Escaping the Metacontrol See-saw: Dissociating Metacontrol via Top-down Modulation

The capacity to direct cognition and behavior towards desired objectives, or cognitive control, is crucial for achieving success in daily life (Miller & Cohen, 2001). Cognitive control becomes particularly critical when “prepotent” behaviors (behaviors that are well-established or otherwise more powerful) interfere with actions that are essential for goal attainment. During a classroom lecture, for instance, it is required to inhibit the habitual tendency to check one’s phone upon receiving a notification, because this habitual tendency disrupts the goal of maintaining focus on the professor. Moreover, certain contexts demand heightened cognitive control. Consider the case where a student may receive numerous text messages during their noon class from their friends regarding lunch plans, resulting in their phone buzzing more frequently in class. Over time, with repeated exposure to similar scenarios, the student may begin to associate an elevated need for control with the midday class. Consequently, the midday class itself becomes an effective cue that can trigger automatic increases in control even before the phone buzzes. This proactive control can then discourage the student’s inclination to check their phone all the more effectively. This example illustrates that control regulation can be triggered by contextual settings or the broader environment in which cognitive control is demanded and exercised. Empirical evidence supporting this contextual regulation of cognitive control has been extensively documented in recent literature (Abrahamse et al., 2016; Braem et al., 2019; Bugg & Egner, 2021; Chiu & Egner, 2019; Egner, 2014). Following this recognition, to differentiate it from cognitive control per se, researchers have started formally referring to the contextual regulation of cognitive control as metacontrol (Goschke, 2013; Hommel, 2015).

Because task demands can vary widely, many different metacontrol states are possible. Two commonly discussed metacontrol states are cognitive flexibility and cognitive stability. Following the example of the student in a classroom lecture, increased flexibility helps the student to readily switch between reading words on lecture slides and jotting notes, while increased stability helps the student effectively ignore buzzing phones. Broadly defined, flexibility entails being in a cognitive control state that prioritizes multiple goals and smoothly transitioning between them, while stability entails being in a cognitive control state that shields prioritized goals from distraction or interference (Braem & Egner, 2018; Eppinger et al., 2021; Goschke, 2013; Hommel & Colzato, 2017). Due to their broad relevance to real life experiences, flexibility and stability are operationalized in many different ways in laboratory studies, leading to ambiguity in conceptual inferences (Ionescu, 2017). To mitigate ambiguity, we narrow our current focus to only examine flexibility and stability of task-set configuration at the list level. First, a task-set, akin to an “if-then” rule, constitutes a collection of mental representations of stimuli, rules, and responses needed to produce goal-appropriate behavior. An example of a task-set that is relevant to a student may be “When the professor introduces a new idea, write it down in your notes.” Second, “at the list level” means that the study concerns metacontrol states that persist across several trials or are ‘list-wide’, as opposed to trial-level changes in control state. The student may learn to associate an increased demand for flexibility and stability with certain class periods. With repeated exposure to similar experiences, these specific class times—equivalent to the “list” term used earlier—could become “contextual cues” triggering a metacontrol shift toward an optimal state of flexibility or stability.

Given this narrower scope of flexibility and stability, our current study and discussion primarily focus on paradigms that are designed to examine cognitive control over task-sets. One example of such paradigms is the cued task-switching paradigm, where participants are instructed with ‘if-then’ rules to achieve specific goals. For example, in the current study, participants were shown pictures of objects across multiple trials. Their task was to categorize one object at a time on each trial, based on one of two rules: whether the object was larger or smaller than a shoebox, or whether the object consisted mostly of metal or non-metal components. Because the two rules were presented with equal frequency from one trial to the next, participants alternated between switching tasks or repeating the same task as the previous trial on any given trial. Task switches typically incur longer response times and more errors compared to task repeats, a phenomenon known as the “switch costs” effect, which suggests the involvement of cognitive control processes. These processes include activating new task-sets in working memory and overcoming lingering activations from previous task-sets (Allport et al., 1994; Altmann, 2002; Meiran, 1996; Rogers & Monsell, 1995). When these processes are upregulated (increased or strengthened) to promote better switching between tasks, switch costs are reduced. Within our circumscribed scope of metacontrol, changes in flexibility are operationalized as changes in switch costs (SC).

The same task switching paradigms can also be used to assess stability, so long as the paradigm utilizes bivalent stimuli that elicit overlapping responses between tasks. For example, a “truck” can be categorized as “larger than a shoebox” according to the size rule and “mostly metal” according to the material rule. When one task is relevant and the other is irrelevant, bivalent stimuli can be either congruent (producing the same response in both tasks) or incongruent (producing different responses). Incongruent stimuli typically incur longer response times and more errors compared to congruent ones, known as task-rule “congruency effects” (Meiran & Kessler, 2008; Wendt & Kiesel, 2008). This effect arises either from interference caused by past experiences of different responses to the same stimulus (Kiesel et al., 2010; Logan, 1988; Vandierendonck et al., 2010) or from categorizing every stimulus based on both task rules (Schneider, 2018; Schneider & Logan, 2015). Regardless of the source, the performance cost observed on incongruent trials reflects the engagement of cognitive control to shield the relevant task-set against goal-irrelevant, detrimental information. When these processes are upregulated (increased or strengthened) to promote better performance on a particular task-set, congruency effects are reduced. Within our circumscribed scope of metacontrol, analogous to flexibility, changes in stability are operationalized as changes in congruency effects (CE).

The most common manipulation used to modulate switch costs is manipulating the number of switch trials within a list (e.g., a block of 30 trials or so). The result of such manipulation, widely replicated and documented, is that switch costs are reduced in lists containing a greater number of switch trials than in lists containing fewer number of switch trials (Dreisbach et al., 2002; Dreisbach & Haider, 2006; Kang & Chiu, 2021; Monsell & Mizon, 2006; Schneider & Logan, 2006). This behavioral finding, known as the list-wide switch probability effect, is thought to reflect increased flexibility as participants become more adept at switching between tasks with lists serving as contextual cues that modulate the efficiency of control over task-sets. Other studies have also demonstrated similar effects using different kinds of contextual cues besides lists, such as spatial locations or stimulus identity (Chiu & Egner, 2017; Crump & Logan, 2010; Leboe et al., 2008). In a very similar way, congruency effects are commonly modulated by manipulating the proportion of incongruent trials, oftentimes demonstrated in the Stroop paradigm (Bugg & Crump, 2012), but also in the task switching paradigm (Geddert & Egner, 2022). Mirroring list-wide switch probability effects for switch costs, differences in congruency effects between frequent vs. rare incongruent lists are referred to as list-wide proportion congruent effects. Together, list-wide switch probability and list-wide proportion congruent manipulations are two methods for inducing different metacontrol states (or control modes), allowing researchers to examine how the cognitive system adapts to contextual task demands. These two effects illustrate context-dependent shifts in metacontrol in laboratory studies, serving as a means to examine shifts in flexibility and stability as a function of task demands. Armed with these specific operationalizations of flexibility and stability, the goal of the present study is to investigate the relationship between these two metacontrol states.

