# Impact of Motor Error Processing on Performance on a Working Memory Task: Effect of Modulating Cognitive Load in High and Low Span Groups

Emilien Brochet, Pierre-Vincent Paubel, Céline Lemercier

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Emilien Brochet, Pierre-Vincent Paubel, Céline Lemercier. Impact of Motor Error Processing on Performance on a Working Memory Task: Effect of Modulating Cognitive Load in High and Low Span Groups. 2024. hal-04795172

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# Impact of motor error processing on performance on a Working Memory task: Effect of modulating cognitive load in High and Low Span groups

Emilien Brochet¹,², Pierre-Vincent Paubel¹,³, and Céline Lemercier¹,²

¹Université Toulouse Jean Jaurès

²Laboratoire Cognition Langues Langage Ergonomie (CLLE) UMR 5263

³CNRS

## Author Note

Emilien Brochet ID http://orcid.org/0000-0001-6395-2728

Pierre-Vincent Paubel ID http://orcid.org/0000-0002-2376-4674

Céline Lemercier ID http://orcid.org/0000-0002-2832-8724

Data from this study can be accessed at https://osf.io/u6pyk/ The author declare there is no conflict of interest in this study

Author roles were classified using the Contributor Role Taxonomy (CRediT; https://credit.niso.org/) as follows: *Emilien Brochet*: conceptualization, data curation, formal analysis, investigation, resources, software (lead), visualization, and writing – original draft. *Pierre-Vincent Paubel*: software (supporting). *Céline Lemercier*: supervision and writing – original draft

Correspondence concerning this article should be addressed to Emilien Brochet, Université Toulouse Jean Jaurès, Email: emilienbrochet@gmail.com
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3 **Impact of motor error processing on performance on a Working Memory task: Effect of modulating cognitive load in High and Low Span groups**

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## Introduction

The study of post-error phenomena has not stopped since the 1960s (Danielmeier & Ullsperger, 2011; Dudschig & Jentzsch, 2009; Dutilh et al., 2012; Laming, 1979; Notebaert et al., 2009; Pfister & Foerster, 2021) and Rabbitt's article (Rabbitt, 1966). From the beginning, studies have been based on the observation of post-error behavioral phenomena: Lengthening of response times (RTs) and subsequent modification of accuracy. These behavioral adjustments, known as Post-Error Adjustments (PEA) (Danielmeier & Ullsperger, 2011), are a way to infer underlying cognitive processes. PEA has been linked to cognitive control and working memory implementation (Regev & Meiran, 2014). PEA could be observed in different types of conflict tasks such as the flanker task (Debener et al., 2005), Stroop task (Gehring & Fensik, 2001), and Simon task (King et al., 2010). Using these types of tasks in a dual-task procedure intertwined with a working memory span task, J. Wessel and Jiang (2021a) has collected data showing the impact of a motor error on working memory maintenance. With this study, error is experimentally linked to higher-order cognitive functions (working memory, cognitive control, attention).

To talk about error Generic Error Modelling System (GEMS), developed by Reason (Reason, 1990), provides a solid foundation. GEMS classifies errors according to levels of processing achieved into three categories: skill-based errors, rule-based errors, and knowledge-based errors. In this work, we are particularly interested in the first level, called 'skill-based' (see Skill-Rule-Knowledge (Rasmussen, 1983), from which Reason's model is derived). This level includes errors committed by lack of attention or by habit. These errors are linked to a lack of attention to the relevant aspects of information to be processed. They can also be caused by irrelevant aspects of the task or stimulus, as in the case of a conflict task. In this case, attention is
diverted from the goals at hand. Cognitive system monitors these errors (Botvinick et al., 2001) and allows them to be detected and corrective actions to be taken if necessary, by engaging cognitive control.

Cognitive control is defined as a set of three factors (inhibiting a prepotent response, updating working memory and shifting between mental sets (Miyake et al., 2000)) with unique variance and correlations between each of them (Friedman & Robbins, 2022). Cognitive control occurs as soon as an error is detected Shalgi et al. (2009) to monitor this error (Botvinick et al., 2004). Unsworth et al. (2022) show that *High Span* individuals (with better working memory capacities: WMC) are less likely to experience attentional fluctuations during the task. These individuals have a better ability to manage error (*error monitoring*). *Low Span* individuals, on the other hand, tend to make more unperceived errors (*error blindness* (Buzzell et al., 2017)) due to attentional fluctuations (*mind wandering* (Christoff et al., 2016)). Cognitive control then plays a role in the ability to manage perceived errors and is related to attention. To detect an error, individuals must remain in a sufficient alert state, expensive in terms of attentional resources. Error awareness is negatively correlated with attentional deficits and positively correlated with working memory capacities (WMC).

According to Botvinick et al. (2001), cognitive system assesses the need for cognitive control by detecting the presence of conflict in information processing. In case of an error, this system switches on (Botvinick et al., 2004) aiming to resolve the conflict generated by difference between formulated response and expected response. Once conflict has been resolved, individual can refocus on the task and mobilize all cognitive and attentional resources to pursue their goals. In fact, error monitoring and its effect observed through post error behavioral adjustments is informative of underlying attentional and cognitive processes. It is informative of lapses of
52 attention (Unsworth et al., 2022) and cognitive control (Regev & Meiran, 2014). According to 53 Engle and Kane (2003), there is a strong link between WMC, attentional control and conflict 54 management system. Improved WMC allow for better conflict detection, and more effective 55 implementation of attentional control. Individuals with better WMC (and thus better attentional 56 control) will be more effective at processing an error Unsworth et al. (2022).

57 "Everyone knows what attention is. It is the taking possession by the mind, in clear and 58 vivid form, of one out of what seem several simultaneously possible objects or trains of thought." 59 (James, 1890). Attention is crucial in processing information. As Egeth and Kahneman (1975) 60 and Wickens (2008) models postulate, reservoirs of attention contain a limited amount of 61 resources necessary for information processing. Selection of relevant information to be processed 62 have to be made to achieve individual's goals (Niedermeyer, 1994). Selectivity defines two 63 distinct functions of attention: divided attention, implying that attention is to be considered as a 64 reserve of processing resources, and selective attention, implying that attention is an instance of 65 conscious control of processing. The idea was first put forward of an early selection at the 66 perceptual level (BROADBENT, 1958; TREISMAN, 1964) with the hypothesis that perception 67 has limited capacities. Then, hypothesis of a later selection (Deutsch & Deutsch, 1963) which 68 sees perception as an automatic process was formulated. Lavie and Dalton (2014) finally 69 proposes a hybrid model that allows for both types of selection.

70 To achieve information selection, attention has to be controled. Attentional control refers 71 to the ability to focus and maintain attentional resources on a specific task/goal, discarding 72 information (e.g., from thoughts or external stimuli) that is not relevant to that goal. Attentional 73 resources are oriented endogenously (a.k.a top-down), according to the individual's goals and 74 objectives, by attentional control (a.k.a executive attention). These resources are then directed in
a controlled and voluntary manner to the relevant aspects of the environment and/or internal
cognitive processes for the achievement of these goals. Prefrontal cortex (particularly the
dorsolateral area) supports the active maintenance of the goals in progress in the task and has
been linked to the WMC of individuals (Kane & Engle, 2002). To understand determinants that
affect the process of selecting relevant information, Lavie proposed a theory that measures the
impact of two types of load, perceptual and cognitive loads.

