, p < .001) also showed expected main effects. There was also a main effect of task transition (F(1,32) = 15.83, p = .01), driven by higher accuracy for stay than switch trials ($M_{diff}=4\%$; t(32) = 3.9, p < .001).

Comparing accuracy between the baseline and transfer phases, we found that the 3-way interaction between phase, task and congruency was significant (F(1,32) = 7.52, p = .01). While during the baseline phase the high proportion congruent task ($M_{diff}=15\%$; t(32) = 4.41, p < .001) and the low proportion congruent task ($M_{diff}=14\%$; t(32) = 4.65, p < .001) showed similar congruency effects, during transfer phase the high proportion congruent task showed a larger congruency effect ($M_{diff}=18\%$; t(32) =6.57, p < .001) than the low proportion congruent task ($M_{diff}=4\%$; t(32) = 2.01, p = .05). The task by congruency interaction (F(1,32) = 11.19, p < .002) and the task by phase interactions (F(1,32) = 4.46, p = .04) were significant, but qualified by the above 3-way interaction.

The interaction betwen task transition and phase (F(1,32) = 7.59, p = .01) was also significant, driven by higher switch cost during the baseline phase ($M_{diff}=7\%$; t(32) = 5.3, p < .001) compared to the transfer phase ($M_{diff}=2\%$; t(32) = 1.51, p = .14).

Additional main effects included those of phase (F(1,32) = 11.96, p = .002), congruency (F(1,32) = 33.91, p < .001) and task transition (F(1,32) = 23.62, p < .001), which were all qualified by interactions.

While accuracy was of only of secondary interest, these results mirrored the effects in the RT data, indicative of significant learning and transfer effects of associations between task set and task focus.

Experiment 1b

Experiment 1a demonstrated a novel effect of task sets becoming associated with task focus level. Experiment 1b had the objective of testing whether this finding was reliable by conducting a direct replication of Experiment 1a.

Participants

We collected data from online participants using Amazon Mechanical Turk (Mturk). The inclusion and exclusion criteria were the same as in Experiment 1a. We collected data until we reached our target sample size of 36 participants who achieved the accuracy criterion (> 75%). A total of 40 participants completed the experiment. Four participants were rejected for not meeting the accuracy criterion, and we excluded data from three participants with 0 correct trials in one of the repeated analysis of variance cells for the RT analysis. As a result, our final sample consisted of 33 participants (mean age = 41, SD = 14; 15 females, 18 males).

Stimuli

Stimuli were identical to the ones used for Experiment 1a.

Task and procedure

The trial timing parameters and procedure were identical to Experiment 1a.

Data analysis

The data analysis procedure was identical to the one performed for Experiment 1a.

Results

Reaction Time

Descriptive statistics are presented in Table 1 and visualized in Figure 2B, ANOVA results are shown in Tables A6 and A7. As in Experiment 1a, the learning phase manipulation was successful, with the learning phase data displaying a proportion congruency effect reflected in a significant interaction between task and congruency (F(1,32) = 51.35, p < .001). As shown in the middle panel of Figure 2B, the difference between congruent and incongruent items in the high proportion congruent task ($M_{diff}=134$; t(32) = 12.0, p < .001) was larger than in the low proportion congruent task ($M_{diff}=6$; t(32) = 0.4, p = .66). Other effects in this phase included the expected main effects of congruency (F(1,32) = 65.16, p < .001), task (F(1,32) = 4.76, p = .04) and task transition (F(1,32) = 38.3, p < .001), as switch trials had larger RTs than stay trials ($M_{diff}=70$; t(32) =6.23, p <.001).

Comparing the baseline and transfer phases to test for task set-focus associations, we again obtained a 3-way interaction between task, congruency, and phase (F(1,32) = 15.11, p < .001). As can be seen when comparing the left and right panels of Figure 2B, this interaction was driven by the fact that, while in the baseline block the congruency effect was similar for the low proportion congruent task ($M_{diff}=58$; t(32) = 3.98, p < .001) and the high proportion congruent task ($M_{diff}=72$; t(32) = 4.3, p < .001), during the transfer block a significant congruency effect was observed in the high proportion congruent task ($M_{diff}=132$; t(32) = 9.62, p < .001) but not in the low proportion congruent task ($M_{diff}=3$; t(32) = 0.19, p = .85). The interaction between congruency and task was also significant (F(1,32) = 27.48, p < .001), but qualified by the above 3-way interaction.

Main effects revealed in this analysis included the effects of phase (F(1,32) = 24.87, p < .001) and congruency (F(1,32) = 55.75, p < .001), replicating the findings from Experiment 1a. Similarly, there was again a main effect task transition (F(1,32) = 44.38, p < .001), driven by a larger RT for switch trials compared with stay trials ($M_{diff}=73$; t(32) = 7.65, p < .001).

Taken together, the RT results of Experiment 1b fully replicated those of Experiment 1a, showing that task set-specific attentional focus levels were acquired during a demand-biased learning phase and remained in effect during an unbiased transfer phase. This provides additional support for the conclusion that task sets can incorporate information about the task focus level with which they need to be implemented to support successful performance.

Accuracy

Descriptive statistics are presented in Table 2 and visualized in figure A1B, the ANOVA results are shown in tables A18 and A19. The interaction between task and congruency in the learning phase was again significant (F(1,32) = 62.74, p < .001). The interaction was driven by a higher percentage of correct responses for the congruent trials on the high proportion congruent task ($M_{diff}=27\%$; t(32) = 7.3, p < .001), compared to the low proportion congruent task ($M_{diff}=3\%$; t(32) = 1.8, p = .08). The main effects of task (F(1,32) = 9.82, p = .004), congruency (F(1,32) = 36.05, p < .001) and transition (F(1,32) = 9.18, p = .005) were also significant, this last effect driven by more error on switch trials ($M_{diff}=2\%$; t(32) = 3.03, p = .004).

Comparing the percentage of accurate trials between the baseline and transfer phases, we replicated the key 3-way interaction between phase, task and congruency (F(1,32) =6.77, p = .01). For the high proportion congruent task, the congruency effect increased from the baseline ($M_{diff}=17\%$; t(32) = 4.79, p < .001) to the transfer phase ($M_{diff}=23\%$; t(32) = 5.5, p < .001). For the low proportion congruent task the congruency effect decreased from the baseline ($M_{diff}=10\%$; t(32) = 4.00, p < .001) to the transfer phase ($M_{diff}=5\%$; t(32) = 2.23, p = .03). The 2-way interaction between task and congruency was significant (F(1,32) = 15.60, p < .001).

Main effects revealed by this repeated measure analysis were those of task (F(1,32) = 8.11, p = .008), congruency (F(1,32) = 36.09, p < .001) and task transition (F(1,32) = 9.88, p = .004). This last main effect was driven by a higher percentage of correct trials for stay trials compared to switch trials ($M_{diff}=4\%$; t(32) = 3.14, p =.003). Overall, the accuracy results mirrored the RT results, and replicated those of Experiment 1a.

Discussion

Experiment 1 sought to find out whether task set representations can acquire information about the level of task focus with which the task set has to be implemented to be performed successfully. We tackled this question by devising a novel design where two task sets were performed under different levels of difficulty (proportion of congruent trials) during a learning phase, and a comparison between a preceding baseline and a subsequent transfer phase allowed us to gauge whether the level of task focus engendered by these difficulty levels had become incorporated within the task sets. The results of Experiment 1 clearly supported the hypothesis that task set representations can entail the level of focus required for their successful performance: Whereas cross-task congruency effects were similar between the tasks at baseline (the task by congruency interaction effects in the baseline were non-significant for experiment 1a (p = 0.77) nor 1b (p = 0.55)), participants displayed significant adaptation effects to the lower/higher rate of interference between the two tasks in the learning phase, and critically, these differences were subsequently expressed in the unbiased transfer phase. Given the use of trial-unique stimuli, precluding the formation of stimulus-demand associations, the most plausible explanation for these findings is that the task set representations became associated with their commensurate level of task focus. To our knowledge, this is the first demonstration that task sets incorporate information about how strongly they need to be implemented, and the successful replication across Experiments 1a and 1b indicates that this is a robust phenomenon.

One limitation in the conclusions that can be drawn from Experiment 1 is that it is not certain what cognitive adaptation (or adaptations) were driving the observed effects. In particular, since both task sets were biased (one to be mostly associated with incongruent trials, and the other one with congruent ones) in a reciprocal fashion (~25 vs ~75% congruent trials), the transfer phase results pattern could be driven by focus level adjustments in either task set, or both. Specifically, if participants primarily enhanced the strength of the low proportion congruent (more demanding) task set, on trials where that set is cued this would result in less interference from the high proportion congruent task set, but it may additionally increase the interference of the low proportion congruent task with the high proportion congruent task when the latter is the one that is currently relevant. Thus, the entire results pattern in the transfer phase could be driven primarily by enhanced activation of the low proportion congruent task representation. Conversely, if participants lowered the strength of the high proportion congruent task set representation, on trials where that set is cued this would allow them to benefit from the congruent impact of the low proportion congruent task on response selection, but at the same time it would also reduce the potential interference from the high proportion congruent task set in the low proportion congruent task set when the latter is cued. Thus, the transfer phase results pattern could also be mediated by exclusive task set weakening of the high proportion congruent task, or it could be derived from a combination of those two context-sensitive adaptations.

