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Disentangling decision errors from action execution in mouse-tracking studies: The case of effect-based action control

November 2024
Attention Perception & Psychophysics

DOI:10.3758/s13414-024-02974-8

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CC BY 4.0

Authors:

Solveig Tonn

Trier University

Moritz Schaaf

Trier University

Wilfried Kunde

University of Wuerzburg

Mouse-tracking is regarded as a powerful technique to investigate latent cognitive and emotional states. However, drawing inferences from this manifold data source carries the risk of several pitfalls, especially when using aggregated data rather than single-trial trajectories. Researchers might reach wrong conclusions because averages lump together two distinct contributions that speak towards fundamentally different mechanisms underlying between-condition differences: influences from online-processing during action execution and influences from incomplete decision processes. Here, we propose a simple method to assess these factors, thus allowing us to probe whether process-pure interpretations are appropriate. By applying this method to data from 12 published experiments on ideomotor action control, we show that the interpretation of previous results changes when dissociating online processing from decision and initiation errors. Researchers using mouse-tracking to investigate cognition and emotion are therefore well advised to conduct detailed trial-by-trial analyses, particularly when they test for direct leakage of ongoing processing into movement trajectories.

Experimental design and previously observed data pattern. (A) Movements began in a starting area in the lower middle of the screen and ended in one of two possible final movement locations. Depending on the response-effect compatibility mapping, action effects either occurred on the same side as the final movement location (dotted cir-

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sualization of the cutoff-criterion. Data from three example participants. (A) Average trajectories over all trajectories (dashed, dark gray lines), over trajectories excluded by the cutoff criterion (solid, light gray lines), and over trajectories surviving the cutoff cri-

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Average trajectories for one exemplary experiment (Pfister et al., 2014, Exp. 2). Average trajectories when using all movements (left) and when excluding multi-step movements (right). Although participant averages (thin lines) are smooth and do not cross our

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Explanation of the velocity profile plots. For all (time-normalized) trajectories, the timepoint of maximal orthogonal deviation (MAD) from the ideal line is computed (left). Trajectories are then separated into pre-and post-MAD parts (middle). The resulting subtrajectories are time-normalized again before velocities can be aver-

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Results from Pfister et al. (2014), Experiment 2. (A) Compatibility effect in area under the curve (AUC) as a function of the used cutoff criterion. The x-axis indicates the allowed horizontal movement between the center of starting area and the center of the wrong target area, normalized to percentage. The y-axis indicates the standardized effect size. The dashed vertical line indicates the cutoff used in the text. (B) Velocity profiles for all movements (left), and move-

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Vol.:(0123456789)

Attention, Perception, & Psychophysics

https://doi.org/10.3758/s13414-024-02974-8

Disentangling decision errors fromaction execution inmouse‑tracking

studies: The case ofeﬀect‑based action control

SolveigTonn1 · MoritzSchaaf1 · WilfriedKunde2 · RolandPster1

Accepted: 9 October 2024

Abstract

Mouse-tracking is regarded as a powerful technique to investigate latent cognitive and emotional states. However, drawing

inferences from this manifold data source carries the risk of several pitfalls, especially when using aggregated data rather

than single-trial trajectories. Researchers might reach wrong conclusions because averages lump together two distinct contri-

butions that speak towards fundamentally diﬀerent mechanisms underlying between-condition diﬀerences: inﬂuences from

online-processing during action execution and inﬂuences from incomplete decision processes. Here, we propose a simple

method to assess these factors, thus allowing us to probe whether process-pure interpretations are appropriate. By applying

this method to data from 12 published experiments on ideomotor action control, we show that the interpretation of previous

results changes when dissociating online processing from decision and initiation errors. Researchers using mouse-tracking

to investigate cognition and emotion are therefore well advised to conduct detailed trial-by-trial analyses, particularly when

they test for direct leakage of ongoing processing into movement trajectories.

Keywords Mouse-tracking· Response-eﬀect compatibility· Ideomotor framework· Action execution· Initial decision

errors

Introduction

Motor actions comprise more than a sequence of movements.

They are driven by certain intentions and involve manifold

cognitive and emotional processes. As recent observations

suggest that the intention behind an action heavily inﬂu-

ences the kinematics of the ensuing movement, the analysis

of unfolding motions is regarded as a powerful tool to shed

light on cognitive and emotional processes (Ansuini etal.,

2014; Georgiou etal., 2007; Sartori etal., 2011; Song &

Nakayama, 2009; Stillman etal., 2018). This potential has

attracted the attention of behavioral scientists, especially in

cognitive psychology, a ﬁeld with a long history of employ-

ing reaction-time setups to test for the speed of processing.