Lavie & Tsal (Lavie & Tsal, 1994) propose perceptual load theory (see also (Lavie & Dalton, 2014) and (Lavie, 2010)). This theory models selective attention and resolves the debate about the location of attentional filtering. According to this theory, primary determinant of locus of attentional filtering is perceptual load. In their protocol, Forster and Lavie (2007) propose participants to detect the presence of a target letter among two pre-specified possibilities (e.g. X or N) in a circle composed of items. Next to this circle, a distractor letter is displayed that corresponds either to the target letter (congruent condition, e.g., target “X” and distractor letter “X”) or to the other alternative (incongruent condition, e.g., target “X” and distractor letter “N”).

The effect of the distractor letter is measured by difference in response time to target between congruent and incongruent conditions. On incongruent trials, where distractor letter is alternative to the target, response times increase. In the low-load condition, circle is composed of small “o”s and target letter, making target letter stand out within the circle (this is referred to as the “pop out” effect (Posner, 1980)). In the high load condition, other letters compose the circle with target letter. The authors observe that in high perceptual load condition (circle composed of other letters) the effect of the distractor letter on response time is almost entirely cancelled. A higher perceptual load decreases or even cancels effects of distractors, in this case an early attentional filtering limits the perception of irrelevant elements.
When perceptual load is lower, then individuals' residual processing abilities may be captured by irrelevant distractor stimuli. This implies that later selection processes must be put in place to prevent these distractors from gaining control over behavior (Lavie, 2010). Lavie and Dalton (2014) proposed a dual-task protocol to measure effect of cognitive load on distractor processing. A memory task in which a digit span to be memorized is followed by a selective attention task before participants have to recognize digit span presented at baseline. For selective attention task, participants are instructed to identify a central target letter (z or x) presented in conjunction with a peripheral distractor letter that is either congruent, incongruent, or neutral. In this set-up, the perceptual load is therefore low, consisting only of a target letter and a distractor letter. The authors vary the number of digits presented in digit span task (from 1 to 6) in order to observe effect of cognitive load on distractor processing. A higher cognitive load then increases the effect of distractor on response time, an opposite effect to that of higher perceptual load.

If the presentation of the stimulus generates a high level of perceptual load, attentional filtering will be early and automatic, and the individual's perceptual limits will be reached. Distractors that are not relevant to the task in hand may not even be perceived. If this level allows for all perceived information (both relevant and irrelevant) to be processed without overload, filtering will occur at the higher (cognitive) level of processing. Depending on where filtering takes place, consequences in terms of behavior are different. A high perceptual load, generating early filtering, will have consequence of minimizing individual's distractibility to irrelevant stimuli, as these will have been filtered, and therefore not perceived. On the other hand, a low perceptual load leads to an increase in distractibility to irrelevant stimuli. Moreover, a high cognitive load further increases effect of distractors. Perceptual and cognitive load have
opposite effects on the processing of distractors such as task-irrelevant stimuli. In our study we will focus more on cognitive load effect on attentional processes.

Differences in WMC observed between groups of High and Low Span participants are due to attentional control. To investigate the methods by which different participant groups effectively select pertinent information while filtering out irrelevant data, Kane & Engle (Kane & Engle, 2000) evaluate the performance of two participant cohorts distinguished by their WMC (High Span vs Low Span). A list of words is proposed. During encoding of this list, participants have to tap a simple sequence with their finger following a controlled rhythm. Following this encoding phase, an interfering task (Trail Making Test in oral version (Armitage, 1946)) is proposed for 16 seconds in order to prevent participants from repeating the list. Participants are then asked to recall the list. Low Spans perform at the same level as the High Spans on first trial. On subsequent trials, however, High Span participants perform better than Low Span participants. Proposed reason is that proactive inter-trial interference is inhibited by High Span participants. They have a better attentional control allowing them to better counter effects of interference. Recall will therefore be more effective in this group when interference effects are to be inhibited.

The authors then propose to increase complexity of the sequence participants type with their finger following the encoding of the word list. Overall cognitive cost of task then increases, making procedure more similar to a dual task. In this case, authors no longer observe greater effect of proactive interference in Low Span compared to High Span. They conclude that High Span participants are no longer able to counter effects of proactive interference in situations of higher cognitive load. Attentional control is a voluntary and resource-intensive process. When cognitive load increases, conflict resolution (proactive interference) is impaired in High Span
143 participants because they are no longer able to deploy sufficient attentional resources. Recall of
144 the word list is then impacted. In Low Span, attentional control is not used to counter effects of
145 proactive interference and induces both a stronger effect of this interference (than in High Span)
146 and absence of difference between load conditions.

147 To test behavioral response to an error, conflict tasks (e.g. flanker task, Simon task,
148 Stroop task) are commonly used in laboratory (Derrfuss et al., 2021; Schroder et al., 2019;
149 Steinhauser et al., 2017). Conflict tasks are also frequently used to show attentional control
150 (Bastian et al., 2020) implementation. This type of task requires participants to choose between
151 several alternatives as quickly as possible. The difficulty of this type of task lies in the
152 manipulation of relevant and irrelevant dimensions of the stimulus. Congruence is similarity
153 between information given by target (relevant) and distractors (irrelevant). On the contrary,
154 incongruence is a divergence between these two dimensions. In congruent condition, trial's
155 response is generally more accurate and faster than in the incongruent condition (EGNER, 2007).
156 Incongruent condition results in interference between information from the two dimensions. This
157 interference causes a conflict in response's choice where conflict management system is
158 triggered. Incongruent trials are more likely to generate participant's error (Gratton et al., 2017).
159 Conflict tasks therefore help to induce participants' error.

160 In error behavioral adjustments, *Post-Error Slowing* (PES) is defined as lengthening of
161 RTs on post-error trials (Laming, 1979). *Post Improvement of Accuracy* (PIA) consists in the
162 increase of response accuracy on post-error trials. Response time and response accuracy of post-
163 error trial are related to the genesis of two main theoretical accounts: Functional and non-
164 functional theories of PES (Fievez et al., 2022), depending on observations of improvement or
165 decrease of accuracy's response level on post-error trial. PIA is not unanimously found in
166 scientific literature. Some studies reporting a link between PES and PIA (Maier et al., 2011;
167 Marco-Pallarés et al., 2008) while others not (Carp & Compton, 2009; Fiehler et al., 2005).

168 These theories are also referred to as adaptive (functional) and maladaptive (non-functional). If
169 post-error accuracy improves, PES is thus explained by functional/adaptive theories. Adaptive
170 theories stream gives functional value to PES. In connection with the concomitant observation of
171 increased accuracy on trials following the error (PIA (Danielmeier et al., 2011)), PES allows
172 participants to regain an optimal level of performance on task. The link between subsequent
173 increase in accuracy and PES has been modeled in a Drift Diffusion type computational model
174 (Ratcliff & McKoon, 2008). Model shows a post-error increase in response caution materialized
175 by a decrease in drift rate (Dutilh et al., 2011). Drift rate is parameter of the model that
176 represents how quickly informations from the stimulus are collected. According to Dutilh et al.
177 (2012), “[...] *participants become more cautious after an error and slightly more daring after a correct response [...]*”.