Experiment 2a

In order to further specify the cognitive processes driving the effects seen on Experiments 1a and 1b we ran two additional experiments (Experiments 2a and 2b), where only one of the two task sets’ demand level was biased while the alternate task’s congruency rate was kept at ~50% (an “unbiased” task). Specifically, in Experiment 2a, we paired a low proportion congruent task (~75% incongruent) with an unbiased task, and in Experiment 2b, we paired a high proportion congruent task (~75% congruent) with an unbiased task. This allowed us to tease apart whether the results of Experiment 1 were primarily driven by an enhanced activation of the low proportion congruent task set (in which case we would expect to replicate the results of Experiment 1 only in Experiment 2a) or of lowered activation of the high proportion congruent task set (in which case we would expect to replicate the results of Experiment 1 only in Experiment 2b), or both (in which case the results of Experiment 1 should replicate both in Experiment 2a and b). The logic is that the inclusion of an unbiased (50% congruent) task set would remove the reciprocality of the design of Experiment 1, where it was not possible to distinguish whether the proportion congruent effect was primarily mediated by upregulating the focus level in the low proportion congruent task set, down-regulating the focus level in the high proportion congruent task, or both. By pairing a low proportion congruent task with an unbiased task in Experiment 2a, we probed whether the putative increase in task focus level in the low proportion congruent condition would produce a significant proportion congruent effect in the learning and transfer phase without the potential reciprocal effects of the alternate high proportion congruent task. Conversely, by pairing a high proportion congruent task with an unbiased task in Experiment 2b, we probed whether the putative decrease in task focus level in the high proportion congruent condition would produce a significant proportion congruent effect in the learning and transfer phase without the potential reciprocal effects of the alternate low proportion congruent task.

Note that, unlike in Experiment 1, the design of Experiment 2 results in some variation in the mean congruency rate between task phases. Specifically, there was an overall higher mean rate of incongruent trials in the learning phase than the baseline and transfer phases in Experiment 2a, and an overall lower mean rate of incongruent trials in the learning phase than the baseline and transfer phases in Experiment 2b. In theory, this temporary increase or decrease in mean difficulty levels in the learning phase could have lingering effects on the transfer phase. However, any effect of block-level demands in the learning phase on subsequent performance should apply equally to biased and unbiased task sets, and since we are interested in differences between the two sets, it should not affect our inferences.

Participants

We collected data from online participants using Mturk. The inclusion and exclusion criteria were the same as in Experiment 1. Given that only one of the two task sets were biased, we anticipated that we would have less power to detect learning and transfer effects in Experiment 2 than in Experiment 1. To mitigate this, we doubled the target sample size for Experiments 2a and 2b, collecting data until we reached our target sample size of 72 participants. A total of 88 participants completed the experiment. Sixteen participants were rejected for not meeting the accuracy criterion, and we excluded data from six participants with 0 correct trials in one of the repeated analysis of variance cells for the RT analysis. As a result, our final sample consisted of 66 participants (mean age = 38, SD = 11; 29 females, 37 males).

Stimuli

Stimuli were identical to the ones used in Experiment 1.

Task and procedure

The trial timing parameters and procedure were identical to Experiment 1. The only difference between Experiment 1 and Experiment 2a was in the learning phase, where we biased only one of the two tasks. Specifically, the low proportion congruent task contained approximately 75% of incongruent stimuli, while the unbiased task contained approximately 50% of incongruent stimuli. The baseline and transfer phases maintained an approximate 50% distribution of congruent and incongruent trials for both tasks. The upper right panel of Figure 1B depicts the approximate proportion of congruent/incongruent trials for each phase.

Data analysis

The data analysis procedure was identical to the one performed for Experiment 1.

Results

Reaction time

Descriptive statistics are presented in Table 3 and visualized in Figure 3A, ANOVA results are shown in Tables A8 and A9. For Experiment 2a, the learning phase data displayed a proportion congruency effect, revealed by an interaction between task and congruency (F(1,65) = 18.55, p < .001). As shown in the middle panel of Figure 3A, the difference between congruent and incongruent items in the unbiased task ($M_{diff}=83$ ; t(65) = 9.36, p < .001) was larger than in the low proportion congruent task ($M_{diff}=22$; t(65) = 2.36 , p = .02), indicating that the learning manipulation was once again successful. We also observed expected main effects of congruency (F(1,65) = 78.9, p < .001), and task transition (F(1,65) = 118.20 , p < .001), driven by a larger RT for switch trials compared with stay trials ($M_{diff}=76$; t(65) = 10.87, p < .001).

Table 3.

Mean RT values and standard deviations for experiments 2.a and 2.b.

		Baseline			Learning			Transfer
Experiment 2a		Unbiased Proportion Congruent	Low Proportion Congruent	High Proportion Congruent	Unbiased Proportion Congruent	Low Proportion Congruent	High Proportion Congruent	Unbiased Proportion Congruent	Low Proportion Congruent	High Proportion Congruent
Incongruent	Switch	1293 (191)	1278 (183)		1257 (193)	1221 (183)		1236 (199)	1207 (204)
	Stay	1179 (185)	1197 (188)		1179 (185)	1152 (184)		1162 (206)	1135 (205)
Congruent	Switch	1185 (181)	1198 (176)		1175 (170)	1188 (185)		1137 (188)	1169 (206)
	Stay	1134 (200)	1154 (197)		1098 (170)	1137 (181)		1070 (191)	1118 (230)
Experiment 2b
Incongruent	Switch	1305 (230)		1283 (185)	1245 (196)		1237 (199)	1217 (203)		1221 (223)
	Stay	1227 (204)		1204 (187)	1171 (193)		1190 (207)	1143 (226)		1175 (221)
Congruent	Switch	1236 (208)		1198 (223)	1164 (204)		1136 (204)	1128 (198)		1126 (218)
	Stay	1188 (220)		1175 (213)	1123 (199)		1100 (198)	1104 (222)		1089 (225)

Figure 3.

Mean RT (standard mean error) values are displayed as a function of task (High Proportion Congruent vs. Low Proportion Congruent), cross-task congruency (Congruent vs. Incongruent), and experimental phase (Baseline, Learning, and Transfer), for Experiments 2a (A) and 2b (B).

Comparing the transfer and baseline phases, we found that the 3-way interaction of interest, between task, congruency, and phase, was significant (F(1,65) = 8.86, p = .004). As evident from comparing the left and right panels of Figure 3A, while in the baseline phase the congruency effect was similar for the unbiased task ($M_{diff}=63$; t(65) = 4.95, p < .001) and the low proportion congruent task ($M_{diff}=56$; t(65) = 4.79, p < .001), during the transfer block there was a larger congruency effect in the unbiased task ($M_{diff}=95$; t(65) = 9.63, p < .001) than in the low proportion congruent task ($M_{diff}=29$; t(65) = 2.5, p = .01). The 2-way interactions between task and congruency (F(1,65) = 8.48, p = .005) was also significant, but qualified by the previously described interaction.

The 3-way interaction between phase, congruency, and transition was significant (F(1,65) = 4.54, p = .04). This interaction was driven by switch cost for incongruent trials being larger ($M_{diff}=102$; t(65) = 7.84, p < .001) than for congruent trials ($M_{diff}=49$; t(65) = 3.17, p = .002) during the baseline phase. Howhever, during the transfer phase switch costs were similar for congruent ($M_{diff}=69$; t(65) = 5.78, p < .001) and incongruent trials ($M_{diff}=78$; t(65) = 7.67, p < .001). The 2-way interaction between congruency and transition (F(1,65) = 8.68, p = .004) was significant, but qualified by the previously described 3-way interaction.

We additionally obtained the expected main effects of congruency (F(1,65) = 84.31, p < .001), task transition (F(1,65) = 75.68, p < .001), and phase (F(1,65) = 7.9, p = .007).

To summarize, the RT results of Experiment 2a replicated those of Experiment 1: significant modulation of congruency effects by task in the learning phase, accompanied by significantly reduced congruency effects for the low proportion congruent task and increased congruency effects in the unbiased task, in the transfer compared to the baseline phase. Crucially, these results were obtained in the absence of a reciprocally biased high proportion congruent task, thus suggesting that the effects observed in Experiment 1 are at least partly driven by a context-sensitive up-regulating the strength of the low proportion congruent task set.

Accuracy

Descriptive statistics are presented in Table 4 and visualized in figure A2A, ANOVA results are shown in Tables A20 and A21. In the learning phase, we observed a 3-way interaction between task, congruency and task transition (F(1,65) = 10.62, p = .002). Switch cost were similar for congruent ($M_{diff}=4\%$; t(65) = 2.86, p = .005) and incongruent trials ($M_{diff}=4\%$; t(65) = 4.40, p < .001) on the low proportion congruent task, the switch cost for congruent trials ($M_{diff}=2\%$; t(65) = 1.83, p = .08) were smaller than the switch cost for incongruent trials during the unbiased task ($M_{diff}=8\%$; t(65) = 6.25, p < .001). The 2-way interactions between task and congruency (F(1,65) = 36.27, p < .001) and between congruency and task transition (F(1,65) = 5.98, p = .02) were also significant, but qualified by the 3-way interaction.

Table 4.

Mean percentage accuracy values and standard deviations for experiments 2.a and 2.b.

		Baseline			Learning			Transfer
Experiment 2a		Unbiased Proportion Congruent	Low Proportion Congruent	High Proportion Congruent	Unbiased Proportion Congruent	Low Proportion Congruent	High Proportion Congruent	Unbiased Proportion Congruent	Low Proportion Congruent	High Proportion Congruent
Incongruent	Switch	73.9 (17.6)	75.9 (15.5)		72.6 (15.1)	82.4 (10.2)		72 (15.3)	80.3 (13.9)
	Stay	81.6 (15.5)	84.3 (15)		80.6 (11.4)	86.7 (9.1)		81.1 (13.6)	83.1 (14)
Congruent	Switch	89.7 (11.3)	88.8 (13.6)		91.3 (7.4)	87.1 (9.4)		91.8 (8.4)	90.1 (9.7)
	Stay	93.1 (8.8)	90.2 (12.6)		92.9 (6)	91.3 (10)		95.5 (7.2)	91.8 (9.6)
Experiment 2b
Incongruent	Switch	68.7 (20.5)		70.8 (18.2)	75.2 (13.4)		63.6 (23.3)	74.7 (19.8)		72.4 (18.7)
	Stay	73.8 (19.2)		78.2 (17.5)	80.2 (12.2)		70.7 (20.1)	80.4 (18.2)		73.8 (19.3)
Congruent	Switch	87.1 (11.6)		89.6 (12.7)	90.5 (6.7)		92.5 (6)	91.6 (9)		93.6 (8.8)
	Stay	89.8 (9.1)		89.5 (11.9)	91.8 (6.4)		94.2 (5)	91.9 (9)		93.9 (9.3)

Significant main effect of task (F(1,65) = 5.39, p = .02), congruency (F(1,65) = 118.8, p < .001) and task transition (F(1,65) = 52.36, p < .001) were also significant.