Flexibility and stability have traditionally been viewed as opposing ends of a single dimension, predicting a trade-off relationship (Cools, 2016; Dreisbach, 2012; Goschke, 2003, 2013; Hommel, 2015; Paul et al., 2021) ². This trade-off is analogous to how movement on one end of a seesaw must unavoidably be compensated on the other end (Figure 1a). We refer to this conceptualization as the unidimensional framework of metacontrol. Flexible behavior allows for efficient attention shifting and task switching, but it may also lead to increased susceptibility to distraction. In contrast, stable behavior enables better attention maintenance on goal-relevant information but can result in inflexibility. The balance between flexibility and stability depends on goals and context, as each can have both beneficial and detrimental effects according to circumstance. According to the unidimensional framework, flexibility and stability are antagonistic, always varying inversely. It is important to note that this trade-off is primarily discussed within a single level of cognition, such as goal or task-set instantiation, rather than across multiple levels of processing. This provides a precedent and justification for our own circumscribed definitions of flexibility and stability mentioned earlier which exist within the same level of information processing — switching between and shielding task-sets.

The unidimensional framework has intuitive appeal and is undoubtedly supported by several lines of behavioral evidence. For example, (Dreisbach & Goschke, 2004) conducted a study where participants were tasked with categorizing a target stimulus while ignoring a distractor. Critically, the target was defined by a specific color which changed midway through the experiment. The experimenters were interested in the performance cost associated with this color change. The study had two conditions that allowed this cost to be interpreted in two distinct ways, respectively. In their first condition, the old target color became the new distractor; therefore, the cost was interpreted as an indicator of how quickly participants could deactivate the old task set and switch to the new one, akin to flexibility discussed here. In their second condition, the old distractor became the new target, and the cost was akin to a shift in stability discussed here. In other words, small costs in the first condition indicate high flexibility, whereas small costs in the second condition indicate high stability. To shift metacontrol states, in their Experiment 2, the authors induced positive affect in participants. Positive affect, as hypothesized to promote flexibility at the expense of stability, indeed reduced performance costs in the first condition but increased the costs in the second condition. Besides Dreisbach and Goschke’s (2004) seminal findings, many additional studies document a flexibility-stability trade-off (Cools et al., 2010; Dreisbach, 2006; Fischer & Hommel, 2012a; Held et al., 2024; Liu et al., 2020; Locke & Braver, 2008). In each of these studies, a manipulation or individual difference which impacts flexibility had an inverse impact on stability, suggesting a trade-off between the two metacontrol states.

However, when relating the unidimensional framework to real-world scenarios, the framework would suggest that a student switching smoothly between the two goal-relevant, beneficial tasks (listening to the lecture and taking notes) cannot effectively shield against the goal-irrelevant task of checking their phone. Treating flexibility and stability as a zero-sum trade-off might not reflect how daily life sometimes requires both simultaneously. More importantly, when explicitly evaluating the relationship between flexibility and stability, researchers should not claim that observing increased flexibility automatically corresponds to decreased stability. This assumes that the unidimensional framework has already been proven correct universally, and that a joint measurement of flexibility and stability is sufficient. While all of the evidence we cite in support of the unidimensional framework above satisfies this requirement for separate measurement, a considerable body of research which also satisfies the separation requirement fails to support the unidimensional framework. These studies span a wide range of paradigms and measurements, and their implications regarding metacontrol have been largely overlooked (Nack & Yu-Chin, 2023).

On the other hand, until recently, many of these studies noted in Nack & Yu-Chin (2023) were not explicitly designed to investigate the relationship between flexibility and stability. Instead, they often reported “not finding the expected trade-off” as a secondary objective of their studies. Here, we delve into one exception in detail because the study was designed explicitly to adjudicate the trade-off versus the independence hypotheses. Geddert and Egner (2022) manipulated both the probability of task switches (frequent vs. rare switches) and the proportion incongruence (mostly incongruent vs. mostly congruent trials) within-subjects. Thus, it was possible to measure both (1) changes in congruency effects as switches became more frequent and (2) changes in switch costs as incongruent trials became more prevalent. According to the unidimensional framework, there should be an interaction between the two manipulations and a trade-off relationship: A larger congruency effect in the frequent switch condition than in the rare one, and a larger switch cost in the frequent incongruent condition than in the rare one.

Unexpectedly, neither effect was observed— (1) adaptation to the higher switch probability did not come with an increase congruency effects, and (2) adaptation to the higher proportion incongruence did not come with an increase in switch costs. When compared to a model including an interaction term, Bayesian statistics indicated evidence seven times greater supporting a model with no interaction. This pattern was consistent across two different implementations of task-rule congruency. Geddert and Egner’s (2022) Experiment 1 employed a standard cued task switching procedure with digits 1-9, except for 5, as stimuli. Participants alternated between categorizing these digits as odd versus even (parity task) or as numerically larger versus smaller than 5 (magnitude task). Since the stimuli were bivalent and the same response keys were used for both tasks, some stimuli were congruent; they required the same response regardless of task. Other stimuli were incongruent; they required opposite responses depending on the current task. Experiment 2 employed a global-local paradigm (Navon, 1977) where stimuli were large/global letters made up of smaller/local letters. Participants in this paradigm switched between categorizing the global or the local stimuli as the letter S or H. Congruency occurs between global and local letters. Incongruent trials were those where the global letter was different from the local letters (e.g., a large S made of small H’s), while congruent trials were those where the global and local letters matched (e.g., a large H made of small H’s). More recently, Geddert and Egner (2024) reanalyzed their 2022 experiment 1 data with a linear mixed-effects model and conducted a new experiment to control for trial count and sequence confounds. Both analyses replicated their 2022 findings, showing no trade-off between switch costs and congruency effects with proportion manipulations.