179 On the other hand, if post-error accuracy does not increase (Schroder et al., 2019), non-
180 functional/maladaptive theories are better suited to explain PES. Maladaptive theories explain
181 PES as a detour of attention to irrelevant aspects of the task at hand. Error is an unexpected event
182 for the participant and directs attention to it. However, when the difficulty of the task increases,
183 and errors become more frequent than correct responses, a so-called *Post-Correct Slowing* effect
184 is observed instead (Notebaert et al., 2009). *Post-Correct Slowing* is an increase of RTs
185 following a correct response, opposite of PES. Here it's the unexpected aspect that causes the
186 slowdown, and depending on the relative frequency of the stimuli, it can be either an error trial
187 or a correct trial. In their protocol, errors are not followed by an improvement of subsequent
188 performance (PIA). PES therefore has no functional value. Other theories in this current
(maladaptive theory) postulate an impossibility to process the additional information constituted by error. These assume that information treatment is blocked in a bottleneck leading to a saturation of the cognitive processes in progress. By varying the response/stimulus interval, Jentzsch and Dudschig (2009) observed, for example, that shortest intervals (50 ms) generate highest PES, related here with a decrease in response accuracy. Over the longest intervals (1000 ms), the authors report a reduction in PES compared to the shortest intervals and no significant variation of response accuracy.

Some research then allowed convergence of divergent data patterns from adaptive and maladaptive theories. Synthesizing these contradictory approaches, J. R. Wessel (2017) shows their complementarity with Adaptive Orienting Theory (AOT). This theory postulates that PES is a phenomenon that takes place in two phases. First, a broad inhibition of perceptual, motor and cognitive processes activated to carry out the task. Here, attention is diverted from goals' task by surprise effect caused by error. But this phenomena are not error specific, any unexpected event is likely to provoke this pattern. This leads to a decrease in accuracy and an increase in RTs. Wessel speaks of ‘orienting-related’ PES. The next stimulus arrives too early during the inhibition period of PES. We then obviously do not observe PIA, which allows us to encompass data from non-functional (maladaptive) theories.

Next J. R. Wessel (2017) describes an error specific phase where the source of attentional disturbance is detected and analyzed. During this one, attentional processes aimed at processing error are gradually redeployed. Here, attention is directed towards error in order to process it. This is followed by a resumption of the current task goals' and recovery of pre-error performance levels. The goal of this second phase is to allow recovery of optimal levels of accuracy in the task at hand. PES is then described as ‘strategic’, a slow and deliberate process
influenced by cognitive control. Once these two stages have been completed, PIA can be
observed, as postulated by adaptive theories. PES has a functional status by allowing the
refocusing of attentional processes on the current task to recover pre-error performance levels.

Making the connection between motor error, processes in WM, and attentional processes,
J. Wessel and jiang (2021a) propose a protocol to test one of the predictions of Adaptive
Orienting Theory (J. R. Wessel, 2017): The impact of a motor error on ongoing cognitive
processes during the task. They use a dual-task protocol (see **Box 1**) consisting of a memory task
and a flanker task (Eriksen & Eriksen, 1974). The trials proceed as follows. Initially, a series of
letters is presented on the screen for 2000ms to be memorized. Then, participants must indicate
the direction of a central arrow (the target, indicating left or right) while ignoring two distractors
arrows symmetrically arranged to the left and right of this target. The distractor arrows both
point in the same direction but can point either in the same direction as the target (congruent
trial) or the opposite direction (incongruent trial). After completing 6 trials of the arrow task, a
series of letters is again presented to the participants. In 50% of the cases, the series corresponds
to the series presented at the beginning of the trial. Participants were asked to judge the
correspondence between the two sets of letters by answering YES/NO. At the beginning of the
protocol, a training phase is used to calibrate the size of the series of letters presented to the
participants' abilities. The set then increases or decreases by one item depending on whether
participants' recognition responses are good or bad. Trials are categorized as correct or error
trials depending on whether or not participants made an error on the arrow task.

The authors observe that error trials lead to a decrease in the level of accuracy on the
recognition of the span compared to correct trials, this is the ERIAM effect (Error Related
Impairment of Active working Memory). In Experiment 2, ERIAM effect has a medium effect
size ($t(52) = 3.29, p = .002$, Cohen's $d = .45$). There is no increase in response times on span
recognition which would then more specifically sign a speed accuracy trade-off (SAT)
adjustment (Donkin et al., 2014). A decrease in working memory recall accuracy, related to a
decrease in response times, would then be more simply explained by a decrease in the time taken
by subjects to formulate and give the correct answer. Moreover, the authors increase the inter-
stimulus interval (from 200 to 2300 ms on Experiment 1 vs Experiment 2 respectively) and
obtain again an ERIAM effect with a longer interval. Thus, they show that ERIAM effect is not
related to the bottleneck passage of information postulated by some non-functional theories of
PES (Jentzsch & Dudschig, 2009). The ERIAM effect is more pronounced in Low Span
participants than in High Span. This provides a link between WM capacities and error
monitoring abilities (Unsworth et al., 2022).

**Box 1:** McIsaac et al. (2015) proposes a taxonomy of dual-task paradigms. A dual task is the concurrent performance of two tasks that can be performed separately, measured separately, and have distinct goals. Thus, each task may be different in character, drawing on distinct domains. For example, a memorization task will be based on mnemonic and cognitive processes. Another task may consist of performing a movement. The two tasks may also be based partly or totally on similar processes. (two tasks of a cognitive nature). In J. Wessel and jiang (2021a), the protocol implemented involves a memory task and a motor task of deciding the direction of an arrow. The motor task requires selective attentional abilities, as it involves not being disturbed by distracting arrows of a flanker-type task (Eriksen & Eriksen, 1974). The memory task proposed by J. Wessel and jiang (2021a), taken independently, is a simple short-term memory task. Participants
are asked to recognize a letter span presented a few seconds earlier. It is the
performance of this task in a dual-task protocol that makes it a Working Memory
task.

The study conducted by J. Wessel and jiang (2021a), while offering interesting results, can be subject to a few limitations, particularly on the methodological level. One limitation, due to post-hoc hypothesizing of a link between the ERIAM effect and WM capacities, is impossible experimental control of claim. In fact, over the course of five experiments in their study, Wessel and colleagues observed a negative correlation between ERIAM effect and participants' WM capacities (r = -.41, p < .001). High Span individuals are less impacted by motor error than are Low Span individuals. One experiment in the protocol proposes to increase the number of items in the memory span. Similar in all respects to the previous experiment, the authors no longer observed a significant correlation between the ERIAM effect and WM capacities when the cognitive load was increased (r = -.37, p = .071). This observation needs further exploration and this work attempts to address it by systematically varying the number of items to be memorized and by performing linear regression analyses.