The three-way interaction between phase, congruency, and transition was not significant (F(1,65) = 2.11, p = 0.15). During the transfer phase, the low-proportion congruent task exhibited a smaller congruency effect ($M_{diff}=9\%$; t(65) = 5.7, p < .001) compared to the unbiased task ($M_{diff}=17\%$; t(65) = 12, p < .001). This lack of a three-way interaction may have been due to an unexpected difference between the two tasks in the baseline phase, where the low-proportion congruent task also showed a smaller congruency effect ($M_{diff}=9\%$; t(65) = 4.8, p < .001) compared to the unbiased task ($M_{diff}=13\%$; t(65) = 7.5, p < .001), which was captured by a significant 2-way interaction between task and congruency (F(1,65) = 10.61, p = .002).

The 2-way interaction between congruency and transition was significant (F(1,65) = 14.37, p < .001), driven by more accurate responses on congruent trials ($M_{diff}=3\%$; t(65) = 3.70, p < .001) compared to incongruent trial ($M_{diff}=7\%$; t(65) = 7.52, p < .001). Significant main effects include those of congruency (F(1,65) = 132.58, p < .001) and task transition (F(1,65) = 70.40, p < .001).

In sum, the accuracy results showed a pattern similar to the one observed in the RT data, but with a non-significant interaction between task, congruency, and phase (i.e., the transfer effect).

Experiment 2b

Experiment 2a showed that combining a low proportion congruent task set with an unbiased task set was sufficient for producing the same pattern of results as Experiment 1, namely, learning and transfer of task set-focus associations. This provides evidence for a context-sensitive upregulation of task focus level in a task set associated with frequent incongruent stimuli. Experiment 2b tested whether these transfer effects could also be driven by weakened task focus level set for a task associated with infrequent incongruent stimuli, by pairing a high proportion congruent with an unbiased task.

Participants

We collected data from online participants using Mturk. The inclusion and exclusion criteria were the same as in Experiment 2a. We collected data until reaching a sample size of 72 participants who reached the accuracy criterion. A total of 81 participants completed the experiment. Nine participants were rejected for not meeting the accuracy criterion, and we excluded data from eight participants with 0 correct trials in one of the repeated analysis of variance cells for the RT analysis. As a result, our final sample consisted of 64 participants (mean age = 38, SD = 12; 30 females, 34 males).

Stimuli

Stimuli were identical to the ones used for Experiment 1.

Task and procedure

The trial timing parameters and procedure were identical to Experiment 2a. The only difference between Experiment 2a and 2b occurred in the learning phase, where we paired a high proportion congruent task containing ~75% of congruent stimuli with an unbiased task containing ~50% of incongruent stimuli. The lower right panel of figure 1B depicts the proportion of congruent/incongruent trials for each phase.

Data analysis

The data analysis procedure was identical to the one performed for Experiment 2a.

Results

Reaction Time

Descriptive statistics are presented in Table 3 and visualized in Figure 3B, ANOVA results are shown in Tables A10 and A11. In the learning phase, as in all previous experiments, we detected an interaction between task and congruency (F(1,63) = 13.22, p < .001), replicating the proportion congruency effect. As shown in the middle panel of Figure 3B, the difference between congruent and incongruent items in the high proportion congruent task ($M_{diff}=110$; t(63) = 11.53, p < .001) was larger than in the unbiased task ($M_{diff}=67$; t(63) = 6.94, p < .001). Significant effects in this phase consisted of expected main effects of congruency (F(1,63) = 136.5, p < .001), and task transition (F(1,63) = 42.48, p < .001), with the latter driven by a larger RT for switch trials compared with stay trials ($M_{diff}=48$; t(63) = 6.52, p < .001).

Unlike in Experiment 2a, the three-way interaction among task, congruency, and phase was not significant (F(1,63) = 3.46, p = .07). During the baseline phase, both the high-proportion congruent task ($M_{diff}=66$; t(63) = 4.7, p < .001) and the unbiased task ($M_{diff}=74$= 74; t(63) = 4.8, p < .001) displayed comparable congruency effects. In the transfer phase, the high-proportion congruent task exhibited a greater congruency effect ($M_{diff}=100$; t(63) = 8.3, p < .001) compared to the unbiased task ($M_{diff}=63$; t(63) = 6.5, p < .001). While this difference is in line with a transfer pattern of task-focus parameters, it did not result in a significant three-way interaction.

The 2-way interaction between congruency and transition was significant (F(1,63) = 4.54, p = .04) driven by higher switch cost for incongruent trials ($M_{diff}=74$; t(63) = 5.2, p < .001) than for congruent trials ($M_{diff}=41$; t(63) = 3.08, p = .003).

The interaction between phase and task was also significant (F(1,63) = 5.23, p = .03), driven by higher RT for the baseline phase ($M_{diff}=21$; t(63) = 1.78, p = .08) than for the transfer phase ($M_{diff}=8$; t(63) = 0.79, p = .43)

The main effects of congruency (F(1, 63) = 99.09, p < .001), task transition (F(1,63) = 44.98, p < .001) and phase (F(1,63) = 26.11, p < .001) were significant, but qualified by the above mentioned interactions.

The RT results of Experiment 2b show that biasing only the high proportion congruent resulted in a pattern descriptively in line with the transfer of task-focus parameters, it did not result in the type of transfer effect seen in Experiments 1a, 1b and 2a. This suggests that the primary context-sensitive adaptation underlying those effects consisted of the strengthening the representation (or focus level) of task sets associated with high difficulty, rather than a weakening of task set representations in less difficult tasks.

Accuracy

Descriptive statistics are presented in Table 4 and visualized in figure S2B, ANOVA results are shown in Tables A22 and A23. The learning phase generated a significant interaction between task and congruency (F(1,63) = 22.70, p < .001), with a greater difference in error rate between congruent and incongruent trials on the high proportion congruent task ($M_{diff}=26\%$; t(63) = 10.31, p < .001) than the unbiased task ($M_{diff}=13\%$; t(65) = 8.23 , p < .001). The two way interaction between congruency and task transition was also significant (F(1,63) = 10.66, p < .001), driven by lower switch cost for congruent trials ($M_{diff}=17\%$; t(63) = 11.75, p < .001), compared to incongruent trials ($M_{diff}=22\%$; t(63) = 11.53, p < .001).

Significant main effects were found for task (F(1,63) = 7.79, p = .007), congruency (F(1,63) = 159.04, p < .001), and task transition (F(1,63) = 30.62, p < .001).

Comparing the baseline and transfer phases we found a significant 3-way interaction between phase, task and congruency (F(1,63) = 5.14, p = .03). During the baseline phase the high proportion congruent task had similar congruency effect ($M_{diff}=15\%$; t(63) = 6.9, p < .001) as the unbiased task ($M_{diff}=17\%$; t(63) = 7.54, p < .001), while during the transfer phase the high proportion congruent task showed greater congruency effects ($M_{diff}=21\%$; t(65) = 6.9, p < .001) compared to the unbiased task ($M_{diff}=14\%$; t(65) = 6.94, p < .001). The interaction between phase and task was also significant (F(1,63) = 4.23, p = .04), as well as the interaction between task transition and congruency (F(1,63) = 11.53, p = .001). This last interaction was driven by a smaller switch cost for congruent trials ($M_{diff}=1\%$; t(63) = 1.14, p = .26) compared to incongruent trials ($M_{diff}=5\%$; t(63) = 4.72, p < .001).

Significant main effects revealed by this analysis were those of phase (F(1,63) = 8.41, p = .005), congruency (F(1,63) = 127.91, p < .001) and task transition (F(1,63) = 19.22, p < .001).

Overall, the accuracy results mirrored the RT results during the learning phase, but in contrast to the RT data, error rates displayed a significant 3-way interaction between phase, task, and congruency between the baseline and transfer phases, indicative of a transfer of the lower task focus level for the high proportion congruent task acquired in the learning phase to the transfer phase. In other words, the accuracy results produced some evidence for that adaptation.

Comparison between experiments 2a and 2b

Ultimately, in order to draw firmer conclusions about the degree to which participants may engage in context-sensitive up- or-downregulation of task focus level in response to tasks associated with frequent or rare cross-task interference, a direct comparison of the data from Experiments 2a and 2b is desirable. In order to examine whether the transfer effects were of different magnitudes in the two scenarios, we submitted RT and accuracy congruency scores for the baseline and transfer phases of the two experiments to 2 rmANOVAs, one for each phase, with within-subjects factors of task (recoded as “biased” (for the low proportion congruent task in experiment 2a and the high proportion congruent task in experiment 2b) vs. “unbiased”) and transition (stay vs switch), and a between-subjects factor of Experiment (2a vs 2b), RT ANOVA results are shown in Table A12 and Table A13.

During the baseline phase, the only significant effect was the main effect of transition (F(1, 128) = 11.75, p < .001), driven by longer RTs during switch trials ($M_{diff}=$ 43; t(129) = 3.45, p = .001). Critically, in the transfer phase there was a significant 2-way interaction between experiment and task (F(1, 128) = 28.16, p < .001). Both experiments displayed a pattern of results consistent with transfer of task-focus parameters: In Experiment 2a the congruency effect during the biased task was smaller (M = 29, SD = 95) than the congruency effect elicited by the unbiased task (M = 95, SD = 80), whereas in Experiment 2b the congruency effect elicited by the biased task was larger (M = 100, SD = 95.76) compared to the unbiased task (M = 63, SD = 78). Critically, the difference between the biased and the unbiased task in the Experiment 2a transfer phase ($M_{diff}=$ 66; t(65) = 4.72, p < .001) was greater than the difference between the biased and the unbiased task in the transfer phase of experiment 2b ($M_{diff}=$ 37; t(63) = 2.76, p = .008). These data are depicted in the upper panel of Figure A4.