It should be noted that Geddert and Egner (2022) attempted a third experiment with a stability manipulation that did not meet their threshold for successfully causing a difference in congruency effects. Like Experiment 1, Experiment 3 also used digits as stimuli and parity/magnitude tasks, except that four response keys were used, two for each task. Thus, there was no response overlap between the two categorization tasks and no opportunity for the type of congruency effects measured in the previous two experiments. Instead, reminiscent of the Flanker paradigm (Eriksen & Eriksen, 1974), each stimulus was flanked by 4 distractors that were also digits (e.g., 22322). When the correct response for the target differed from the distractors, the trial was incongruent. For example, when instructed to perform the even versus odd task, an incongruent trial could be a target 3 flanked by 2’s, while a congruent trial could be a 3 flanked by 3’s. In this experiment, the switch probability manipulation successfully reduced switch costs, but the proportion congruency manipulation had no impact on congruency effects. This latter effect meant that the impacts of stability manipulations upon switch costs could not be investigated like in the first two experiments, somewhat reducing the strength of the conclusions that could be drawn from Experiment 3.

In summary, based on these findings, Geddert and Egner (2022) proposed an alternative to the unidimensional framework (see alos Egner, 2023), which Nack and Yu-Chin (2023) have dubbed the Dual-Dimension Framework (DDF). In this framework, flexibility and stability are independent constructs, capable of varying without impacting the other. Meanwhile, this framework still allows the two constructs to vary in opposite directions, thus displaying a trade-off in some scenarios, akin to a swing set with two independent swings (Figure 1b). However, this would have to be caused by separate forces independently pushing one swing up and the other down, rather than a single force on only one seat like on the seesaw. In other words, the dual-dimensional framework does not prohibit instances of trading off but explains them differently. Since both frameworks allow for a trade-off, detecting a trade-off is not necessarily diagnostic between the two frameworks. Instead, finding instances of no trade-off is highly diagnostic, as this case is strictly prohibited by the unidimensional seesaw account. Accordingly, as we describe next, the present study was aimed at detecting such “no trade-off” scenarios of flexibility/stability independence.

Geddert and Egner (2022) reveal one case of independence between flexibility and stability, but perhaps more evidence is needed. Therefore, we sought additional experiments and manipulations to evaluate the relationship between flexibility and stability by conceptually replicating and extending Geddert and Egner’s (2022) findings using a similar design that allowed for measuring (1) changes in congruency effects as switches became more frequent and (2) changes in switch costs as incongruent trials became more prevalent, but with two major changes.

First, Geddert and Egner’s (2022) metacontrol manipulations were applied entirely within-subjects. Thus, every participant in the study experienced all four of the conditions. While providing better efficiency in terms of sample size, this within-subjects design may lead to concerns that carryover effects from one condition might hide the trade-off in another condition. To illustrate this concern, imagine a participant who just completed the condition aimed at inducing a high flexibility and a low stability state. This participant might be primed to begin the next block with heightened flexibility relative to their baseline. If the very next condition is low flexibility and high stability, this participant might show unexpectedly high levels of flexibility, plus the expected increase in stability. Going from one condition to the next, this would result in a change in stability, but no change in flexibility, as would be interpreted as evidence for flexibility-stability independence. However, someone critical of the flexibility-stability independence account might disagree with this interpretation, arguing that the carryover hid the trade-off that would have occurred had there been no opportunity for the high flexibility on the first block to impact behavior on the second. We wished to design a study in which this objection could not be applied. We eliminated this possibility in our design by manipulating the metacontrol dimension (i.e., flexibility, stability) “between subjects.” Thus, each participant will only be assigned to one metacontrol dimension (either flexibility or stability) and experience two conditions that are designed to induce a high or a low metacontrol state in their assigned dimension.

Second, we employed different metacontrol manipulations than those used by Geddert and Egner (2022). Specifically, we fixed switch and incongruency probabilities at 50% across all experiments. Brosowsky & Egner (2021) noted that metacontrol shifts based on biased switch probabilities and proportion congruencies may be asymmetrical, with all the conditions of a given experiment requiring high stability but varying requirements for flexibility levels across conditions. In other words, some results in the literature might be driven by stability (but not flexibility) levels being at ceiling. Although the authors suggested that this might be a problem for switch probabilities even as low as 50%, the problem would become particularly pronounced for strongly biased probabilities (e.g., 80%). We wanted to address this potential confound and adopted 50% switch and incongruency probabilities. Relatedly, unlike Geddert and Egner (2022), who utilized a single manipulation but conceptually replicated their findings by varying how the congruency effects were measured in two experiments, our conceptual replications involve variations in the manipulation utilized to shift metaocntrol states. Briefly here, Experiment 1 employed explicit instructions to guide participants in setting up the appropriate metacontrol states to meet the upcoming demands while Experiment 2 utilized two different problem-solving tasks to prime distinct thinking styles that are thought to promote flexibility and stability, respectively³.

Despite the manipulations differing between experiments, both entailed a 2 (metacontrol dimension: flexibility, stability) x 2 (metacontrol state: high, low) factorial design with dimension being a between-subject variable and state being a within-subject variable. Our study manipulations were designed to shift participants’ metacontrol states between the high and the low conditions in two separate groups of participants. Accordingly, all experiments also utilized a consistent set of analysis to evaluate the null hypothesis (i.e., high = low) against the alternative hypothesis (i.e., high ≠ low). Specifically, in each group of participants, we conducted two paired t-tests contrasting high versus low metacontrol states assessing whether the manipulation (a) achieves the intended shifts in one dimension and (b) causes a trade-off in the other dimension. In other words, each experiment allows for a test of flexibility trading off with stability and, independently, a test of stability trading off with flexibility. Supporting a seesaw relationship between flexibility and stability requires both tests being upheld in both groups of participants. Finding this pattern in one group would suggest that the trade-off is “asymmetrical” (and the seesaw metaphor is not sufficient to describe the flexibility-stability relationship).

In addition to this very particular pattern of finding supportive of the flexibility-stability trade-off hypothesis, there are many other possible outcomes. Two of these would serve as a starting point to support the DDF. First, if the first test (evaluating whether the manipulation achieves the intended shifts in one dimension) is in favor of the alternative hypothesis (high >, or < low), while the second test (evaluating the trade-off) is in favor of the null hypothesis (high = low) in only one group of participants, it would indicate a single dissociation, where one dimension can be modulated without creating a trade-off. Second, if this pattern is consistent in both flexibility and stability groups, it would suggest a double dissociation, indicating that the two metacontrol dimensions can indeed vary independently without affecting each other. In summary, through these novel manipulations, our goal is to provide empirical evidence describing the relationship between the flexibility and stability of task-set configuration at the list level.