We will observe the effects of an error on a digit span in working memory, by
implementing a complex span protocol. This type of protocol (reading span (Daneman &
Carpenter, 1980); operation span (Turner & Engle, 1989); symmetry span (Kane et al., 2004))
requires participants to maintain items in memory while performing a second concurrent task.
Working memory maintenance and attentional selection of relevant aspects of stimuli are called
upon in the same task. Error on the conflict task allows us to categorise trials according to
whether they are correct or not and to obtain an estimate of the effect of the error on the
maintenance of the working memory span.
The first objective of this work is therefore to attempt to reproduce the ERIAM effect (J. Wessel & jiang, 2021a) by applying a modified version of the authors' Experiment 2, where the largest ERIAM effect was observed. Trials are organized in laboratory in order to collect the most accurate data possible by not being subject to the connection and/or hardware constraints of online runs. The goal is to provide new data to retest J. Wessel and jiang (2021a) finding and try to check Adaptive Orienting Theory's (J. R. Wessel, 2017) prediction of error-induced inhibition of ongoing cognitive processes during the task. We propose that the WM task be closed with digit span recall rather than recognition. Indeed, in the original study, recognition response to the WM task involves same type of response modalities as conflict task. Both involve choosing between two possibilities: YES/NO for the similarity to the set of digits and Left/Right for the direction of the target arrow on the arrow task. Recall of the digit span, using the numeric keypad keys, allows for the dissociation of these response modalities and the observation of performance on the WM task by minimizing the confusion of response modalities (Pashler, 1990).

Furthermore, J. Wessel and jiang (2021a) were able to show a significant negative correlation (in 5 out of 7 experiments) between the ERIAM effect and subjects' average WMC. The authors conclude that the ERIAM effect more strongly impacts subjects for whom the memory task is more demanding. Individuals with better WMC are those who are better able to regulate their attentional processes and to monitor the occurrence of error. The ERIAM effect is less important for High Span individuals than for Low Span individuals. However, one point seems to us to be worth emphasizing. Between experiments 5 and 6, the authors increase the cognitive load (by adding an element to the series of letters). While a significant correlation between the ERIAM effect and WMC is found in Experiment 5 with low cognitive load, this correlation becomes marginal and non-significant in Experiment 6 with high cognitive load. This
apparent decrease of the ERIAM / WMC correlation when cognitive load increases is to be
investigated. The two experiments that lead to this difference in results involve two separate
samples.

**Presentation of assumptions**

We expect to observe a degradation in memory recall performance following a motor
error (i.e., on flanker task). **This constitutes our first hypothesis.** We will replicate, using a
slightly modified task, the ERIAM effect observed by J. Wessel and jiang (2021a).

During an increase in cognitive load, High Span subjects will have their attentional
resources mobilized more extensively on the recall of the span and will have less ability to
inhibit the effect of an error on motor task. Low Span subjects will be less affected by the
increase in cognitive load because their attentional resources will have already been consumed at
lower levels of load. **This constitutes our second hypothesis.** We will test ERIAM effect in
these two groups and under these two conditions of cognitive load.

Following our second hypothesis testing we propose **an exploratory part** (with analysis
made post-hoc after hypothesis 2 testing) to try to increase our understanding of ERIAM effect.
In this part we test more low-level construct (accuracy) within group span and cognitive load
condition.

Then, we will observe the ERIAM/WMC correlation. We will observe this correlation in
both groups and condition of load. Kane and Engle (2000) showed that High Span individuals
were more impacted by an increase in cognitive load than Low Span individuals. Thomassin et
al. (2015) also found a similar pattern in their study, High Span individuals' strategies are more
efficient but also more sensitive to task's complexity. This effect was named *Hard Fall Effect*.
We propose that correlation between ERIAM and WMC will become positive in high span group
as cognitive load increase. In low span group we expect not to see such a difference between
load condition. **This constitutes our third hypothesis.**

Finally, a **second exploratory part** is proposed with post-hoc analysis following
hypothesis 3. Without taking care of cognitive load, we want to observe ERIAM/WMC for the
whole group (as Wessel et al. did in their study), and in the high and low span groups.

## Methods

### Participants / Sample size justification

We choose to take part of information we have to justify our sample size. Original study want to reach a 80% power collecting data on 53 participants. To ensure good probabilities of replication, we increase our a priori power to 90% (Erdfelder et al., 1996). Data on a sample of 63 participants were collected. The participants gave their free and informed consent to undergo the experiment. Research Ethics Committee of Toulouse accepted the research by ruling on the ethical compliance of the present study (2023-596). The study was pre-registered on OSF (Brochet et al., 2022). The final sample consisted of 58 participants after data processing (as 5 participants did not fulfill the whole experiment) with 68.25% women and 31.75% men (age: M = 25.84, SD = 9.54).

### Material/Stimuli

Stimuli for conflict task (the target arrow and the four winged arrows surrounding it) were composed of a five-character string with symbols ">" and "<". Width and height of stimuli represent 10.8° and 3.3° of visual angle, respectively (centered on a 17-inch screen located 60 centimeters from participants. Stimulus for flanker task consists of target and four flankers distributed two by two on each side of target (e.g. >>>>). For memory task, digits from 0 to 9 are presented in *Times New Roman* font size 80. Each digit in series is separated from the other
digits by the ‘-’ character to limit deliberate chunking (Gobet & Lane, 2012). Series of digits are
constructed in random mode, with possible repetition (to make series larger than 10 digits
possible). All stimuli are displayed in white on a black background. The task was programmed
on Eprime 3.0 software (Psychology Software Tools, Pittsburgh, PA).

354 **Procedure**

Structure of the task is shown in **Figure 1**. Each trial is structured in the same way. Trial begins with presentation of a fixation cross centered on screen for 1,000 ms, followed by presentation of series of digits at the same location on screen for 2000 ms. A neutral screen (black screen) is then presented for 200 ms before the start of flanker task. Flanker task consists of a sequence of four stimuli for a total duration of 4800 ms. Stimulus consists of target accompanied by 4 flankers, presented on screen for 200 ms. Each stimulus is followed by a black screen for 1000ms allowing participants to respond. We did not proceed to a priming unlike the replicated study (100 ms of advance for flankers, then addition of target for 100 ms). The 4 flankers all pointed in the same direction (left or right) and depending on whether central target pointed in direction of the flankers or the opposite direction, the trial was considered congruent or incongruent, respectively. Participants were asked to respond to the orientation of the central target regardless of the flankers as quickly as possible by pressing the “A” or “P” keys for left and right, respectively. The 4 stimuli of flanker task are followed by the number series recall task. Participants are then instructed to recall series presented to them at beginning of trial using number pad and then validate with ENTER. There is no time limit defined on this recall task, next trial is presented only after participants have validated.
<figure><img src="image_3.png" /><figcaption>Figure 1: Task procedure</figcaption></figure>

Training trials for span calibration

Experiment consists of two parts. First part consists of a training of 24 trials during which length of the span varies according to participant's response accuracy. Objective is to calibrate length of the series requested in memory task to subjects' capacities. Span could thus increase by one, remain stable or decrease by one digit depending on participants' two previous answers accuracy (for two correct answers, one correct answer or zero correct answer respectively). Initial span is set on four digits. Participants were not aware of the purpose of these calibration trials. This calibration portion consists only of congruent flanker stimuli so that:

* Participants could become familiar with structure of the trials and response modalities.

* Digit span recall is not overly impacted by motor errors in calibration phase.