The accuracy analysis (results are shown in Table A24 and Table A25) during the baseline phase revealed a significant main effect of experiment task (F(1, 128) = 4.4, p = .03), with smaller congruency effect for experiment 2a (M = 12%, SD = 12%), compared to experiment 2b (M = 16%, SD = 13%; t(126) = 2.1, p = .04). There was also a significant main effect of transition (F(1, 128) = 18.73, p < .001), with a more accurate responses during stay, compared to switch trials ($M_{diff}=5\%$; t(129) = 4.35, p < .001).

In the transfer phase there was a significant interaction between experiment and task (F(1, 128) = 16.68, p < .001). Replicating the RT data, both experiments showed evidence of transfer of task-focus parameters: In Experiment 2a the biased task produced a smaller congruency effect (M= 9%, SD = 13%), than the unbiased task (M = 17%, SD = 12%), while in Experiment 2b the biased task displayed a larger congruency effect (M = 21%, SD = 19%) compared to the unbiased task (M = 14%, SD = 16%). Critically, the difference between the biased and the unbiased task was larger in the Experiment 2a transfer phase ($M_{diff}=8\%$; t(65) = 3.77, p < .001 ) than the difference between the biased and the unbiased task in the transfer phase of Experiment 2b ($M_{diff}=7\%$; t(63) = 2.28, p = .03). There was also a main effect of experiment (F(1,128) = 4.39, p = .04) due to a generally smaller congruency effect Experiment 2a than Experiment 2b, qualified by the task by experiment interaction described above. Finally, the main effect of transition was also significant (F(1,128) = 8.97, p = .003), driven by more accurate responses during stay compared to switch trials ($M_{diff}=3\%$; t(129) = 3.01, p = .003). See the lower panel of figure A4 for a depiction of the results.

In sum, the RT results of the direct comparison of Experiments 2a and 2b support the interpretation that the changes in task focus level observed in Experiments 1a and 1b are likely primarily attributable to an increased task focus level in association with the more demanding (low proportion congruent) task set than a decrease in task focus level in association with the less demanding (high proportion congruent) task set. However, the accuracy results show a less clear picture of what might drive the effect observed in experiment 1.

Discussion

Experiments 2a and 2b had the objective of clarifying the context-sensitive adaptations responsible for the effect observed in Experiment 1, namely, whether participants increased their task focus level in the more demanding task or decreased their task focus level in the less demanding task, or both. To this end, we ran two experiments in which we kept the rate of helpful versus unhelpful contributions from the alternative task set at ~50% (unbiased) for one task set, while varying this rate in the other task set, between a high rate of interference (or low rate of facilitation) from the alternative task in Experiment 2a, and a low rate of interference (or high rate of facilitation) in Experiment 2b.

While we were able to replicate the RT results of Experiment 1 by increasing the demand-level of the biased task (Experiment 2a), we failed to replicate this result in RT data when we decreased the demand-level for the biased task (Experiment 2b), though transfer effects were observed in accuracy data for the latter. Moreover, a direct comparison of the two experiments revealed RT transfer effects were significantly larger in Experiment 2a than 2b. Thus, in Experiment 2a, the putatively increased task focus level in the low proportion congruent task set clearly differentiated performance on that task from performance on the unbiased task, by displaying substantially reduced congruency effects. We interpret this to reflect less interference from the alternate unbiased task set in trials where the low proportion congruent task was cued, and in increased interference from the low proportion congruent task set in trials where the unbiased task was cued, due to an increased task focus level in the low proportion congruent task.

However, in Experiment 2b there was a significant transfer effect in the accuracy data and, while non-significant, the RT data during the transfer phase showed a pattern consistent with the accuracy results. Given this pattern, we cannot rule out a transfer of task-focus settings when only the high-proportion congruent task is biased.

As noted in the introduction of this experiment, the chosen design led to some variation in the mean congruency rates, with an overall higher mean rate of incongruent trials in the learning phase than the baseline and transfer phases in Experiment 2a, and an overall lower mean rate of incongruent trials in the learning phase than the baseline and transfer phases in Experiment 2b. While we argue that any knock-on effects of this variance in mean congruency rate on subsequent transfer phase performance should apply equally to biased and unbiased task sets, future studies could employ a conceptually cleaner design. For example, one could potentially employ three different tasks and assign low (e.g., 25%), neutral (50%), and high (75%) congruency rates to these tasks, such that the overall congruency level is maintained at 50% in the learning phase, and transfer effects could be contrasted between the neutral, low, and high proportion congruent tasks.

Experiment 3

We interpreted the results of Experiments 1 and 2 as showing that task set representations can acquire information about the strength of task focus required for successful task performance, and that this effect was primarily driven by associating a greater task focus level with a more demanding task. However, it can be argued that both experiments entail a potential confound that allows for an alternative interpretation. Specifically, while we employed trial-unique task stimuli in order to avoid the formation of stimulus-control associations, each task was associated with a single cue that remained constant over the learning and transfer phases. This means that participants may have learned to associate the specific physical cues (i.e., a red or blue square) rather than the task sets with different attentional demands (proportions of congruent trials). If that were the case, the above experiments would be demonstrations of a special case of stimulus-control associations (specifically, a cue task focus level association) rather than documenting the integration of control settings into task sets. To rule out this alternative explanation, we conducted a third experiment that replicated the design of Experiment 1, except that we introduced a new pair of task cue stimuli between the learning and transfer phases. If the results of Experiment 1 had been driven by cue-task focus associations, this change in cue stimuli from the learning to the transfer phase should abolish the transfer effect. By contrast, if the results of Experiment 1 had been driven by associations between the task sets and task focus level, we would expect to replicate the results of these experiments even in the presence of changing cue stimuli.

Participants

We collected data from online participants using Mturk. The inclusion and exclusion criteria were the same as in Experiment 1a. We collected data until we reached our target sample size of 36 participants who achieved the accuracy criterion (> 75%). A total of 43 participants completed the experiment. Seven participants were rejected for not meeting the accuracy criterion, and we excluded data from two participants with zero correct trials in one of the repeated analysis of variance cells for the RT analysis. As a result, our final sample consisted of 34 participants (mean age = 41, SD = 15; 17 females, 17 males).

Stimuli

Stimuli were identical to the ones used in Experiment 1, except for the inclusion of two new cues (purple and orange circles) that were introduced between the learning and the transfer phase.

Task and procedure

The trial timing parameters and procedure were identical to Experiment 1. The only difference between Experiment 1 and Experiment 3 was that in Experiment 3, we changed the shape and color of each cue between the learning and the transfer phase. While the cues used in the baseline and learning phases were red and blue rectangle frames around the task stimuli (as in the prior experiments), the cues used in the transfer phase were purple and orange circles that served as frames for the stimuli. Thus, both of the defining features of the task cues (shape and color) were changed between the learning and transfer phases. We informed participants of this change on an instructions screen presented between the learning and transfer phases, which stated that the task that had previously been cued by the blue rectangle would now be cued by a purple circle, and the task that had previously been cued by the red rectangle would now be cued by an orange circle.

Data analysis

The data analysis procedure was identical to the one performed for Experiment 1.

Reaction Time

Descriptive statistics are presented in Table 5 and visualized in Figure 4, ANOVA results are shown in Tables A14 and A15. As in the previous experiments, the learning phase induced an adaptation to varying task difficulty, as indicated by a significant interaction between task and congruency (F(1,33) = 68.27, p < .001). This interaction was driven by a larger difference between congruent and incongruent trials in the high proportion congruent task ($M_{diff}=181$; t(33) = 14.33, p < .001) than in the low proportion congruent task ($M_{diff}=27$; t(33) = 1.98, p = .06). There were also main effects of task (F(1,33) = 8.61, p = .006), congruency (F(1,33) = 85.97, p < .001) and transition (F(1,33) = 57.83, p < .001), the latter due to shorter RT on switch trials ($M_{diff}=72$; t(33) = 7.6, p < .001).

Table 5.

Mean reaction time values and standard deviations for experiment 3.

		Baseline		Learning		Transfer
Experiment 3		Low Proportion Congruent	High Proportion Congruent	Low Proportion Congruent	High Proportion Congruent	Low Proportion Congruent	High Proportion Congruent
Incongruent	Switch	1314 (202)	1330 (176)	1253 (156)	1360 (195)	1309 (154)	1355 (156)
	Stay	1258 (123)	1262 (151)	1159 (132)	1285 (136)	1200 (171)	1252 (163)
Congruent	Switch	1245 (181)	1265 (197)	1222 (172)	1172 (171)	1244 (164)	1211 (150)
	Stay	1195 (148)	1194 (145)	1146 (139)	1099 (141)	1162 (139)	1127 (157)

Figure 4.

Mean RT (standard mean error) values are displayed as a function of task (High Proportion Congruent Task vs. Low Proportion Congruent Task), cross-task congruency (Congruent vs. Incongruent), and experimental phase (Baseline, Learning, and Transfer), for Experiment 3.

We next interrogated the crucial 3-way interaction between task, phase, and congruency. Similar to experiments 1a and 1b, this interaction was significant (F(1,33) = 12.27, p < .001). As can be seen when comparing the left and right panels of Figure 4, while the difference between congruent and incongruent trials during the baseline phase was similar between the low proportion congruent task ($M_{diff}=54$; t(33) = 3.53, p = .001) and high proportion congruent task ($M_{diff}=63$; t(33) = 4.0, p < .001), during the transfer phase the the congruency effect was smaller in the low proportion congruent task ($M_{diff}=47$; t(33) = 3.26, p = .002) compared to the high proportion congruent task ($M_{diff}=139$; t(33) = 9.02, p < .001). The interactions between task and congruency (F(1,33) = 8.15, p = .007), and between phase and congruency (F(1,33) = 9.19, p = .005) were also significant, but were qualified by the above 3-way interaction.

Significant main effects included those of phase (F(1,33) = 5.25, p = .0.3), congruency (F(1,33) = 65.67, p < .001), and transition (F(1,33) = 64.82, p < .001), with the latter being driven by higher RT for switch trials ($M_{diff}=72$; t(33) = 8.05, p < .001).