While conventional, chronometric setups yield essentially

one data point per correct response, movement trajectories

are able to provide multiple data points for every movement,

substantially increasing the amount of information that can

be analyzed (Bundt etal., 2018; Fischer & Hartmann, 2014;

Maldonado etal., 2019; Zgonnikov etal., 2017).

One particular prominent way to capture movement tra-

jectories is the simple and elegant means of logging the coor-

dinates of a mouse cursor across time (Freeman & Ambady,

2009; McKinstry etal., 2008). Mouse-tracking has generated

valuable insights in numerous ﬁelds, including social cat-

egorization (Dale etal., 2007; Hehman etal., 2014; Lazerus

etal., 2016; Stolier & Freeman, 2017), self-control in deci-

sion-making (Buttlar & Walther, 2019; O’Hora etal., 2016;

Stillman etal., 2017, 2018), and semantic processing (Dale

& Duran, 2011; Spivey etal., 2005; Wirth etal., 2019). Fur-

ther, it has been employed to investigate motivational topics

like approach and avoidance tendencies (Boschet etal., 2022;

Dignath etal., 2014, 2020; Wirth etal., 2016), rule-breaking

(Jusyte etal., 2017; Pﬁster etal., 2016; Wirth etal., 2018),

and cognitive conﬂict (Boschet etal., 2022; Erb etal., 2016;

Mittelstädt etal., 2023; Quétard et al., 2023; Scherbaum

etal., 2010).

Despite its widespread use, comprehensive standards for

experimental design and especially data analysis have not

* Solveig Tonn

tonn@uni-trier.de

1 Department ofPsychology, University ofTrier,

Johanniterufer 15, 54290Trier, Germany

2 Department ofPsychology, University ofWürzburg,

Würzburg, Germany

Attention, Perception, & Psychophysics

yet been established. Mouse-tracking experiments diﬀer,

for example, regarding their starting procedure (dynamic

vs. static), response mode (terminating a response by click-

ing vs. reaching a target), or cursor speed (Kieslich etal.,

2018; Scherbaum & Kieslich, 2018). In fact, recent obser-

vations suggest that these seemingly slight diﬀerences in

the experimental procedure can lead to puzzling diﬀerences

in observed results and corresponding conclusions (Grage

etal., 2019; Kieslich etal., 2020; Schoemann etal., 2019,

2021; Wirth etal., 2020).

The only aspect of mouse-tracking analyses that enjoys

widespread consensus is the use of aggregated means instead

of individual trajectories to plot experimental results (Buttlar

& Walther, 2019; Dieciuc etal., 2019; Pﬁster etal., 2016;

Stillman etal., 2018; Ye & Damian, 2022). Ironically, this

consensus comes with major limitations as it neglects that

one and the same average trajectory can derive from highly

diﬀerent trajectories on a by-participant or by-trial level

(e.g., Matejka & Fitzmaurice, 2017).

Single movements versusaggregate statistics

The observation that identical trajectory averages can result

from profoundly diﬀerent individual movements calls for

methods to evaluate diﬀerent trajectory types. Such meth-

ods include the classiﬁcation via cluster-analytical methods

(Wulﬀ etal., 2018) or graphical approaches such as heat-

maps of individual movements (Garcia-Guerrero etal.,

2022; Scherbaum etal., 2010; Vogel etal., 2018). These

highly sophisticated methods have not been adopted widely,

however.

Thus, we suggest an easy-to-implement method that aims

to reach a similar goal. Our approach provides a straight-

forward way to assess the particularly relevant distinction

of smooth, single-step movements versus multi-step move-

ments in which an initial movement is re-evaluated and

then revised along the movement trajectory. Single-step

and multi-step movements clearly involve diﬀerent cognitive

processes and, therefore, this distinction must be considered

when interpreting the results of an experiment (see van der

Wel etal., 2009 and Spivey etal., 2010, for a conceptually

related discussion of discrete vs. continuous inﬂuences on

movement trajectories in a lexical decision task).

A simple criterion

Multi-step movements often come in the shape of initial

movements in the wrong direction that are corrected by

pausing and changing direction along the way. Such move-

ments reﬂect errors in the initial decision of where to move,

and should therefore not be considered when movement exe-

cution (rather than decision making) is targeted by an experi-

ment. Although statistical clustering (Wulﬀ etal., 2018) is

the currently most elegant and sophisticated method to dis-

tinguish diﬀerent types of movements, it may not always be

ideal for two reasons. First, it does not take the experimen-

tal design into account. This includes the display geometry

in terms of common home and target areas that deﬁne a

movement’s start and endpoint. Second, current clustering

algorithms are inherently spatial, whereas multi-step move-

ments may also come as stop-and-go movements with breaks

or decelerations along the trajectory (Dale & Duran, 2011;

Fishbach etal., 2005, 2007; Kieﬀaber etal., 2023).