On this training phase, after each of the participants' actions, feedback is given (green dot for good response, red dot for bad response or "not fast enough" on flanker task if participants do not respond fast enough, response to digit span is not time limited). No participant achieved a memory digit span of less than four digits.
387 **Completion of the task**

388 Second part consists of the task itself, composed of 60 memory trials. Flanker stimuli are
389 congruent and incongruent (same proportion of 50-50%) within each memory trial. In order to
390 test our second hypothesis, an increase in digit span is performed adding one digit to the set
391 calibrated in the training phase, on half of the trials. Total duration of the experiment is
392 approximately 20 minutes.

393 **Data analysis**

394 We proceeded to analyze the behavioral data (accuracy and RT) from portion of task
395 without training/calibration trials. We remove trials where participants did not respond on
396 flanker task or memory task. Trials where response on flanker task was less than 200ms were
397 also deleted. Data from memory span responses were, as in replicated study, transformed into
398 proportion of correct responses to conduct analyses. Analyses are between-subjects, data were
399 agglomerated between participants, allowing to invoke central limit theorem.

400 To test our first hypothesis we compared digit span response accuracy between error and
401 correct conditions (depending on whether an error was produced on interfering flanker task) by
402 two-sided paired-samples T-test at .029 alpha threshold corrected for two-stage study
403 (POCOCK, 1977). In these two conditions level of congruence is similar (of 50%) in order not to
404 confuse ERIAM effect with a congruence effect.

405 In order to test our second hypothesis of greater impact of an increase in cognitive load in
406 high span participants on ERIAM effect, we fitted a linear mixed model (estimated using
407 restricted maximum likelihood) to predict ERIAM effect with cognitive load (CL) and High/Low
408 span group (formula: ERIAM ~ CL * span + (1 | Subject) ). Groups are differentiated by number
409 of digits in digit span (above and below the sample median). Cognitive load levels differ by
adding one item in the digit span (for the increased load condition) compared to the moderate condition. ERIAM effect is calculated as the difference in Working Memory recall accuracies between error and correct conditions on conflict task.

Next, we also reported correlation between ERIAM effect and WMC for comparison with the replicated study. WMC are operationalized as overall digit span average response accuracy without taking into account error and correct conditions on the flanker task. We then observed this correlation in the High span and Low span group and under both conditions of cognitive load. Regression analyses were conducted to test for significance, with participants' WMC as predictors of the ERIAM effect.

## Results

We conducted a interim data analysis on this study (at N/2 in April 2023). To preserve the significance of our hypothesis tests, we chose to apply a Pocock correction (POCOCK, 1977) to the alpha thresholds of our primary hypotheses. Employing a two-stage design with two looks at the data, the Pocock correction indicates an alpha level of **0.029** for two-tailed tests.

Consequently, we apply this alpha level throughout the remainder of the study. Summary statistics is available in **Table 1**.

(*#tab:unnamed-chunk-8*) Summary of descriptive statistics on each task of the protocol

<table><thead><tr><th></th><th>Task</th><th>Mean_SE_CI</th></tr></thead><tbody><tr><td>Accuracy.erroroweal</td><td>WORKING MEMORY</td><td>0.35 (0.23) [0.29 : 0.41]</td></tr><tr><td>AccuracyCORRECTWEAL</td><td>WORKING MEMORY</td><td>0.44 (0.28) [0.37 : 0.52]</td></tr><tr><td>RT.erroroweal</td><td>FLANKER</td><td>5.8 (1.7) [5.4 : 6.3]</td></tr><tr><td>RT.CORRECTWEAL</td><td>FLANKER</td><td>6 (1.6) [5.6 : 6.4]</td></tr><tr><td>RT.CONGRUENTWEAL</td><td>FLANKER</td><td>0.44 (0.066) [0.43 : 0.46]</td></tr></tbody></table>
<table><thead><tr><td>Task</td><td>Mean_SE_CI</td></tr></thead><tbody><tr><td>RT.incongruent trial</td><td>0.51 (0.075) [0.49 : 0.53]</td></tr><tr><td>Accuracy.congruent trial</td><td>0.95 (0.1) [0.92 : 0.98]</td></tr><tr><td>Accuracy.incongruent trial</td><td>0.73 (0.15) [0.69 : 0.77]</td></tr></tbody></table>

Note. For each task of the protocol, Mean, Standard Error (SE), and 95% Confidence Interval [CI] are represented. For the Working Memory task, accuracy and response time (RT in second) are represented according to error or correct trial on Conflict Task. For flanker task, RT and accuracy are represented according to congruent or incongruent trials.

431

432 **Hypothesis 1 testing**

433 **Conflict task results**

434 An illustration of the results observed on the conflict task is offered in **Figure 2 (a&b)**, 435 summary statistics is available in **Table 1**. Compared to congruent trials, incongruent trials were 436 less accurate ($t(57) = 10.94, p < .001$, Cohen's $d = 1.44$) and had longer RTs than congruent 437 trials ($t(57) = -13.99, p < .001$, Cohen's $d = 1.84$). This indicates that the manipulation in the 438 conflict task worked by replicating the conflict interference effects widely documented in the 439 literature.

440 **Figure 2: Accuracy and Response Time on conflict task**
<figure><img src="image_4.png" /></figure>
<figure><img src="image_5.png" /></figure>

Memory task results

An illustration of the observed results is shown in **Figure 3**(a&b), summary statistics is available in **Table 1**. The participants' memory load consisted of 4 to 10 digits ($M = 6.97, SD = 1.25$). The first key question of this work, constituting the attempt to replicate the work of J. Wessel and jiang (2021a) and our first hypothesis, is the effect of an error on the conflict task on subsequent WM recall. The data show no significant deviation from a normal distribution.
<figure><img src="image_6.png" /><figcaption>Figure 3: Accuracy and Response Time on Working Memory Task</figcaption></figure>
<figure><img src="image_7.png" /></figure>

We compared response accuracy of Working Memory recall in the two conditions (according to an error has been produced on conflict task or not) using paired-sample t-tests. Trials with an error on the conflict task are significantly less accurate than trials without (t(55) = 4.46, p < .001, Cohen's d = 0.37). This effect is slightly larger than in the experiment 2 of Wessel et al. where the authors find a Cohen d = .32. Response accuracy between the correct and error conditions thus fell on average from 0.44 to 0.35 respectively. This effect does not appear
458 to be linked to an adjustment of the participants' response time/accuracy function, as response
time of two conditions do not differ significantly ($t(55) = 1.36, p = 0.181$, Cohen's $d = 0.1$).

460 Action error committed during the delay period thus impaired subsequent working memory
461 accuracy on the digit span recall. Our first hypothesis is thus corroborated by data, and ERIAM
462 effect has been replicated.