In sum, the RT results of Experiment 3 fully replicated those of Experiments 1a and 1b, in spite of employing a new set of cues following the learning phase. This finding rules out the possibility that transfer effects were driven by cue-based stimulus-task focus associations, and instead suggests that participants acquired associations between tasks sets and set-specific demands on attentional focus.

Accuracy

Descriptive statistics are presented in Table 6 and visualized in Figure S3, ANOVA results are shown in Tables A26 and A27. During the learning phase, there was a significant 3-way interaction between task, congruency and task transition (F(1,33) = 6.75, p = .01). While there were more accurate trials in switch compared to stay trials $M_{diff}=5\%$; t(33) = 4.64, p < .001), the interaction was driven by the high proportion congruent task having greater switch cost for incongruent trials ($M_{diff}=11\%$; t(33) = 4.36, p < .001) than for congruent trials ($M_{diff}=1\%$; t(33) = 1.90, p = .06), compared to the low proportion congruent task in which switch cost between incongruent trials ($M_{diff}=3\%$; t(33) = 2.86, p = .007) and congruent trials ($M_{diff}=1\%$; t(33) = 0.52, p = .6) were similar.

Table 6.

Mean percentage accuracy values and standard deviations for experiment 3.

		Baseline		Learning		Transfer
Experiment 3		Low Proportion Congruent	High Proportion Congruent	Low Proportion Congruent	High Proportion Congruent	Low Proportion Congruent	High Proportion Congruent
Incongruent	Switch	79.1 (17.7)	78.6 (18.2)	84.8 (7.7)	64.9 (19)	86.2 (13.1)	70.8 (19.3)
	Stay	82.7 (15.3)	84.9 (14.9)	87.9 (9.2)	76 (16.2)	88.7 (13.5)	79.4 (16.6)
Congruent	Switch	94.4 (6.9)	92.5 (8)	91.7 (8.6)	94.7 (4.3)	92.7 (11)	93.1 (9.4)
	Stay	92.5 (7.6)	92.7 (7.5)	92.5 (6.3)	96.1 (3.3)	89.9 (11.8)	91.4 (10.6)

The interaction between task and congruency (F(1,33) = 49.34, p < .001), congruency and task transition (F(1,33) = 10.34, p = .003) and between task and task transition were also significant (F(1,33) = 9.00, p = .005).

Significant main effects were those of task (F(1,33) = 24.27, p < .001), congruency (F(1,33) = 76.16, p < .001) and task transition (F(1,33) = 21.55, p < .001)

Comparing accuracy between the baseline and transfer phases, we found that the three way-interaction between phase, task, and congruency was significant (F(1,33) = 20.02, p < .001). While the congruency effect was similar in the low proportion congruent task ($M_{diff}=13\%$; t(33) = 5.98, p < .001) and the high proportion congruent task ($M_{diff}=11\%$; t(33) = 4.25, p < .001) during the baseline phase, during the transfer phase the low proportion congruent task displayed a smaller congruency effect ($M_{diff}=4\%$; t(33) = 2.22, p = .03) compared to the high proportion congruent task ($M_{diff}=17\%$; t(33) = 6.1, p < .001). The interactions between task and congruency (F(1,33) = 6.82, p = .013) and between phase and task (F(1,33) = 14.06, p = .004) were also significant, as was the interaction between congruency and transition (F(1,33) = 16.71, p < .001), due to higher switch cost on incongruent trials ($M_{diff}=5\%$; t(33) = 3.18, p < .001) compared to congruent ones ($M_{diff}=2\%$; t(33) = 1.79, p = .08).

The main effects of task (F(1,33) = 5.69, p = .023) and congruency (F(1,33) = 41.55, p < .001) were significant.

In summary, the accuracy results were similar to the effects in the RT data, documenting both a proportion congruent effect during the learning phase, and the subsequent maintenance of that effect in the transfer phase.

Cue - Task set associations

One interesting pattern in the Experiment 3 data is that, unlike in the prior experiments, switch costs increased from the baseline to the transfer phase (switch costs across experiments are detailed in Table A3). Previous research by Gade & Koch (2007) demonstrated that cues signaling a task build associations with that task set, such that changing the cue (as we did in Experiment 3) tends to increase the time required to switch between tasks sets due to cue-task set associative interference. To examine the impact of cue-based associations and its potential relation to the associations between task and focus level, we conducted a statistical comparison between Experiments 1a and 3.

We conducted a rmANOVA of the RT data (see table A28 for all the interactions and main effects) with experiment (1a and 3) as a between-subject factor and phase (baseline, transfer), task (high-proportion congruent, low-proportion congruent), transition (switch, stay) and congruency (congruent, incongruent) as within-subject factors. Supporting the association between cues and task-sets, there was a significant 3-way interaction between experiment, phase and transition (F(1,65) = 10.15, p = .001). This interaction was driven by Experiment 1a showing a decrease in switch cost between the baseline (M_diff = 130, t(32) = 8.99, p < .001) and transfer phases (M_diff = 86, t(32) = 5.51, p < .001), while Experiment 3 displayed the opposite pattern, an increase in switch cost between the baseline (M_diff = 55, t(33) = 3.72, p < .001) and transfer phases (M_diff = 87, t(33) = 8.76, p < .001).

As expected, there was also a significant 3-way interaction between phase, task and congruency (F(1,65) = 20.53, p < .001), supporting the conclusion of Experiment 3, that the transfer effect was not due to cue-control associations. Critically, the 5-way interaction between experiment, phase, task, transition and congruency was non-significant (F(1,65) = 0.59, p = .45), which suggests that cue-based interference effects in Experiment 3 were independent from the transfer of focus level.

Discussion

The design of Experiments 1 and 2 entailed a potential confound, namely, that each task set was associated with a single cue that stayed the same throughout the learning and transfer phases of the experiments. This meant that, in spite of using trial-unique task stimuli, participants may have formed associations between low or high attentional task focus and the specific physical cue for each task, rather than with the task sets themselves. We ruled out this possibility in Experiment 3, by supplying completely new cues for the two tasks between the learning and transfer phases. In spite of this change in cue stimuli - which would preempt the expression of learned cue-task focus associations - we obtained a full replication of the results of Experiments 1a, 1b, and 2a: the low proportion congruent task was associated with smaller congruency effects in the transfer phase than the high proportion congruent task. This result clearly supports our interpretation of the observed effects as stemming from an integration of task focus level settings within each task set, and it rules out the alternative possibility that the effects are mediated by cue-based stimulus-task focus learning.

General Discussion

Traditional definitions of what a task set is focus exclusively on the mapping between stimuli and responses for achieving a task goal (e.g., Kiesel et al., 2010; Monsell, 2003; Vandierendonck et al., 2010). The objective of the current study was to examine the intuitive notion that task sets may additionally incorporate information about the strength with which they need to be implemented to ensure successful task performance, or the level of attentional focus required for performing the task. To this end, we manipulated the level of focus that participants needed to perform two intermixed classification tasks with stimulus-response mappings that could interfere with each other. By varying the number of trials that elicited cross-task interference we aimed to manipulate the level of focus that participants needed to correctly perform the tasks. In Experiment 1, we demonstrated that task sets can become associated with the level of focus needed to perform the task. In Experiment 2, we found evidence that this association was primarily driven by an enhancement of the task set representation of the more demanding task. In Experiment 3, we ruled out an alternative interpretation of these findings based on cue-based stimulus-task focus associations.

The logic of our experiments involved randomly assigning two task sets to be of lower or higher average demand during a learning phase, and to probe whether different demand levels would (a) lead to adaptation of how strongly participants focused on each task to during the learning phase, and (b) become associated with the task sets in the longer term, as tested in a comparison between a baseline and post-learning transfer phase where both tasks were performed at equal difficulty. The response time data of Experiments 1a and b fully conformed to our expectations about baseline and learning phase performance, and thus allowed the crucial question of transfer of demand settings to be tested. Specifically, the two tasks elicited equivalent cross-task congruency effects at baseline (the RT task by congruency interaction effects in the baseline phase were non significant in all experiments: 1a (p = 0.77), 1b (p = 0.55), 2a (p = 0.69), 2b (p = 0.71), 3 (p = 0.71)), and the learning phase successfully induced the expected proportion congruent effect, whereby mean congruency effects were significantly reduced for the low proportion congruent compared to the high proportion congruent task, replicating classic proportion congruent effects (e.g., Braem et al., 2019; Bugg & Crump, 2012) in the domain of cross-task interference (e.g., Geddert & Egner, 2022). The subsequent transfer phase revealed that the proportion congruent effects (and by inference, the level of focus associated with each task) during the learning phase persisted. The data exhibited similar patterns of congruency effects for both task sets during transfer, despite both tasks featuring an equal number of congruent and incongruent trials. This indicates that the initially acquired focus level for each task set during learning persisted into the transfer phase. Moreover, this asymmetric pattern of cross-task interference differed significantly from the null-difference in the baseline phase. Experiment 1 thus provided a novel, clear demonstration that task sets can acquire and retain information about their respective levels of difficulty. This may have considerable utility in real-world behavior, as it allows task sets to be instantiated from memory with the likely required level of task focus already in place, rather than having to be figured out from scratch by trial and error.

To better understand the mechanisms underlying the effect observed in Experiment 1, we conducted two additional experiments (2a and 2b) in which we kept the proportion of cross-task congruent and incongruent trials equal in one (unbiased) task, and biased the proportion of congruent trials to be either low (Experiment 2a) or high (Experiment 2b) in the other task. The aim was to probe whether the results from Experiment 1 could be replicated in either or both of these scenarios, which would indicate whether strengthening of the high-demand task set representation or weakening of the low-demand task set representation (or both) was the more likely cognitive adaptation underlying the results of Experiment 1. The effects observed in Experiment 1 were replicated in RT when the biased task had a high attentional demand, but only for accuracy and not for RT data when it had a low attentional demand. Moreover, when comparing the two experiments directly, the RT transfer effect was found to be significantly larger in Experiment 2a than 2b.