We therefore suggest combining a simple spatial criterion

relating to initial decision errors with a validation of this

criterion in terms of a movement’s corresponding velocity.

As a spatial cutoﬀ, we suggest using a simple vertical cutoﬀ

line based on the display geometry of a given study. This

method allows to easily exclude movements with wrong ini-

tial decisions. Doing so focuses the analyses on trials with

completed decisions before movement start. As a spatio-

temporal method, we suggest using velocity plots to assess

whether trajectories on diﬀerent sides of the spatial cutoﬀ

do indeed come with diﬀerent attributes.1

A topical example: Eﬀect‑based action control

To demonstrate the combined application of both strategies

and to document the importance of distinguishing between

smooth single-step movements versus multi-step move-

ments, we re-evaluated a set of ﬁndings from a particular

experimental design – the response-eﬀect compatibility

paradigm (Kunde, 2001; Pﬁster etal., 2014). We chose this

speciﬁc paradigm for two reasons: First, we prefer to criti-

cize (and potentially deconstruct) our own previous work

rather than the work of others. Second, and more impor-

tantly, this area of research has its historical origin in theo-

ries of motor control (Harleß, 1862; Herbart, 1825; James,

1890; for historical comments, see Pﬁster & Janczyk, 2012;

Stock & Stock, 2004), not in theories of decision making. As

a result, investigators utilized mouse-tracking to derive con-

clusions about action execution rather than decision mak-

ing. This aim is, of course, not applicable to all research

using mouse-tracking. As we outline in the Discussion, other

research domains are particularly interested in movements

with non-completed decisions upon movement start (e.g.,

Boschet etal., 2022; Dale & Duran, 2011; Dshemuchadse

etal., 2013). Instead of disregarding these movements, such

studies might intentionally utilize experimental designs

evoking movements with incomplete decisions. If, however,

1 Another simple spatial cutoﬀ is related to the measure of x-ﬂips,

i.e., the number of directional changes along the x-axis (Dale &

Duran, 2011; Duran etal., 2010). Movements with many x-ﬂips are

commonly multi-step movements.

Attention, Perception, & Psychophysics

the underlying question is whether eﬀect anticipations inﬂu-

ence responses even beyond the categorical selection of an

action goal (Pﬁster etal., 2014), excluding inﬂuences from

(partial) errors is pivotal.

Studies using the response-eﬀect compatibility design

typically assess the content of action representations by

coupling actions with eﬀects that share or oppose charac-

teristics of the action. In other words, these experiments

introduce feature overlap (dimensional overlap; Kornblum

etal., 1990) between responses (i.e., body movements) and

response-contingent perceptual eﬀects (e.g., in the agent’s

environment). In the case of mouse-tracking, this common

feature is usually manipulated through a spatial left-versus-

right arrangement of movement targets and the visual eﬀects

that are triggered by reaching a target (Fig.1; see Pﬁster

etal., 2014; Schonard etal., 2021). These eﬀects can be

compatible (i.e., when a movement to the right evokes a

visual eﬀect on the right-hand side) or they can be incom-

patible (i.e., when a movement to the right evokes a visual

eﬀect on the hand side). Crucially, previous studies observed

ongoing movements to be attracted towards the movement-

contingent eﬀect. Put diﬀerently, if the completion of move-

ments triggered an eﬀect on the other side of the screen,

movements deviated more to that side than when they trig-

gered an eﬀect on the same side. This result was interpreted

as evidence suggesting that the visual eﬀect was anticipated

during motor execution and, thus, plays a pivotal role for

the control of eﬀerent activity. That is, these studies speciﬁ-

cally sought to investigate inﬂuences on action execution,

and regarded spatial aspects of the trajectory as “postselec-

tion measures” (Hommel etal., 2017, p.825).

In-depth analyses of a recent experiment, however, chal-

lenged this interpretation by showing that such compatibility

eﬀects may derive from a subset of movements with initial

decision errors (Tonn etal., 2023). In fact, excluding these

movements made the response-eﬀect compatibility eﬀect

disappear in spatial measures. Therefore, re-evaluating pre-

vious evidence (and previous interpretations) from this par-

ticular paradigm is ideal as a ﬁrst estimate of how prevalent

and pervasive the inﬂuence of multi-step movements is.

Method

All mouse-tracking experiments that were included in the

present re-analyses investigated the influence of action

eﬀects on action execution (Hommel etal., 2017; Pﬁster

etal., 2014; Schonard etal., 2021; Tonn etal., 2023; Wirth

etal., 2015).