Experiment 1 was similar to Geddert & Egner (2022) except for two aspects. First, the probabilities of switches or incongruent trials in our study were not biased. However, participants were given false instructions, asking them to prepare for frequent switches or incongruent trials in some blocks and rare ones in others. This manipulation was grounded in recent studies revealing that top-down expectations induced by false instructions are capable of triggering adjustments of flexibility (Kang & Yu-Chin, 2024; Liu & Yeung, 2020) and stability (Bugg et al., 2015; Desender, 2018; Entel et al., 2014) similar to the bottom-up adjustments triggered by real experiences of biased switch probabilities or proportion congruence. To illustrate, Entel et al. (2014) divided participants into two groups, both instructed to name the ink color in a color-word Stroop paradigm, with one group informed that most stimuli would be congruent and the other that most would be incongruent. In the block with a 50% proportion, participants expecting mostly incongruent trials exhibited diminished congruency effects compared to those anticipating mostly congruent trials from the experiment’s beginning. Similarly, Liu & Yeung (2020) found smaller costs of switching (in error rates) in lists where participants expected frequent switches compared to lists where they expected rare switches, despite both lists containing 50% switches. These findings suggest that metacontrol states can be instantiated merely by expectation or intention. Building on these findings, our goal here was to investigate whether the false instruction would upregulate one metacontrol dimension at the expense of downregulating the other dimension. As the second difference from Geddert and Egner’s (2022) study, each participant in our study was only assigned to either up- or down-regulate their flexibility or stability (not both). Our design allowed us to further test whether there was any asymmetry in the relationship to independently test the trade-off hypothesis in each group of participants. This approach also avoided concerns that carryover effects from one condition might hide the trade-off in another condition.

We report how we determined our sample size, all data exclusions (if any), all manipulations, and all measures in the study, and the study follows JARS (Appelbaum, et al., 2018). Data was analyzed using Python 3.8.10. Data reported in this article are available at https://osf.io/z2e53/. ChatGPT-3.5 has been employed to ensure that the texts are grammatically correct and flow smoothly, with instructions such as “check grammar and smooth” provided to the chatbot.

One hundred and forty-six undergraduates (68 female, 75 male, M_age = 19.01, SD_age = 1.32) provided consent to participate in the study in exchange for course credits, following procedures approved by the Purdue University Institutional Review Board. The final sample analyzed and reported below included 138 participants (68 in the flexibility group and 70 in the stability group) after excluding participants due to their overall accuracy lower than 80% (n = 8) or falling outside of the group mean ± 2.5 SD (n = 0) according to the preregistration procedure. This final sample met the minimum target sample size to provide over 95% power for the present design with an alpha set to .05, as determined using η_p² = .20 (Liu & Yeung, 2020) in a simulation-based power analysis. The preregistration protocol can be found at: https://aspredicted.org/HHL_2F5⁴.

The experiment was run in-person on a 22-inch Dell Flat Panel Monitor using PsychoPy version 2023.1.2 (Peirce et al., 2019). Stimuli consisted of 16 images of human-made objects drawn from Moreno-Martínez & Montoro (2012). A separate set of 8 images was used exclusively for practice blocks. All images could be categorized based on “size” (larger vs. smaller than a shoebox) and “material” (primarily metal vs. nonmetal); the stimuli were bivalent with regard to these categorization tasks. This bivalency, combined with orthogonal category-to-response-key mappings, resulted in 50% of stimuli requiring the same response regardless of which categorization rule was applied, i.e., congruent stimuli, or different responses according to the two rules, i.e., incongruent stimuli. A pilot experiment was conducted to ensure that all images could be easily categorized according to both the size and the material categorization rules. Images were presented with a stimuli visual angle of ~15.19° × 11.18°. The task cues were red or blue rectangular frames surrounding the images.

Participants alternated between a size categorization task (larger vs. smaller than a shoebox) and a material categorization task (primarily metal vs. nonmetal). Every participant completed two sequential lists of trials, with non-overlapping sets of stimuli in each list (8 unique stimuli per list). Because different stimuli were used in each list, bottom-up associations formed during one list should not influence performance in the other list. Both tasks were equally represented in both lists, and the switch probability was 50%. Likewise, the proportion of congruent and incongruent stimuli was 50% in each list. However, as the primary manipulation to separately shift the two metacontrol dimensions (flexibility, stability), participants were randomly assigned into one of the two groups. Participants in the flexibility group were misinformed about the switch probability by two sets of false instructions, one for each list. One set of false instructions warned participants that switches would be frequent in the upcoming list while the other set informed them that switches would be rare. The purpose of these false instructions was to induce either a high or a low flexibility state within each participant in the flexibility group. Likewise, participants in the stability group were misinformed about the proportion congruence of each list, with one set of instruction warning them about the frequent incongruent trials and the other about the rare incongruent trials in the upcoming list. These false instructions were presented every 32 trials. Moreover, the same information was presented in truncated form beneath the stimulus during each trial. Participants completed 384 trials in the main experiment, divided into 12 blocks of 32 trials. For each participant, list instructions only changed once at the midpoint of the experiment. The order of the two metacontrol states was counterbalanced across participants.

At the beginning of the experiment, participants completed a minimum of 160 practice trials to learn the assigned category to response-key mappings. Participants performing below 85% accuracy during the final 64 trials of practice were given additional practice in increments of 64 trials, until 85% accuracy was reached. During practice, participants’ attention was directed to task switches or incongruent stimuli, depending on their assigned dimension group. This ensured participants understood exactly what features of the experiment were indicated by the frequent/rare instructions. Finally, the last two blocks of practice exposed participants to true probabilities of their metacontrol state manipulation. Specifically, in the flexibility group, participants experienced one practice block (32 trials) with frequent switches (80%), then one block with rare switches (20%). Likewise, participants in the stability group experienced one block with frequent incongruent trials (80%) and then one with rare incongruent trials (20%). These last practice blocks were intended to increase participants’ belief in the later (false) instructions. Midway through the main experiment, participants completed one more practice block with the veridical probability matching the false probability for the second half of the experiment as a reminder. Given that different stimuli were used for practice vs. the main experiment, no bottom-up associations from practice were present during the main experiment. Practice blocks were not analyzed.

Both the practice and the main experimental trials followed the same trial progression. Each trial began with a fixation cross for 300 ms, followed by simultaneous onset of stimulus and task cue (a colored frame around the stimulus). The stimulus and task cue remained onscreen for 3000 ms or until a response was recorded. Responses were made using Q and P keys on a QWERTY keyboard. Following response, feedback was presented for 600 ms. Feedback could be “Correct!,” “incorrect,” “too slow,” or “wrong key,” depending on participants’ response. All response key mappings and frame color-to-task-mappings were counterbalanced across participants.