This finding supports the notion that the results observed in Experiment 1 were likely primarily driven by increasing the strength of the more demanding, low proportion congruent task set representation to overcome interference from the alternate task set. Nevertheless, we also found some evidence suggesting that weakening the representation of the less demanding could also contribute to the effect found in Experiment 1.

A context-sensitive adaptation of strengthening the protection of high-demand task sets may be more adaptive in the real world, because here interference can arise from many other possible task sets that could be performed on a given stimulus (think, for instance, about the myriad different activities that can be prompted by your computer screen). By contrast, an adaptation that relies on benefitting from facilitation of responses by other task sets may incur real-life benefits only rarely, and it carries a high risk of being interfered with by other task sets that do not share the same responses to particular stimuli. Note that the motivation for down-regulating focus level in the high proportion congruent task may not solely be about benefiting from cross-task facilitation, but may also - relatedly - reflect the desire to expend as little cognitive effort as necessary (e.g., Kool & Botvinick, 2014)

It is also possible that selective down-regulation of task focus level is less efficient than up-regulating, in that the latter might reflect an active process whereas the former might involve a more passive release of control. The present data are not able to answer this question, but there are some phenomena in the psychology literature at large that suggest that, in principle, cognitive representation can be actively down-regulated or inhibited. For instance, people appear to be able to selectively suppress the mnemonic encoding of cued stimuli, as observed in the think/no-think paradigm (Anderson & Green, 2001; for a recent review of related forms of cognitive inhibition, see Wessel & Anderson, 2023). However, whether the same applies to the inhibition of task set representations remains an open question.

In Experiment 3, we addressed an important potential alternative interpretation of the data obtained in Experiments 1 and 2. In particular, while our design involved trial-unique task stimuli, specifically so that participants would not be able to form stimulus-specific associations with low or high focus requirements, each task was nevertheless cued by a single, constant symbolic stimulus (a red vs. blue rectangular frame around the task stimulus). Thus, it is plausible that participants could have learned to associate these physical cue features with the need to apply a low or high task focus during the learning phase, and continue to do so during the subsequent transfer phase. To rule out this alternative possibility, in Experiment 3 participants were given entirely new cues (different shapes, different colors) prior to the transfer phase. In spite of this new set of cues, which should abolish the possible use of any cue-control associations in the transfer phase, we obtained identical effects to Experiments 1a, 1b, and 2a. This finding disambiguates the interpretation of the data pattern and clearly supports the notion that the effects we observed in the learning and transfer phase reflect the association between attentional focus settings with task sets, rather than with task cues.

We interpret the proportion congruent effects (and their transfer) as reflecting adjustment in task focus level. While this is in line with a large prior literature on proportion congruent effects, it is worth considering alternative mechanisms that might be able to produce this data pattern. One such alternative mechanism could be the adjustment of response caution or threshold rather than of task focus level. For instance, one could imagine participants lowering their response threshold in the high proportion congruent condition and raising it in the low proportion congruent condition. Such a strategy would produce a speed-accuracy tradeoff, resulting in slower but more accurate responses in the low than the high proportion congruent conditions. Inspection of the current result patterns does not bear out this pattern, however, as there were no differences in mean RT for correct trials between the two tasks in any of the experiments/phases, with the exception of the learning phases of Experiments 1b and 3. Moreover, in those two cases, it was in fact the high proportion congruent task that displayed longer mean RTs than the low proportion congruent task, arguing against a tighter response threshold in the former condition.

It should also be noted that the overall pattern of results argues against the presence of speed-accuracy tradeoffs in the current data sets. Such tradeoffs would predict that the conditions with the slowest response times should be the most accurate, and conditions with the fastest response times the least accurate. However, the opposite is the case in our data sets, in that the slowest conditions are also the least accurate, and the fastest conditions the most accurate (see section 4 of the appendix for visualizations of the accuracy data). Having said all that, we cannot conclusively rule out the possibility that adjustments in response threshold may contribute to the proportion congruent effect (in addition to task focus level adaptations) in the present data, and this question could be addressed more formally by applying drift diffusion modeling to the type of protocol we employed here (see e.g., Desender, 2018; Luo et al., 2023; Mittelstädt et al., 2023).

More broadly, the current results are in line with previous research showing that control parameters can become associated with other task-related representations. Importantly, however, the prior literature has demonstrated these associations exclusively at the level of specific stimuli or stimulus features. For example, particular objects have been shown to become associated with specific task sets (e.g., Moutsopoulou et al., 2015; Pfeuffer et al., 2017; Waszak et al., 2003), attentional settings (e.g., Brosowsky & Crump, 2018; Bugg et al., 2011; Bugg & Hutchison, 2013; Spinelli & Lupker, 2020), and the need to switch tasks (Chiu & Egner, 2017; Whitehead et al., 2020), and such stimulus-control associations can display transfer to different tasks (Ileri-Tayar et al., 2022). By contrast, the present study documents, for the first time, the association of control parameters with an abstract task set as opposed to with concrete stimuli. In other words, the present work documents that a task set not only entails information about which stimulus features need to be attended to (due to task-relevance), but also specifies how much attention needs to be paid to those features. In addition to other recent findings in this literature that have suggested that information about the modality compatibility of task stimuli and the sensory effects of the required response is incorporated in task sets (e.g., Fintor et al., 2018) , the present findings contribute to a continued expansion and refinement of the concept of what a task set is (reviewed in Koch et al., 2018).

The key design feature of the current study that allowed us to cleanly demonstrate this linkage between task sets and task focus levels was the use of trial-unique stimuli. The fact that no stimulus was encountered more than once throughout all task phases rules out any possibility of forming task stimulus-based control associations, and the introduction of new task cues between the learning and transfer phases in Experiment 3 preempted the possibility of employing cue stimulus-based task focus associations. Moreover, the balancing-out of demand levels (the proportion of congruent items) across all four stimulus classes (small natural, small human-made, etc.) prevented any formation of category-demand associations. Future studies can build on this basic protocol to delineate conditions that may promote or impede the association between task sets and task focus settings.

While switch costs were not of primary interest in the current study, we nevertheless analyzed them as a function of the congruency, task, and phase factors. Significant switch costs were observed in all phases of all experiments, but interactions with other factors were inconsistent. The most commonly observed interaction was with the congruency factor, producing a well-known pattern of larger mean switch costs on incongruent compared to congruent trials (e.g., Meiran, 2000; Rogers & Monsell, 1995). However, none of the higher-order interactions were observed reliably, in that switch costs were not consistently modulated by the proportion congruent manipulation or by task phases across the experiments (mean switch cost by experiment, phase, and task are displayed in the appendix table A3). This observation runs counter to expectations that increased task focus would lead to larger switch cost (e.g., Dreisbach, 2012; Goschke, 2003) but it aligns well with findings from another recent study, wherein the authors concurrently manipulated the proportion of congruent trials and of switch trials in a task switching protocol similar to the one used in the current study (Geddert & Egner, 2022). Akin to the results presented here, there was no effect of the rate of congruent trials on switch costs (and no effect of the rate of switch trials on congruent effect) in that study (Geddert & Egner, 2022), which suggest that switch costs and congruency effects can in principle be independent of each other (reviewed in Egner, 2023).

In conclusion, across three experiments we have shown that task sets can become associated with specific levels of attentional demand. This novel finding expands conventional definitions of the type of information that makes up a task set, adding to the traditional ensemble of task goals and associated stimulus-response links a control parameter specifying the strength with which a given task set needs to be implemented.

Appendix

1). Proportion of congruent and incongruent trials for each phase and experiment.

Table A1.

Mean percentage and standard deviation of congruent and incongruent trials for each phase and experiment.

	Baseline		Learning		Transfer
Experiment 1a	Low Proportion Congruent	High Proportion Congruent	Low Proportion Congruent	High Proportion Congruent	Low Proportion Congruent	High Proportion Congruent
Congruent	25% (2%)	25% (2%)	12% (1%)	38% (2%)	25% (2%)	26% (2%)
Incongruent	25% (2%)	25% (2%)	37% (2%)	12% (1%)	24% (2%)	25% (2%)
Experiment 1b	Low Proportion Congruent	High Proportion Congruent	Low Proportion Congruent	High Proportion Congruent	Low Proportion Congruent	High Proportion Congruent
Congruent	25% (2%)	25% (2%)	12% (1%)	38% (2%)	25% (2%)	25% (2%)
Incongruent	25% (2%)	25% (2%)	37% (2%)	13% (1%)	25% (2%)	25% (2%)
Experiment 2a	Unbiased Proportion Congruent	Low Proportion Congruent	Unbiased Proportion Congruent	Low Proportion Congruent	Unbiased Proportion Congruent	Low Proportion Congruent
Congruent	25% (2%)	25% (2%)	25% (1%)	13% (1%)	25% (2%)	25% (2%)
Incongruent	25% (2%)	25% (2%)	25% (1%)	38% (2%)	25% (2%)	25% (2%)
Experiment 2b	Unbiased Proportion Congruent	High Proportion Congruent	Unbiased Proportion Congruent	High Proportion Congruent	Unbiased Proportion Congruent	High Proportion Congruent
Congruent	25% (2%)	25% (2%)	25% (1%)	38% (2%)	25% (2%)	25% (2%)
Incongruent	25% (2%)	25% (2%)	25% (1%)	13% (1%)	25% (2%)	25% (2%)
Experiment 3	Low Proportion Congruent	High Proportion Congruent	Low Proportion Congruent	High Proportion Congruent	Low Proportion Congruent	High Proportion Congruent
Congruent	25% (2%)	25% (2%)	13% (1%)	37% (2%)	25% (2%)	25% (2%)
Incongruent	24% (2%)	25% (2%)	38% (2%)	12% (1%)	25% (2%)	25% (2%)

2). Proportion of task transitions

Table A2.

Mean percentage and standard deviation of switch and stay trials.

Experiment 1a	Stay	Switch
	46% (2%)	54% (2%)
Experiment 1b	Stay	Switch
	46% (1%)	54% (1%)
Experiment 2a	Stay	Switch
	46% (2%)	54% (2%)
Experiment 2b	Stay	Switch
	46% (2%)	54% (2%)
Experiment 3	Stay	Switch
	46% (1%)	54% (1%)

3). Switch costs as a function of tasks.