463 **Hypothesis 2 testing**

464 Then we want to know if this ERIAM effect is differently impacting high and low span
465 group within our two cognitive load conditions. To test this hypothesis we fit a linear mixed
466 model using restricted maximum likelihood (REML) to assess for change in ERIAM level
467 according to cognitive load and subject span group with the formula:

$468 \quad eriam \rightarrow cognitive.load * span + (1|subject)$

469 Mixed models allow us to deal with repeated measure within subject and non-
470 independence of data. Proceeding by model comparison, we start fitting a null model with formula
471 and then we add predictors one by one:

$472 \quad eriam \rightarrow 1 + (1|subject)$

473 This first model allow us to check for intraclass correlation index (ICC).

474 We found an *ICC* = 0.6, indicating strong data dependency within subject. Design effect
475 is telling us that we artificially increase the sample size by a 2.59 factor not considering random
476 effect. Mixed model is appropriated in this case. Compared to the *null model*, first model with
477 span as a predictor do not yield significative improvement of fit to the data. *AIC* = 506.27 for the
478 *null model* and *AIC* = 506.68 for the model with predictors while *BIC* = 516.2 and 506.68
479 respectively for *null model* and model with predictors. Finally, *Bayes Factor* do not really favor
480 model, *Bf*<sub>10</sub> = 0.156, *p* = .098. Adding one predictor (cognitive load) to this model exhibits a
481 significantly worse fit to the data compared to the null model. *AIC* = 506.27 for the *null model*
482 and *AIC* = 508.41 for the model with predictors while *BIC* = 516.2 and 508.41 respectively for
483 *null model* and model with span and cognitive load as predictors. Finally, *Bayes Factor* favored
484 *null model*, *Bf*<sub>10</sub> = 0.002, *p* = .024. So we don't analyze the model with predictors (but you'll find
485 results in the script). Thus our second hypothesis of a more pronounced ERIAM effect in *high*
486 *span* group with increased cognitive load compared to *low span* group, with the analyses we
487 carried out, is not supported by data. Nethertheless, we propose a visualization of these non-
488 significant results in **Figure 4**.

489 **Figure 4: ERIAM effect according to cognitive load and group**
<figure><img src="image_8.png" /></figure>

None of the results yield significance

**Exploratory part for in-depth understanding of the ERIAM effect**

Going further in our understanding of the pattern beyond the data we collect, we want to analyse accuracy on working memory recall as a more low level construct than ERIAM. We fit a new linear mixed model using restricted maximum likelihood (REML) to assess for change in
response accuracy on working memory task according to cognitive load, error on conflict task

and subject span group with the formula:

$$ accuracy = > cognitive.load * span * error + (1|subject) $$

In Figure 5 you can find residuals distribution of the model.

<figure><img src="image_9.png" /><figcaption>Figure 5: Mixed Model residuals</figcaption></figure>
Again, ICC = 0.51, indicates strong data dependency within subject and design effect = 2.35. Model REML is 424.38. Compared to the *null model*, the model with predictors exhibits a significantly improved fit to the data. AIC = 525.85 for the *null model* and AIC = 444.38 for the model with predictors while BIC = 535.77 and 444.38 respectively for *null model* and model with predictors. Finally, *Bayes Factor* overwhelmingly favored model with predictors, $Bf_{10}$ = 4.6e+12, *p* < .001. Residuals visually do not differ from a normal distribution. The model's total explanatory power is substantial (conditional $R^2$ = 0.77) and the part related to the fixed effects alone (marginal $R^2$) is of 0.29. The model's intercept, corresponding to span = lowspan, charge = moderate and Condition = Correct, is at 1.1 (95% CI [0.74, 1.46], *t*(192) = 5.96, *p* < .001).

Accuracy values are standardized, hereafter we only report standardized *beta* coefficients for better visibility. Within this model:

513 • The effect of span [highspan] is statistically significant and negative, *t*(192) = -4.57, *p* < .001; *Std. beta* = -1.11, 95% CI [-1.58, -0.63])

515 • The effect of charge [increased] is statistically significant and negative, *t*(192) = -7.15, *p* < .001; *Std. beta* = -1.08, 95% CI [-1.38, -0.78])

517 • The effect of Condition [Error] is statistically significant and negative, *t*(192) = -3.60, *p* < .001; *Std. beta* = -0.54, 95% CI [-0.83, -0.24])

519 • The effect of span [highspan] × charge [increased] is statistically significant and positive, *t*(192) = 2.24, *p* = 0.026; *Std. beta* = 0.46, 95% CI [0.06, 0.87])

521 • The effect of span [highspan] × Condition [Error] is statistically non-significant and positive, *t*(192) = 1.56, *p* = 0.122; *Std. beta* = 0.30, 95% CI [-0.08, 0.69])

523 • The effect of charge [increased] × Condition [Error] is statistically non-significant and positive, *t*(192) = 1.08, *p* = 0.279; *Std. beta* = 0.23, 95% CI [-0.19, 0.65])

525 • The effect of (span [highspan] × charge [increased]) × Condition [Error] is statistically non-significant and negative, *t*(192) = -0.80, *p* = 0.426; *Std. beta* = -0.23, 95% CI [-0.80, 0.34]) 95% Confidence Intervals (CIs) and p-values were computed using a Wald t-distribution approximation.

529 (#tab:unnamed-chunk-15) Summary of mixed model on accuracy

<table><thead><tr><th>Effect</th><th>Test</th><th>Std..beta</th><th>X95..CI</th></tr></thead><tbody><tr><td>span [highspan]</td><td>t(192) = -4.57, p &lt; .001</td><td>-1.11</td><td>[-1.58, -0.63]</td></tr></tbody></table>
<table><thead><tr><th>Effect</th><th>Test</th><th>Std..beta</th><th>X95..CI</th></tr></thead><tbody><tr><td>charge [increased]</td><td>t(192) = -7.15, p &lt; .001</td><td>-1.08</td><td>[-1.38, -0.78]</td></tr><tr><td>Condition [Error]</td><td>t(192) = -3.60, p &lt; .001</td><td>-0.54</td><td>[-0.83, -0.24]</td></tr><tr><td>span [highspan] × charge [increased]</td><td>t(192) = 2.24, p = 0.026</td><td>0.46</td><td>[0.06, 0.87]</td></tr><tr><td>span [highspan] × Condition [Error]</td><td>t(192) = 1.56, p = 0.122</td><td>0.30</td><td>[-0.08, 0.69]</td></tr><tr><td>charge [increased] × Condition [Error]</td><td>t(192) = 1.08, p = 0.279</td><td>0.23</td><td>[-0.19, 0.65]</td></tr><tr><td>(span [highspan] × charge [increased]) × Condition [Error]</td><td>t(192) = -0.80, p = 0.426</td><td>-0.23</td><td>[-0.80, 0.34]</td></tr></tbody></table>

Note. For every effect tested, t test and pvalue, standardized beta coefficient and 95% CI

are mentioned

**Figure 6** represent response accuracy according to group span (high and low span) and working memory load (moderate and increased load). Following our model results, increasing the cognitive load has a significant negative effect on digit span accuracy. Then, error made on the conflict task also significantly impair accuracy, arguing again for the ERIAM effect. Finally, increasing cognitive load in *high span* does not impact accuracy level as in *low span* group.

<caption>**Figure 6:** Accuracy on Working Memory task</caption>
<figure><img src="image_10.png" /></figure>

Hypothesis 3 testing

As mentioned in our preregistration (Brochet et al., 2022), we then check for correlation between ERIAM and WMC as in J. Wessel and Jiang (2021b). In Table 3 are represented ERIAM and correlation ERIAM/WMC in both groups of participants within level of cognitive load. Remember that our alpha threshold for significance is set to .029 due to Pocock correction. With this precision, we see that ERIAM effect seems to be significant only in *high*
span/increased load and low span/moderate load, and correlation ERIAM/WMC is significant in low span group in increased load condition. Our third hypothesis cannot be corroborated by data we collected. We cannot say that ERIAM/WMC correlation significantly increase in high span group within cognitive load as linear link does not yield significativity. Nethertheless, in low span group, the linear relation between ERIAM/WMC become significant as cognitive load increase.