Before the main analysis, the data was cleaned according to the pre-registered subject-level and trial-level exclusion procedures. Specifically, participants performing below 80% accuracy overall were excluded. From the remaining sample, participants with an overall accuracy more than 2.5 standard deviations from the group mean were also excluded. For calculating response time means, we excluded the first trial in each block, error trials, trials with no response, trials immediately following an error, and trials with a response time more than 3 standard deviations from each condition’s mean.

To address our main research question regarding the relationship between flexibility and stability, we derived two dependent variables to index each separately: switch costs (SC) and congruency effects (CE). Switch costs are defined as the performance difference (response time and error rate) between task-switch and task-repeat trials. Similarly, congruency effects are defined as the performance difference between task-rule incongruent trials and congruent trials. We then assessed both dependent variables as a function of metacontrol dimensions (flexibility, stability) and metacontrol states (high, low). Specifically, we conducted two paired t-tests (high vs. low state), one with SC and one with CE, separately within each group⁵.

Starting with the flexibility group, the two tests were intended to test whether the flexibility manipulation (1) reduced SC in the high metacontrol state than in the low metacontrol (i.e., H₁: SC_low > SC_high), as intended, and (2) increased CE (i.e., H₁: CE_high > CE_low), as would be consistent with the trade-off hypothesis (H₁). Likewise, the two 1-tailed t-tests in the stability group probed the success of the stability manipulation upon congruency effects and then probed for a possible trade-off in switch costs. Given the strong directional prediction of the trade-off hypothesis, we opted to conduct directional t-tests. Because our manipulations were designed to assess the possibility of finding spurious differences between conditions (H₁) by chance, we adopted the frequentist inference framework when interpreting our results. Therefore, we reported one-tailed p-values, controlling for a Type I error rate of 5% in each of the t-test. This approach increases sensitivity in detecting successful manipulations and trade-off effects without introducing any bias against observing a trade-off effect. However, due to the importance of making claims about finding no difference between conditions (H₀) in light of the literature reviewed earlier, we provided an equivalent statistic in the form of Bayes factors (BF₀₁), using the tool provide by Francis & Jakicic (2023) ⁶. We also adopted a general interpretation rule that a BF₀₁ greater than 3 indicates substantial evidence for the null hypothesis (Rouder et al., 2009).

The overall mean error rate was 8.41% (SD = 4.53) and the overall mean response time was 1016 ms (SD = 172). On average, the ER calculation excluded 3.68% (SD = .70) of trials, and the mean RT estimation excluded 19.26% (SD = 7.92) trials. See Table 1  for descriptive statistics.

Beginning with the flexibility group, the first test examined whether the flexibility manipulation succeeded in reducing switch costs and it did, t(67) = 2.61, p = .006, BF₀₁ = .33, Cohen’s d = .316, revealing that switch costs were smaller when participants were instructed to expect frequent switches (M = 145 , SD = 106) than rare switches (M = 185 , SD = 133). The next test revealed that this did not come with an increase in congruency effects, t(67) = -.15, p = .439, BF₀₁ = 7.43, Cohen’s d = -.019. In the stability group, the manipulation was not successful and did not effectively reduce congruency effects, t(69) = .23, p = .408, BF₀₁ = 7.42, Cohen’s d = .028, nor increase switch costs, t(69) = -.39, p = .349, BF₀₁ = 7.08, Cohen’s d = -.047. See Figure 2  for a summary of the tested effects.

In the flexibility group, the flexibility manipulation did not reduce switch costs, t(67) = -.58, p = .282, BF₀₁ = 6.39, Cohen’s d = -.070, nor did it increase congruency effects, t(67) = .66, p = .257, BF₀₁ = 6.10, Cohen’s d = .080. Likewise, in the stability group, the stability manipulation neither reduced congruency effects, t(69) = .38, p = .352, BF₀₁ = 7.10, Cohen’s d = .046, nor increased switch costs, t(69) = -.10, p = .459, BF₀₁ = 7.58, Cohen’s d = -.012.

In Experiment 1, following prior studies, we employed false instructions to induce top-down expectations about the upcoming metacontrol demands in participants by misinforming the probability of upcoming task switches or incongruent trials within a block. Our findings regarding switch costs replicate these prior studies. Notably, while Liu and Yeung (2020) observed a significant modulation of switch costs in error rates, we observed it in response times. Unlike the flexibility false instructions, the stability false instructions did not reduce congruency effects in our stability group, making the lack of increased switch costs in this group inconclusive for adjudicating the flexibility-stability trade-off. This seems to contrast with previous studies mentioned earlier, except that the cited studies (Bugg et al., 2015; Desender, 2018; Entel et al., 2014) did not employ a cued task switching paradigm but rather a Stroop paradigm, where proportion congruency effects have often been demonstrated. We suspect that the lack of manipulation success in our stability group may not be due to a failure to induce shifts through false instructions but rather to relatively smaller congruency effects in our paradigm. For instance, when comparing our results to Geddert & Egner’s (2022) Experiment 1 and Experiment 3, where they found success in Experiment 1 but not in Experiment 3, we notice that their Experiment 3 had a smaller overall congruency effect than Experiment 1. In other words, future studies should try to avoid potential floor effects by increasing the baseline congruency effects in such switching paradigms. Finally, our results differ from those of Geddert and Egner (2022), particularly their Experiment 1, which was most similar in design to ours. Despite the design similarities, several notable differences may have caused the difference in results, including the change from actual to only believed probability manipulations, the shift from fully within-subjects to partially between-subjects, and the difference in samples used (in-person undergraduates vs. online M-Turkers). Each difference is worthy of potential follow-up to replicate Geddert and Egner’s (2022) results. In summary, we observed a single dissociation in the flexibility group: reduced switch costs without an increase in congruency effects. This challenges the conventional trade-off between flexibility and stability, suggesting that one aspect of metacontrol can vary without impacting the other. In the next experiment, we turned to another approach to shift flexibility and stability.