Table A3.

RT Switch costs (ms) means and standard deviations during the baseline and transfer phases for experiment 1 and 3.

	Baseline			Learning			Transfer
	Unbiased Proportion Congruent	Low Proportion Congruent	High Proportion Congruent	Unbiased Proportion Congruent	Low Proportion Congruent	High Proportion Congruent	Unbiased Proportion Congruent	Low Proportion Congruent	High ProportionCongruent
Experiment 1a		146 (130)	114 (93)		101 (90)	98 (83)		76 (92)	96 (102)
Experiment 1b		75 (87)	88 (119)		77 (73)	63 (81)		55 (81)	72 (92)
Experiment 2a	80 (126)	71 (95)		80 (68)	71 (65)		72 (108)	75 (84)
Experiment 2b	62 (118)		54 (89)	54 (68)		42 (81)	57 (90)		42 (91)
Experiment 3		49 (103)	63 (111)		80 (59)	63 (72)		89 (73)	86 (91)

4). Accuracy figures

Figure A1.

Average proportion of correct trials (standard mean error) values are displayed as a function of task (High Proportion Congruent vs Low Proportion Congruent), cross-task congruence (congruent vs. incongruent), and experimental phase (Baseline, Learning, and Transfer), for Experiments 1a (A) and 1b (B).

Figure A2.

Average proportion of correct trials (standard mean error) values are displayed as a function of task (High Proportion Congruent vs Low Proportion Congruent), cross-task congruency (unbiased vs. biased), and experimental phase (Baseline, Learning, and Transfer), for Experiments 2a (A) and 2b (B).

Figure A3.

Average proportion of correct trials (standard mean error) values are displayed as a function of task (High Proportion Congruent vs Low Proportion Congruent), cross-task congruency (congruent vs. incongruent), and experimental phase (Baseline, Learning, and Transfer), for Experiments 3.

5). RT rmANOVA tables

Experiment 1a

Table A4.

repeated measures ANOVA results of the learning phase.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Task	1	32	1.47	.234	.002
Congruency	1	32	24.95	.000	.031
Transition	1	32	62.14	.000	.073
Task x Congruency	1	32	65.85	.000	.037
Task x Transition	1	32	0.06	.816	.000
Congruency x Transition	1	32	17.31	.000	.004
Task x Congruency x Transition	1	32	0.32	.578	.000

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Table A5.

repeated measures ANOVA results between the baseline and transfer phases.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Phase	1	32	13.50	.001	.044
Task	1	32	0.41	.524	.000
Congruency	1	32	15.49	.000	.014
Transition	1	32	80.55	.000	.069
Phase x Task	1	32	0.69	.414	.000
Phase x Congruency	1	32	0.80	.377	.000
Task x Congruency	1	32	13.12	.001	.006
Phase x Transition	1	32	8.48	.006	.003
Task x Transition	1	32	0.11	.740	.000
Congruency x Transition	1	32	4.62	.039	.001
Phase x Task x Congruency	1	32	9.34	.004	.004
Phase x Task x Transition	1	32	3.07	.089	.001
Phase x Congruency x Transition	1	32	0.40	.534	.000
Task x Congruency x Transition	1	32	0.26	.616	.000
Phase x Task x Congruency x Transition	1	32	0.95	.337	.000

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Experiment 1b

Table A6.

repeated measures ANOVA results of the learning phase.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Task	1	32	4.76	.037	.006
Congruency	1	32	65.16	.000	.042
Transition	1	32	38.83	.000	.042
Task x Congruency	1	32	51.35	.000	.035
Task x Transition	1	32	0.96	.334	.000
Congruency x Transition	1	32	0.01	.919	.000
Task x Congruency x Transition	1	32	0.06	.805	.000

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Table A7.

repeated measures ANOVA results between the baseline and transfer phases.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Phase	1	32	24.87	.000	.069
Task	1	32	3.08	.089	.006
Congruency	1	32	55.75	.000	.035
Transition	1	32	44.38	.000	.042
Phase x Task	1	32	0.75	.394	.000
Phase x Congruency	1	32	0.02	.888	.000
Task x Congruency	1	32	27.48	.000	.011
Phase x Transition	1	32	1.78	.192	.001
Task x Transition	1	32	0.81	.375	.001
Congruency x Transition	1	32	1.15	.291	.001
Phase x Task x Congruency	1	32	15.11	.000	.007
Phase x Task x Transition	1	32	0.02	.878	.000
Phase x Congruency x Transition	1	32	2.14	.153	.001
Task x Congruency x Transition	1	32	1.42	.242	.001
Phase x Task x Congruency x Transition	1	32	1.37	.250	.000

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Experiment 2a

Table A8.

repeated measures ANOVA results of the learning phase.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Task	1	65	0.53	.470	.000
Congruency	1	65	78.90	.000	.021
Transition	1	65	118.20	.000	.043
Task x Congruency	1	65	18.55	.000	.007
Task x Transition	1	65	1.17	.284	.000
Congruency x Transition	1	65	1.49	.227	.000
Task x Congruency x Transition	1	65	2.07	.155	.000

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Table A9.

repeated measures ANOVA results between the baseline and transfer phases.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Phase	1	65	7.90	.007	.009
Task	1	65	0.04	.835	.000
Congruency	1	65	84.31	.000	.023
Transition	1	65	75.68	.000	.035
Phase x Task	1	65	0.12	.726	.000
Phase x Congruency	1	65	0.05	.817	.000
Task x Congruency	1	65	8.48	.005	.002
Phase x Transition	1	65	0.02	.877	.000
Task x Transition	1	65	0.05	.827	.000
Congruency x Transition	1	65	8.68	.004	.002
Phase x Task x Congruency	1	65	8.86	.004	.001
Phase x Task x Transition	1	65	0.43	.517	.000
Phase x Congruency x Transition	1	65	4.54	.037	.001
Task x Congruency x Transition	1	65	0.34	.561	.000
Phase x Task x Congruency x Transition	1	65	1.05	.309	.000

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Experiment 2b

Table A10.

repeated measures ANOVA results of the learning phase.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Task	1	63	0.08	.781	.000
Congruency	1	63	136.50	.000	.044
Transition	1	63	42.48	.000	.014
Task x Congruency	1	63	13.22	.001	.003
Task x Transition	1	63	1.16	.285	.000
Congruency x Transition	1	63	2.72	.104	.000
Task x Congruency x Transition	1	63	0.51	.479	.000

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Table A11.

repeated measures ANOVA results between the baseline and transfer phases.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Phase	1	63	26.11	.000	.029
Task	1	63	0.63	.429	.000
Congruency	1	63	99.09	.000	.029
Transition	1	63	44.98	.000	.011
Phase x Task	1	63	5.23	.026	.001
Phase x Congruency	1	63	0.83	.364	.000
Task x Congruency	1	63	1.24	.269	.000
Phase x Transition	1	63	0.75	.391	.000
Task x Transition	1	63	0.88	.351	.000
Congruency x Transition	1	63	4.54	.037	.001
Phase x Task x Congruency	1	63	3.46	.068	.001
Phase x Task x Transition	1	63	0.14	.709	.000
Phase x Congruency x Transition	1	63	0.32	.571	.000
Task x Congruency x Transition	1	63	0.00	.944	.000
Phase x Task x Congruency x Transition	1	63	3.43	.069	.001

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Comparison between experiments 2a and 2b

Table A12.

repeated measures ANOVA results comparing the baseline phases of experiments 2a and 2b.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Experiment	1	128	0.72	.397	.002
Task	1	128	0.30	.585	.001
Transition	1	128	11.75	.001	.022
Experiment x Task	1	128	0.00	.971	.000
Experiment x Transition	1	128	0.64	.425	.001
Task x Transition	1	128	0.86	.355	.001
Experiment x Task x Transition	1	128	1.27	.262	.001

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Table A13.

repeated measures ANOVA results comparing the transfer phases of experiments 2a and 2b.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Experiment	1	128	2.65	.106	.01
Task	1	128	2.17	.143	.00
Transition	1	128	2.76	.099	.00
Experiment x Task	1	128	28.16	.000	.05
Experiment x Transition	1	128	0.37	.543	.00
Task x Transition	1	128	0.07	.793	.00
Experiment x Task x Transition	1	128	3.34	.070	.01

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Experiment 3

Table A14.

repeated measures ANOVA results of the learning phase.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Task	1	33	8.61	.006	.008
Congruency	1	33	85.97	.000	.094
Transition	1	33	57.83	.000	.047
Task x Congruency	1	33	68.27	.000	.054
Task x Transition	1	33	1.92	.175	.001
Congruency x Transition	1	33	0.29	.591	.000
Task x Congruency x Transition	1	33	0.28	.600	.000

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Table A15.

repeated measures ANOVA results between the baseline and transfer phases.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Phase	1	33	5.25	.028	.012
Task	1	33	0.49	.490	.001
Congruency	1	33	65.67	.000	.047
Transition	1	33	64.82	.000	.043
Phase x Task	1	33	0.05	.831	.000
Phase x Congruency	1	33	9.19	.005	.003
Task x Congruency	1	33	8.15	.007	.005
Phase x Transition	1	33	3.03	.091	.002
Task x Transition	1	33	0.13	.719	.000
Congruency x Transition	1	33	1.28	.266	.001
Phase x Task x Congruency	1	33	12.27	.001	.004
Phase x Task x Transition	1	33	0.30	.589	.000
Phase x Congruency x Transition	1	33	2.09	.157	.001
Task x Congruency x Transition	1	33	0.50	.485	.000
Phase x Task x Congruency x Transition	1	33	0.00	.956	.000

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

6). ACCURACY RMANOVA TABLES

Experiment 1a

Table A16.

repeated measures ANOVA results of the learning phase.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Task	1	32	15.25	.000	.051
Congruency	1	32	33.48	.000	.231
Transition	1	32	15.83	.000	.033
Task x Congruency	1	32	37.38	.000	.088
Task x Transition	1	32	1.26	.270	.002
Congruency x Transition	1	32	1.41	.243	.002
Task x Congruency x Transition	1	32	0.33	.567	.000