(#tab:unnamed-chunk-17) ERIAM effect and correlation ERIAM/WMC in high and low span groups according to cognitive load(CL)

<table><thead><tr><th>group</th><th>CL</th><th>ERIAM</th><th>SD</th><th>pvalue</th><th>ERIAM_WMC</th><th>f_value</th><th>p</th><th>df</th></tr></thead><tbody><tr><td>highspan</td><td>increased</td><td>0.05</td><td>0.11</td><td>= 0.015</td><td>0.20</td><td>1.14</td><td>= 0.264</td><td>30</td></tr><tr><td>highspan</td><td>moderate</td><td>0.06</td><td>0.17</td><td>= 0.042</td><td>0.15</td><td>0.83</td><td>= 0.415</td><td>31</td></tr><tr><td>lowspan</td><td>increased</td><td>0.09</td><td>0.21</td><td>= 0.068</td><td>0.51</td><td>2.67</td><td>= 0.015</td><td>20</td></tr><tr><td>lowspan</td><td>moderate</td><td>0.15</td><td>0.22</td><td>= 0.003</td><td>0.00</td><td>0.02</td><td>= 0.986</td><td>21</td></tr></tbody></table>

It is noteworthy that the ERIAM effect is only significant in lowspan group in the moderate cognitive load condition and in highspan group in the increased load condition. We will discuss this particular pattern.

## Second exploratory part

We finally observed the link between WMC and ERIAM effect for the whole group in the same way as J. Wessel and Jiang (2021a) propose in their study. In the opposite direction to the replicated study, we observe a positive correlation between WM capacities and ERIAM effect, *r*(54) = 0.37. This correlation is significant for the whole group, *F*(1, 54) = 2.93, *p* = 0.005. For the Low Span group, the link between WM capacities and ERIAM effect is not significant *r*(20) = 0.3, *F*(1,20) = 1.43, *p* = 0.169. Concerning High Span group, we observe a trend for positive linear relationship *r*(32) = 0.37, *F*(1,32) = 2.23, *p* = 0.033 which does not reach .029
threshold of significance. **Figures 7, 8 and 9** show graphic representation of linear relationships observed at group level (Figure 7), in low-span (Figure 8) and high-span (Figure 9) groups. In **Table 4** you can find means and standard errors values for ERIAM and WMC within each span group. It is worth noting that WMC is larger for the lowspan group than for the highspan group, probably due to our task complexity and the way we split participants into span groups.

<caption>**Figure 7: Linear relationships between ERIAM and Working Memory Capacities for whole group**</caption>

(#tab:unnamed-chunk-18) Summary of mean ERIAM and WMC and Standard Error within span groups

<table><thead><tr><th>Source</th><th>ERIAM</th><th>SEM.eriam</th><th>WMC</th><th>SEM.WMC</th></tr></thead><tbody><tr><td>highspan</td><td>0.08</td><td>0.03</td><td>0.31</td><td>0.04</td></tr><tr><td>lowspan</td><td>0.13</td><td>0.04</td><td>0.54</td><td>0.05</td></tr></tbody></table>
<figure><img src="image_11.png" /><figcaption>Figure 8: Linear relationships between ERIAM and Working Memory Capacities</figcaption></figure>

for low span

`geom.smooth()` using formula = 'y ~ x'
<figure><img src="image_12.png" /><figcaption>Figure 9: Linear relationships between ERIAM and Working Memory Capacities</figcaption></figure>

for high span

`geom.smooth()` using formula = 'y ~ x'

Warning: Removed 348 rows containing non-finite outside the scale range

`(stat.smooth())`.
<figure><img src="image_13.png" /></figure>

Discussion

To test our first hypothesis, we observed the effect of a motor error on Working Memory maintenance (ERIAM), by carrying out a replication/extension of experiment 2 by J. Wessel and jiang (2021a). We succeeded in replicating this effect for the whole group. When participants made a mistake on the flanker task, memory recall was significantly impaired. The authors mention that in experiments where they use an arrow flanker task, ERIAM effect was probably
facilitated by the similarity of the processes involved in the response modalities of the two parts of the task, both of which are dichotomous. Through different operationalization proposed in our study (recall of the digit rather than recognition) we show that ERIAM effect is also present when two parts of the task do not rely on the same response keys. Moreover, as our participants were not stressed by short response time on Working Memory task, ERIAM is still observable at longer delay period after error is made, probably signifying loss of memory trace.

To explain these results, going back to Adaptive Orienting Theory (AOT) (J. R. Wessel, 2017) is useful. AOT predicts that errors lead to an impairment of cognitive processes in progress. Memory tasks involve encoding, storage (with rehearsal for WM) and retrieval of information. We probably can exclude here effect of the error on retrieval process because our operationalisation of recall was not time-limited and should have normally enabled participants to perform equally in both conditions (error or correct). Nethertheless, we cannot conclude which of the other two processes (encoding or storage) is impacted by the effect of the error. If we assume that encoding is done before the conflict task starts, probably error compete with rehearsal processes in Working Memory, as it diverts limited attentional ressources also in use for Working Memory maintenance (Barrouillet & Camos, 2020).

Oberauer (2019) reminds us that of “theoretical options for spelling out the idea of WM as relying on an attentional resource”, that of a shared resource for storage and processing has received the most theoretical support. In our case and on the basis of functional theories of PES, error detection engage deployment of cognitive control (Botvinick et al., 2001) to be monitored. As this process take place, processing resource are focused on error monitoring and take up some of the common attentional resources allocated to information storage in working memory.
This needs to be disentangled by proposing other protocols specifically studying these constructs.

Concerning our second hypothesis of a differential impact of increased cognitive load in the two High and Low Span groups, we implemented a mixed model using REML handling non-independent data to predict ERIAM. Neither cognitive load nor group span are good predictors of ERIAM effect in our model. Proceeding by model comparison and a one by one factor incremental method, neither model reach better fit to the data than null model. We believe in this case that ERIAM is already a highly transformed summary of data (□ between mean correct and mean error accuracy). Our model cannot explain a significantly sufficient part of variance of ERIAM when controling for span group nor cognitive load. This may be because of insufficient statistical power due to low sample size (e.g. low span group in this case has a 20 participants sample). But it may also be a consequence of mixed model and all variance falling into random factor. This conclusion is far from being trustworthy in our study and need further investigation.

Next we proposed an exploratory part trying to predict accuracy with group span, cognitive load and error made on conflict task. Accuracy is a lower-leveled construct than ERIAM. While turning back to this level our goal is to have a simplified understanding of predictors and data. This time, model with predictors is significantly better fitted to our data than null model. With this model we find that all simple predictors' effect are significant. Error made on conflict task (ERIAM effect), cognitive load and High span group all have a significant negative effect on accuracy. Interestingly, interaction of group span and cognitive load is significant too. The combination of High span group and increased cognitive load have a significant positive effect on accuracy. More precisely (see **Figure 6**), we can see that accuracy is less impaired by the increase of cognitive load in High span than in Low span group. It is
possible that High span participants are more engaged in task when cognitive load increase and thus perform better.