Metacontrol states can persist for a while after being established (Fischer & Hommel, 2012b; Memelink & Hommel, 2006; Surrey et al., 2017). Thus, our Experiment 2 was based on the idea that one task can be used to “prime” a particular metacontrol state, while an unrelated “probe” task can be used to measure the resultant metacontrol state. To do so, we selected two well-known creativity tasks: the Alternative Uses Task (Guilford, 1967) and the Remote Associates Task (Mednick, 1962) to shift flexibility and stability, respectively. Previous research has shown that the Alternative Uses Task (AUT) promotes a “divergent” thinking style by encouraging participants to broaden their thinking and explore various paths to generate novel uses for common objects. This thinking style has been argued to bear similarity with cognitive flexibility, prompting us to utilize it as a priming task to shift flexibility. On the other hand, the Remote Associates Task (RAT) is thought to promote a “convergent” thinking style by encouraging participants to narrow their thinking until they converged upon finding a common word that connects three seemingly unrelated words. This thinking style can be considered analogous to cognitive stability (Mekern et al., 2019; Nijstad et al., 2010), prompting us to utilize it as a priming task to shift stability.

Evidence also exists demonstrating the feasibility of using the AUT and the RAT as primes to assess metacontrol states in separate tasks such as those that are relatively well-understood in terms of their underlying attention and cognitive control processes. For instance, (Akbari Chermahini, 2011) showed that with the AUT as the priming task, participants exhibited relaxation of top-down control (becoming more flexibility), as evidenced by reduced attentional blinks (Raymond et al., 1992). In contrast, participants’ performance benefited from having the RAT as the priming task in tasks requiring greater top-down control, such as the color-word Stroop task (Stroop, 1935), the global-local task (Navon, 1977), and the Simon tasks (Simon, 1969). (Fischer & Hommel, 2012a) then further extended this metacontrol priming approach in a dual-task paradigm and found that, relative to the AUT-group, the RAT-group indeed showed enhanced stability. Specifically, in this dual-task paradigm, one stimulus (T1) appears on the screen, prompting a categorization response. Before the response is made, a second stimulus (T2) appears, requiring another response immediately after T1. Typically, the shorter the time between the appearance of T1 and T2, the longer it takes to respond to T2 (Pashler, 1994; Smith, 1967; Welford, 1952). Therefore, a reduction in this delay indicates that T1 and T2 are being processed more simultaneously, suggesting increased cognitive flexibility (Lien & Proctor, 2002; Logan & Gordon, 2001). Another finding is ‘crosstalk interference,’ where T1 performance is hindered if T2 requires an opposite response (Hommel, 1998). Similarly, reductions in crosstalk interference indicate that T1 is better shielded from T2 intrusion, suggesting increased stability.

Critically, before this dual-task paradigm, one group of participants was primed for flexibility using the AUT, while another group was primed for stability using the RAT. The authors hypothesized that AUT-primed participants would show a reduction in the delay to respond to T2 but increased crosstalk interference. Conversely, RAT-primed participants were expected to show decreased crosstalk interference on T1 but an increased delay in responding to T2. One of these predictions was indeed observed: Metacontrol priming with the RAT reduced crosstalk, indicating that RAT-primed participants exhibited greater stability compared to the AUT group. Together, the work of Akbari Chermahini (2011) and Fischer & Hommel (2012a) provide us some confidence that the AUT and the RAT promote distinct thinking styles, potentially fostering greater flexibility and stability, respectively. We now seek to extend this metacontrol priming procedure to the task switching paradigm.

Same as Experiment 1.

Two hundred and twenty-three undergraduates (110 female, 111 male, mean age = 18.81, SD = 1.20) participated in the study for course credits, following procedures approved by the Purdue University Institutional Review Board. The final sample reported below comprised 208 participants (105 in the flexibility group; 103 in the stability group), after excluding participants due to their overall accuracy lower than 80% (n = 15) or falling outside of the group mean ± 2.5 SD (n = 0) according to the preregistration procedure. This final sample met the minimum target sample size to provide over 95% power for the present design with an alpha set to .05, as determined using η_p² = .09 (Fischer & Hommel, 2012a) in a simulation-based power analysis. The preregistration protocol can be found at: https://aspredicted.org/SQ9_R6N.

Hardware and software used in the experiment were the same as Experiment 1. Stimuli for cued task switching were also the same. Stimuli for the RAT were taken from Bowden & Jung-Beeman (2003) and consisted of three words separated by vertical pipe symbols (e.g., cottage | Swiss | cake). An editable text box below allowed for participants to type responses (e.g., cheese), and a clickable “submit” button ended the trial. Stimuli for the AUT were words selected by the authors which did not overlap with items pictured in task switching stimuli. These words were piloted prior to data collection to ensure their value as AUT stimuli. Stimuli for the low metacontrol condition’s typing task consisted of 40 words, separated by commas. For all three conditions, the stimuli were presented in the top one-third of the screen in­ Arial font, immediately below instructions for the task.

As in the previous experiments, participants alternated between a size categorization task and a material categorization task with nonoverlapping stimuli in two lists and the order of the list was counterbalanced across participants. During the high metacontrol state condition, in the flexibility group, every 32 cued task switching trials were preceded by a 1-minute AUT trial, while in the stability group, every 32 switch trials were preceded by a 1-minute RAT trial. This design incorporated frequent re-exposure to AUT and RAT to ensure metacontrol priming did not dissipate easily. During the low metacontrol state condition⁷, participants in both groups completed a simple typing task every 32 trials: Participants were asked to type up to 40 words as they appeared on screen for 1 minute.

The analysis followed the same procedure as in Experiment 1.

The overall mean error rate was 7.25% (SD = 3.87) and the overall mean response time was 970 ms (SD = 159). On average, the ER calculation excluded 3.72% (SD = 1.05) of trials, and the mean RT estimation excluded 17.39% (SD = 6.97) trials. See Table 2  for descriptive statistics for all experimental conditions.

Beginning with the flexibility group, the AUT failed to prime flexibility and reduce switch costs, t(104) = -.28, p = .937, BF₀₁ = 8.90, Cohen’s d = -.027. However, the AUT increased congruency effects, with larger congruency effects in the high metacontrol condition (M =146, SD = 119) than in the low metacontrol condition (M = 124, SD = 105), t(104) = 1.75, p = .042, BF₀₁ = 2.12, Cohen’s d = .171. See Figure 2 . In the stability group, the RAT succeeded in reducing congruency effects, t(102) = 2.14, p = .018, BF₀₁ = 1.03, Cohen’s d = .210, with smaller congruency effects in high metacontrol condition (M = 137, SD = 115) than in the low metacontrol condition (M = 163, SD = 137), but failed to increase switch costs, t(102) = .66, p = .256, BF₀₁ = 7.41, Cohen’s d = .065. See Figure 2  for a summary of the tested effects.