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Table A17.

repeated measures ANOVA results between the baseline and transfer phases.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Phase	1	32	11.96	.002	.045
Task	1	32	2.96	.095	.006
Congruency	1	32	33.91	.000	.153
Transition	1	32	23.62	.000	.019
Phase x Task	1	32	4.46	.043	.005
Phase x Congruency	1	32	3.76	.061	.004
Task x Congruency	1	32	11.19	.002	.016
Phase x Transition	1	32	7.59	.010	.006
Task x Transition	1	32	0.30	.589	.000
Congruency x Transition	1	32	0.31	.579	.000
Phase x Task x Congruency	1	32	7.52	.010	.009
Phase x Task x Transition	1	32	0.97	.333	.001
Phase x Congruency x Transition	1	32	0.86	.362	.001
Task x Congruency x Transition	1	32	0.70	.409	.000
Phase x Task x Congruency x Transition	1	32	0.56	.458	.000

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Experiment 1b

Table A18.

repeated measures ANOVA results of the learning phase.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Task	1	32	9.82	.004	.067
Congruency	1	32	36.05	.000	.235
Transition	1	32	9.18	.005	.007
Task x Congruency	1	32	62.74	.000	.158
Task x Transition	1	32	0.00	1.0	.000
Congruency x Transition	1	32	1.79	.191	.001
Task x Congruency x Transition	1	32	0.27	.608	.000

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Table A19.

repeated measures ANOVA results between the baseline and transfer phases.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Phase	1	32	4.14	.050	.009
Task	1	32	8.11	.008	.032
Congruency	1	32	36.09	.000	.168
Transition	1	32	9.88	.004	.014
Phase x Task	1	32	2.28	.141	.004
Phase x Congruency	1	32	0.01	.912	.000
Task x Congruency	1	32	15.60	.000	.041
Phase x Transition	1	32	2.04	.163	.001
Task x Transition	1	32	2.72	.109	.002
Congruency x Transition	1	32	0.39	.536	.000
Phase x Task x Congruency	1	32	6.77	.014	.009
Phase x Task x Transition	1	32	0.18	.675	.000
Phase x Congruency x Transition	1	32	0.06	.804	.000
Task x Congruency x Transition	1	32	0.63	.432	.001
Phase x Task x Congruency x Transition	1	32	0.51	.482	.000

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Experiment 2a

Table A20.

repeated measures ANOVA results of the learning phase.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Task	1	65	5.39	.023	.015
Congruency	1	65	118.70	.000	.200
Transition	1	65	52.36	.000	.048
Task x Congruency	1	65	36.27	.000	.067
Task x Transition	1	65	0.26	.614	.000
Congruency x Transition	1	65	5.98	.017	.006
Task x Congruency x Transition	1	65	10.62	.002	.006

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Table A21.

repeated measures ANOVA results between the baseline and transfer phases.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Phase	1	65	0.99	.324	.002
Task	1	65	0.49	.486	.001
Congruency	1	65	132.58	.000	.187
Transition	1	65	70.40	.000	.033
Phase x Task	1	65	0.81	.370	.000
Phase x Congruency	1	65	1.16	.286	.001
Task x Congruency	1	65	10.61	.002	.014
Phase x Transition	1	65	0.59	.446	.000
Task x Transition	1	65	3.26	.076	.002
Congruency x Transition	1	65	14.37	.000	.007
Phase x Task x Congruency	1	65	2.11	.151	.001
Phase x Task x Transition	1	65	2.65	.108	.001
Phase x Congruency x Transition	1	65	0.76	.386	.000
Task x Congruency x Transition	1	65	0.11	.742	.000
Phase x Task x Congruency x Transition	1	65	2.87	.095	.001

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Experiment 2b

Table A22.

repeated measures ANOVA results of the learning phase.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Task	1	63	7.79	.007	.024
Congruency	1	63	159.04	.000	.359
Transition	1	63	30.62	.000	.020
Task x Congruency	1	63	22.70	.000	.054
Task x Transition	1	63	0.85	.361	.000
Congruency x Transition	1	63	10.66	.002	.007
Task x Congruency x Transition	1	63	0.55	.463	.000

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Table A23.

repeated measures ANOVA results between the baseline and transfer phases.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Phase	1	63	8.41	.005	.010
Task	1	63	0.13	.718	.000
Congruency	1	63	127.91	.000	.236
Transition	1	63	19.32	.000	.008
Phase x Task	1	63	4.23	.044	.003
Phase x Congruency	1	63	0.74	.392	.000
Task x Congruency	1	63	0.94	.335	.001
Phase x Transition	1	63	2.03	.159	.001
Task x Transition	1	63	0.94	.336	.000
Congruency x Transition	1	63	11.53	.001	.005
Phase x Task x Congruency	1	63	5.14	.027	.005
Phase x Task x Transition	1	63	0.44	.511	.000
Phase x Congruency x Transition	1	63	0.86	.358	.000
Task x Congruency x Transition	1	63	0.01	.915	.000
Phase x Task x Congruency x Transition	1	63	2.58	.114	.002

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Comparison between experiments 2a and 2b

Table A24.

repeated measures ANOVA results comparing the baseline phases of experiments 2a and 2b.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Experiment	1	128	4.41	.038	.014
Task	1	128	2.68	.104	.007
Transition	1	128	18.73	.000	.019
Experiment x Task	1	128	0.29	.593	.001
Experiment x Transition	1	128	0.07	.792	.000
Task x Transition	1	128	2.59	.110	.003
Experiment x Task x Transition	1	128	0.21	.648	.000

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Table A25.

repeated measures ANOVA results comparing the transfer phases of experiments 2a and 2b.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Experiment	1	128	4.39	.038	.014
Task	1	128	0.15	.697	.000
Transition	1	128	8.98	.003	.008
Experiment x Task	1	128	16.69	.000	.039
Experiment x Transition	1	128	0.00	.988	.000
Task x Transition	1	128	3.14	.079	.004
Experiment x Task x Transition	1	128	0.00	.978	.000

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Experiment 3

Table A26.

repeated measures ANOVA results of the learning phase.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Task	1	33	24.27	.000	.083
Congruency	1	33	76.14	.000	.347
Transition	1	33	21.55	.000	.037
Task x Congruency	1	33	49.34	.000	.171
Task x Transition	1	33	9.00	.005	.010
Congruency x Transition	1	33	10.34	.003	.019
Task x Congruency x Transition	1	33	6.75	.014	.007

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

Table A27.

repeated measures ANOVA results between the baseline and transfer phases.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Phase	1	33	0.19	.668	.001
Task	1	33	5.69	.023	.012
Congruency	1	33	41.55	.000	.153
Transition	1	33	3.28	.079	.005
Phase x Task	1	33	14.06	.001	.012
Phase x Congruency	1	33	0.65	.427	.001
Task x Congruency	1	33	6.82	.013	.012
Phase x Transition	1	33	0.03	.865	.000
Task x Transition	1	33	3.14	.086	.003
Congruency x Transition	1	33	16.71	.000	.017
Phase x Task x Congruency	1	33	20.02	.000	.020
Phase x Task x Transition	1	33	0.14	.713	.000
Phase x Congruency x Transition	1	33	0.46	.501	.000
Task x Congruency x Transition	1	33	0.59	.449	.001
Phase x Task x Congruency x Transition	1	33	0.63	.435	.000

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

7). RT comparison between experiments 1 and 3

Table A28.

repeated measures ANOVA comparing the baseline and transfer phases between experiments 1 and 3.

Predictor	dfNum	dfDen	F	p	${{\mathrm{\eta }}^2}_{\mathrm{g}}$
Experiment	1	65	10.80	.002	.100
Phase	1	65	18.88	.000	.026
Task	1	65	0.89	.348	.000
Transition	1	65	145.32	.000	.056
Congruency	1	65	66.18	.000	.027
Experiment x Phase	1	65	2.92	.092	.004
Experiment x Task	1	65	0.02	.894	.000
Experiment x Transition	1	65	5.88	.018	.002
Experiment x Congruency	1	65	3.74	.057	.002
Phase x Task	1	65	0.29	.594	.000
Phase x Transition	1	65	0.26	.610	.000
Task x Transition	1	65	0.00	.972	.000
Phase x Congruency	1	65	5.86	.018	.001
Task x Congruency	1	65	20.73	.000	.006
Transition x Congruency	1	65	5.37	.024	.001
Experiment x Phase x Task	1	65	0.63	.430	.000
Experiment x Phase x Transition	1	65	10.15	.002	.002
Experiment x Task x Transition	1	65	0.24	.626	.000
Experiment x Phase x Congruency	1	65	0.83	.365	.000
Experiment x Task x Congruency	1	65	0.15	.701	.000
Experiment x Transition x Congruency	1	65	0.51	.477	.000
Phase x Task x Transition	1	65	0.72	.399	.000
Phase x Task x Congruency	1	65	20.53	.000	.004
Phase x Transition x Congruency	1	65	0.13	.721	.000
Task x Transition x Congruency	1	65	0.00	.960	.000
Experiment x Phase x Task x Transition	1	65	2.63	.110	.001
Experiment x Phase x Task x Congruency	1	65	0.27	.604	.000
Experiment x Phase x Transition x Congruency	1	65	1.89	.174	.000
Experiment x Task x Transition x Congruency	1	65	0.71	.404	.000
Phase x Task x Transition x Congruency	1	65	0.69	.408	.000
Experiment x Phase x Task x Transition x Congruency	1	65	0.59	.445	.000

Note. df_Num indicates degrees of freedom numerator. df_Den indicates degrees of freedom denominator. ${{\mathrm{\eta }}^2}_{\mathrm{g}}$ indicates generalized eta-squared.

7). Congruency effects comparison experiments 2a and 2b during the transfer phase

Figure A4.

Difference values between congruent and incongruent trials (± standard mean error) during the transfer phase are displayed as a function of task (Biased vs Unbiased) and experiment (Experiments 2a vs 2b) for RT (A) and Acuraccy (B).