To say more about simple effects of predictors within this model, first we can see that error factor has a significant negative effect on accuracy. That doesn't come as much of a surprise because it reflects ERIAM effect already found in hypothesis 1 testing. This time however, we find this fixed effect of error while controlling for random effect. Then, High span group has a lower accuracy level than low span group. This probably comes from our experimental design that categorizes High and Low span groups according to the number of digits reached in the empanel at the end of the training phase. For High span participants, it may be that trials have been more challenging and their performance significantly lower than Low span participants. Finally, cognitive load has a detrimental effect on accuracy for all participants. As we can imagine, adding one digit to a span already calibrated on your own capacities is likely to make the task even more complex. This effect of cognitive load is nevertheless modified by an interaction effect with the group of participants.

Effect of interaction between span group and cognitive load on accuracy is significant and positive (see **Figure 6**). We can see on the graph that when cognitive load increase, High span individuals are less impacted than Low span. Their accuracy on working memory task is less impaired than these of Low span when cognitive load increase. Even if our predictions of hypothesis 2 concerning ERIAM effect do not raise significativity, it can be interesting here to compare visual observations of increasing cognitive load on ERIAM against accuracy. As proposed by Thomassin et al. (2015), High span individuals have more complex strategies that lead to both better performance and greater susceptibility to an increase in cognitive load. It seems that our data go in this way. ERIAM effect is visually as important in both conditions of
load for High span group, which can be related to the performance susceptibility part of the High span group. On the other way, their more complex strategies lead to a more stable accuracy performance within the two cognitive load conditions. But this is open to caution, as we are dealing in this part with an exploratory approach and, what's more, using results that are not significant.

Our third hypothesis has not be corroborated by data. Correlation between ERIAM and WMC, when controling for group span and cognitive load, only reach significance in Low span group and increased cognitive load condition. No particular patern in our data is observed, probably because in this part of our study our analysis rely on complex constructs (ERIAM and WMC are highly transformed data) and need more power (increased sample size) to reach significance. On this part of our work, it seems we cannot go further with our sample size. Here is a limit of our study.

Finally, we conducted linear regression analyses to test the link between WMC and the ERIAM effect for the whole group. We observed a positive and significant link between WMC and ERIAM effect. These results are in the opposite direction to those obtained by J. Wessel and jiang (2021a), who find a negative correlation and explained that "ERIAM most affected subjects for whom the WM aspect of the task was more challenging." In our study, ERIAM effect increases as WMC increases for the whole group. Splitting our sample in High and Low span groups, we can observed that correlation ERIAM/WMC does not reach our alpha level (Pocock corrected for one interim analysis). Nethertheless, a trend of a positive linear relationship is observed in High span group. However, as we can see in **Table 4**, this particular results are probably due to our span group splitting, as lowspan have better average WMC than highspan. With this in mind, we can better understand the correlation between ERIAM and WMC.
Highspan participants have a less impaired performance on digits span recall when they commited an error on flanker task (lower ERIAM levels). Nethertheless, their WMC is lower than lowspan group probably because they have reached high levels of task complexity. On the other hand, lowspan participants are more prone to ERIAM. This results drive the correlation between ERIAM and WMC in our sample, as higher WMC are reached by lowspan participants probably because of less complexity of the task in this group. As J. Wessel and jiang (2021a) say, “*The likely explanation for this finding is that subjects with a lower overall WM accuracy maintain less stable WM representations, which are then more susceptible to the impairing effects of errors.*” In our data, this lower “*WM accuracy*” are observed for highspan individuals, what probably leads to our positive relationship between ERIAM and WMC.

According to Lavie (2010), “*The ability to focus attention [...] deteriorates under conditions of high load on cognitive control processes such as working memory.*” In our study we find data in the direction of this theoretical prediction as accuracy levels on Working Memory task seem to decrease as we increase cognitive load (see exploratory part 2.3). Interestingly, Lavie’s theory of load encompass both the effects of perceptual and cognitive loads. While a high perceptual load reduces the processing of irrelevant stimuli, a high cognitive load increases it. Turning back to PEA functional and non-functional explanations, it is commonly accepted that error is an irrelevant stimulus to the task at hand. Error diverts attention and engage or not (depending on theory) further processing to regain maximum performance levels.

ERIAM effect is only significant in lowspan group in the moderate cognitive load condition and in highspan group in the increased load condition (Table 3). Refering to Lavie’s load theory, we can presume that for lowspan participants the increased cognitive load condition
exceeds their capacities. Lowspan in this condition probably withdraw their cognitive control on task at hand, probably explaining why ERIAM is not found in this group under this load condition. Error has probably been filtered at a perceptual level and so does not engage any further processing leading to ERIAM. On the other hand, the opposite pattern is observed for highspan participants. Highspan within moderate cognitive load condition probably do not engage further processing on flanker task and treat it at a perceptual level, focusing only on digit span part of the task (but we can see a non-significant trend for ERIAM even in this condition). When cognitive load is increased however ERIAM becomes significant in this group. This may be because highspan are more motivated by task and treat all stimuli at a cognitive level. This can lead to increasing interference of error events as Lavie postulated.

## Conclusion

In conclusion, our study provides significant insights into the relationship between motor errors and Working Memory maintenance (ERIAM), as well as the influence of cognitive load and individual differences in working memory capacity. Firstly, we successfully replicated previous findings demonstrating that motor errors impair memory recall, extending this effect to tasks with different response modalities, indicating a broader applicability of ERIAM across task variations. Our results align with Adaptive Orienting Theory, suggesting that error detection diverts attentional resources from memory maintenance processes, particularly rehearsal in Working Memory. However, the exact impact on encoding versus storage remains inconclusive and warrants further investigation.

Secondly, while our hypotheses regarding differential effects of cognitive load and working memory capacity on ERIAM were not fully supported, our exploratory analysis revealed intriguing patterns. High-span individuals exhibited more stable accuracy under
728 increased cognitive load compared to low-span individuals, possibly due to their engagement in
729 more complex strategies. This suggests that individual differences in working memory capacity
730 may modulate the impact of cognitive load on task performance.

731 Additionally, our study highlights the intricate interplay between cognitive load, error
732 processing, and working memory capacity. High cognitive load conditions seemed to exacerbate
733 the ERIAM effect, particularly in high-span individuals, potentially due to increased interference
734 from error events. Conversely, low-span individuals may disengage cognitive control under high
735 load conditions, leading to reduced susceptibility to ERIAM.

736 Moreover, our findings regarding the correlation between ERIAM and Working Memory
737 Capacity (WMC) diverged from previous research, with a positive relationship observed in our
738 study. This discrepancy may be attributed to differences in task complexity and individual
739 cognitive strategies. High-span individuals exhibited lower ERIAM levels but also lower WMC,
740 possibly indicating a ceiling effect due to task complexity for this group.

741 Overall, our study contributes to the understanding of how motor errors impact working
742 memory maintenance, shedding light on the moderating roles of cognitive load and individual
743 differences in working memory capacity. Future research should further elucidate the underlying
744 mechanisms of ERIAM and its implications for cognitive control processes. Additionally,
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