In the flexibility group, the AUT did not reduce switch costs, t(104) = .47, p = .321, BF₀₁ = 8.31, Cohen’s d = .046, nor did it increase congruency effects, t(104) = 1.22, p = .113, BF₀₁ = 4.50, Cohen’s d = .119. Likewise, in the stability group, the RAT did not reduce congruency effects, t(102) = .60, p = .275, BF₀₁ = 7.69, Cohen’s d = .059, nor increase switch costs, t(102) = 1.37, p = .086, BF₀₁ = 3.70, Cohen’s d = .135.

Experiment 2 evaluated the relationship between flexibility and stability using metacontrol priming. We observed a single dissociation similar to Experiment 1, except that it occurred here in the stability group: reduced congruency effects without an increase in switch costs. In addition, the AUT also resulted in an increase in congruency effects in the flexibility group, indicating an influence of the prime on stability. Yet, this effect was selective, as there was no increase in flexibility within the same group of participants. This pattern of results appears to look like a single dissociation, except that it was caused by the “wrong manipulation” (i.e., should have been a stability priming task). Because of this, we recommend caution in interpreting this result as evidence in favor of flexibility-stability independence.

This unexpected finding underscores two key points: (1) It may be difficult to predict in advance whether a particular priming task will primarily impact flexibility or stability, and intuitions or even examples from past literature may not always hold true. (2) There is a need for clearer conceptualizations and operationalizations of flexibility and stability. Specifically, if flexibility had been operationalized as “increased congruency effects” instead of “decreased switch costs” initially, the results would have been interpreted as a single dissociation. Both of these perspectives echo cautions made recently in Nack & Yu-Chin (2023) about the increasingly complex relationship between construct and operationalization in a dual-dimension framework. In sum, Experiment 2 revealed a single dissociation in the stability group but still fell short of doubly dissociating flexibility from stability.

To complement the previous reporting, we conducted an analysis of mean response times and error rates using a 2 (list: high, low) x 2 (transition: switch, repeat) x 2 (congruency: congruent, incongruent) ANOVA, separately for the flexibility and stability groups. Descriptive statistics can be found in Table 4  and Table 6 . The ANOVA findings, summarized in Table 3  and Table 5 , aligned with our earlier reporting. Specifically, for Experiment 1, the significant list x transition interaction and the absence of a significant list x congruency interaction indicated successful manipulation without trade-off in the flexibility group. Similarly, in Experiment 2, the significant list x congruency interaction, coupled with the lack of a significant list x transition interaction, suggested successful manipulation without trade-off in the stability group. It is important to note that each ANOVA also revealed a significant transition x congruency interaction. While Geddert and Egner (2024) interpreted this as evidence of a flexibility-stability trade-off, we contend that this interaction reflects a trial-level trade-off (as also noted by Geddert and Egner). Our investigation remained focused on the list level, consistent with our initial goal.

The present study investigated the relationship between cognitive flexibility and stability by manipulating one dimension at a time while measuring the changes in the other dimension. Given that the manipulation worked as we expected, the unidimensional framework predicted a trade-off relationship, whereas the dual-dimensional framework predicted independence (Egner, 2023; Geddert & Egner, 2022, 2024; Nack & Yu-Chin, 2023). We employed a between-subjects design, hoping to achieve a double dissociation: Shifts in flexibility are observed without shifts in stability in one group of participants, while shifts in stability are observed without shifts in flexibility in the other group. However, no such double dissociations were revealed. Specifically, Experiment 1 explored the impact of top-down expectations about upcoming metacontrol demand, drawing from prior evidence demonstrating their effectiveness in instantiating metacontrol states (Entel et al., 2014; Liu & Yeung, 2020). This manipulation revealed a single dissociation: Flexibility was shifted without affecting stability. Experiment 2, employing metacontrol priming, revealed another single dissociation: Stability was shifted without affecting flexibility. Despite identifying two single dissociations from two different types of manipulations, our study ultimately fell short of cleanly dissociating flexibility from stability.

Intriguingly, in Experiment 2, we employed metacontrol priming and observed the following result in the flexibility group: stability was shifted independently of flexibility. This data pattern appears to represent a single dissociation in favor of the flexibility-stability trade-off hypothesis. Specifically, due to the necessity of performing the AUT, participants broadened their attentional focus, which necessarily increased their flexibility. Consequently, this enhanced flexibility led to an increased congruency effect, interpreted as decreased stability. However, explaining why switch costs did not decrease in this group of participants remains challenging. A possible explanation is that the priming task functioned as a third task for the participants, which may have reduced the switch costs in the cued task switching portion. Specifically, we observed that the mean switch costs in Experiment 2 were numerically smaller than those in Experiments 1 (~132 ms vs. ~159 ms). This reduction in switch costs might have created a floor effect, minimizing our ability to detect changes. Future studies should aim to improve methods to ensure manipulation success while measuring the outcome as operationalized at the outset of the study.

We hope this set of experiments helps to explain the challenges in detecting a clear double dissociation, but also explains instances where an expected trade-off is not easily observed. This insight dovetails with recent works which also reveal the importance of individual differences in high-level cognitive processes such as flexibility and stability (Held et al., 2024; Reineberg et al., 2018). When combining these findings with the present work, the possibility emerges that each individual might have a unique parameter governing the degree to which they trade off flexibility for stability. However, there is as yet little to no theory in the literature to describe what this parameter might be. We also acknowledge that, as noted by Dreisbach and colleagues in a commentary (Dreisbach et al., 2024), the relationship between flexibility and stability is influenced by the underlying mechanisms and the ways in which these concepts are operationalized. In this context, we do not aim to make claims about all possible operationalizations of flexibility and stability or the specific mechanisms that drive their trade-off or independence. Instead, our goal here is to present a rigorous assessment of the frequently asserted flexibility-stability trade-off of task-set configuration at the list level. Furthermore, we believe that the unidimensional framework is a good and parsimonious choice. It is reasonable to adopt this framework for theorizing and generating testable hypotheses by accepting the flexibility-stability trade-off assumption. However, unless the trade-off (or lack thereof) is explicitly the focus of a particular study (as in our study and in Geddert & Egner, 2022, 2024), or when flexibility and stability are measured separately, researchers should exercise caution when making claims regarding the trade-off per se and should limit their claims to the underlying mechanisms that modulate a specific mode of control.

The limited success of these manipulations compared to the manipulation used by Geddert and Egner (2022) might be explainable via the Metacontrol State Model (Hommel, 2015), a commonly referenced framework conceptualizing the relationship between flexibility and stability when there are two response alternatives available. Flexibility and stability are governed by two model parameters—the degree to which a current goal causes top-down bias for one of the response alternatives (goal activation parameter), and the degree to which the response alternatives inhibit one another (mutual inhibition parameter). Beginning with the manipulation set used by Geddert and Egner (2022), switch probability and proportion congruency effects are often conceptualized in terms of the Metacontrol State Model (Hommel, 2015), particularly the mutual inhibition parameter: When task switches are frequent, mutual inhibition is relaxed. This can also be called “concurrent activation” of task-sets (Dreisbach & Fröber, 2019). This has been thought be the primary means by which switch probability manipulations modulate switch costs: The cognitive system responds to high demands for switching by keeping both task representations active, due to the likelihood that either one will need to be performed again soon. Recently, (Nack & Yu-Chin, 2024) presented several lines of direct evidence that switch probability manipulations impact switch costs via concurrent activation, or, in the language of the Metacontrol State Model, by relaxing mutual inhibition. In sum, the manipulations used by Geddert and Egner (2022) have been linked to the mutual inhibition parameter of the Metacontrol State Model.

In contrast, our manipulations might be more closely tied to the goal activation parameter than to the mutual inhibition parameter. In Experiment 1, top-down goal activation of the correct representation may be especially suited to instantiate the top-down effects of false expectations regarding necessary metacontrol states. Likewise, switch conditioning effects⁸ can be described in terms of the goal activation parameter: To maximize rewards, participants learn to relax this top-down control for the current task. Braem (2017) employed a similar explanation for his findings: Participants were conditioned by rewards to “break task control” after each trial more effectively, allowing for the other task to be selected more rapidly if needed. Finally, the past literature on metacontrol priming was directly inspired by the Metacontrol State Model: The authors in both papers describe the impact of the AUT on relaxing top-down bias, while the RAT was expected to strengthen this parameter (Akbari Chermahini, 2011; Fischer & Hommel, 2012a).

Combining our findings with those of Geddert and Egner (2022), the possibility emerges that manipulations based on the mutual inhibition parameter have a larger impact on cued task switching performance than manipulations based on top-down goal activation. This speculation must be limited to cued task switching, as the manipulations that didn’t work well here do work in other cognitive control paradigms such as voluntary task switching (Bream, 2017), global-local tasks, attentional-blink paradigms (Akbari Chermahini, 2011). However, if supported by future research, this currently speculative difference is of theoretical interest: While creating the Metacontrol State Model, Hommel (2015) questioned whether the contributions of the two model parameters could be separated, given that they both produce largely indistinguishable outcomes in terms of behavior. The present findings might offer an additional (admittedly preliminary) piece to solving this puzzle.

The current study has several limitations, three of which we will now highlight in detail. First, the manipulations yielded limited success. While top-down expectation and priming are all well-known manipulations from the arsenal of techniques in cognitive psychology literature, it’s conceivable that employing more nuanced measures beyond traditional behavioral outputs like response time and error rate could offer greater insights into the effectiveness of the manipulation. For instance, in Kang & Yu-Chin (2024)’s study, the false instruction had an effect on event-related potentials measured with electroencephalography but no detectable effect in behavior. Second, the task switching paradigm chosen here provides a very narrow operationalization of flexibility (switch costs) and stability (congruency effect). Thus, the possibility remains that the present results were idiosyncratic to the measurements used in the present experiment. Other paradigms, with some adaptation, might offer simultaneous measurement but a different operationalization of flexibility/stability (Dreisbach & Goschke, 2004; Sali & Key, 2021). It is also possible that tasks that measure flexibility/stability over larger time intervals (as opposed to our trial length of ~3 seconds) might demonstrate a much more robust flexibility/stability trade-off (or independence). One example would be to use performance in the priming task (e.g., AUT/RAT) as dependent rather than independent variables as in our Experiment 2.

The current dataset cannot be used to determine what distinguishes individuals who exhibit a flexibility-stability trade-off from those who do not. Future research should aim to unravel the underlying factors, perhaps including working memory capacity, motivation, and strategy choice, that could predict which individuals exhibit a flexibility-stability trade-off and which do not. By conducting in-depth investigations into the cognitive profiles of individuals with the trade-off trait versus those who do not, researchers could uncover the cognitive mechanisms that drive the variability in the relationships between these constructs. Relatedly, we acknowledge that our between-subjects dissociation design has its limitations. By not creating a situation in which both stability and flexibility are encouraged simultaneously, we may not be effectively testing their independence. As noted by Geddert & Egner (2022, 2024), the contextual demands placed on stability and flexibility likely influence whether a trade-off data pattern is observed. Specifically, based on the “cost-of-control” assumption proposed by Shenhav and colleagues (Shenhav et al., 2013), when only stability is promoted or incentivized, participants tend to focus their efforts on maintaining stability rather than being flexible (Geddert & Egner, 2022, 2024). This can lead to the emergence of a trade-off pattern that arises not from structural reasons but from effort-saving strategies.

Lastly, as emphasized earlier in the introduction, we have provided evidence through one approach—among many possible ways—to examine the relationship between one conceptualization of flexibility and stability. Consequently, our claims regarding our specific operationalizations of flexibility and stability are limited. Additionally, we cannot address the specific mechanisms driving their independence, as this was not investigated in our study. We recognize that oversimplifying a theoretical issue that is inherently multifaceted can pose significant risks for both understanding and application. When concepts are reduced to a single operationalization, their richness may be lost. Furthermore, without careful inductive reasoning, researchers risk drawing conclusions that do not accurately reflect the complexities of the phenomena under study, which can lead to misguided interpretations and applications in practice. Therefore, it is imperative to approach these theoretical issues with a nuanced perspective that acknowledges their complexity and facilitates a more robust exploration of their implications.

This study examined the relationship between cognitive flexibility and stability through two experiments, revealing patterns of independence at the group level. However, we suspect that individual differences may play a significant role in determining the interplay between these metacontrol states. Our findings emphasize the complexity of cognitive control dynamics and highlight the necessity for tailored approaches to enhance our understanding of cognitive functioning across diverse populations.

The authors declare no conflicts of interest.

Data reported in this article are available at https://osf.io/z2e53/..

Chiu Yu-Chin: Writing – review & editing (Lead), Conceptualization (Equal), Formal Analysis (Supporting), Writing – original draft (Supporting).

Corey A. Nack: Conceptualization (Lead), Data curation (Lead), Project administration (Lead), Writing – original draft (Lead), Formal Analysis (Lead).