Experimental design

The common denominator of all analyzed studies is that they

used a setup with ﬁve relevant areas, as shown in Fig.1:

Fig. 1 Experimental design and previously observed data pattern. (A)

Movements began in a starting area in the lower middle of the screen

and ended in one of two possible ﬁnal movement locations. Depend-

ing on the response-eﬀect compatibility mapping, action eﬀects either

occurred on the same side as the ﬁnal movement location (dotted cir-

cle) or on the respective other side (solid circle). (B) The previously

observed data pattern: Movements were biased towards the antici-

pated eﬀect location, resulting in a more curved movement trajectory

with incompatible eﬀects (solid trajectory) compared to compatible

eﬀects (dotted trajectory)

Attention, Perception, & Psychophysics

A home area at the bottom center, two target areas in the

upper left and right corner, and two eﬀect locations directly

above the target areas. Before the start of each trial, partici-

pants were informed about the current mapping of their own

responses to the ensuing eﬀects (compatible vs. incompat-

ible) through visual cues in the target areas. In other words,

compatibility was varied trial-wise, and participants could

prepare for the upcoming response-eﬀect relation. After

signaling that they were ready for the current trial by mov-

ing to the home area, an imperative stimulus instructed par-

ticipants to produce an eﬀect at either the left or the right

location. This required a movement to the target area directly

below the desired eﬀect location in the compatible condi-

tion whereas it required a movement to the respective other

target area in the incompatible condition. While participants

were instructed to execute the task as quickly and accurately

as possible, no explicit movement initiation deadline was

implemented. The underlying rationale for this design deci-

sion was to ensure that participants started the movement

only after completing their decision. Consequently, to isolate

inﬂuences on movement execution, the analyzed trajecto-

ries were truncated to the part between leaving the starting

area and reaching the target area. All experiments assessed

how anticipating an action eﬀect shapes action execution

(see Fig.1B), that is, whether movements are systematically

biased towards the location of their ensuing eﬀect. With

eﬀect sizes ranging from dz = 0.38 to dz = 1.38, all experi-

ments consistently showed that incompatible movements

were more curved than compatible movements. However, we

argue here that these eﬀects were mainly driven by incom-

plete decisions in a fraction of the trials.

Analyses

Basic approach

For analyzing mouse-movement trajectories, we used the R

package mousetRajectory (Pﬁster etal., 2024). We extracted

initiation time (IT), movement time (MT), area under the

curve (AUC), and maximum absolute deviation (MAD) from

the individual trajectories. IT was measured as the time from

the onset of the imperative stimulus until the cursor left the

starting area. MT was measured from this point in time until

the cursor arrived at the target area. AUCs were computed

as the (signed) area between the executed and the optimal

path (straight line through start and end coordinates), and

MADs were computed as the (signed) maximum orthogo-

nal deviation of the executed path from the optimal path.

Deviations towards the opposite target area were counted

as positive, whereas deviations in the other direction were

counted as negative. All movements were ﬂipped to the

right, the coordinates of each trial were time-normalized

and re-sampledwith linear interpolation before computing

AUCs and MADs, and the resulting normalized trajectories

were used for plotting.

For our re-analyses, we used a consistent approach across

studies in terms of preprocessing and outlier correction,

which naturally leads to minor diﬀerences between the re-

analyses and the original results: For all analyses, we omit-

ted trials with downward movements of the mouse, trials

with errors, and outlier trials. Outliers were deﬁned as trials

where any of the four measures deviated more than 2.5 SDs

from the corresponding cell mean, computed separately for

each participant and condition. For brevity, we report only

the eﬀect of compatibility, and omit the inﬂuences of all

other experimental factors (i.e., we report F-statistics for

the main eﬀect of compatibility in multifactorial designs and

t-statistics in unifactorial designs). Full data sets and analy-

sis scripts are available via the Open Science Framework at:

https:// osf. io/ hrpk6.

Trial‑level analyses

All studies reported a consistent impact of upcoming action

eﬀects on movement trajectories which had previously been

taken to suggest an important role of action eﬀect represen-

tations for motor control (Hommel etal., 2017; Pﬁster etal.,

2014; Schonard etal., 2021; Wirth etal., 2015). The sug-

gested spatial criterion for detecting multi-step movements

(including initial decision errors) provides a simple and

elegant tool to assess the truth value of this interpretation.

Therefore, we separated all movements previously clas-

siﬁed as correct (i.e., movements ending on the correct

target area) into two groups: Movements directly starting

towards the correct target and movements ﬁrst starting to

the wrong side and later changing the course of movement.

This excludes movements with initially wrong decisions and

puts increased focus on data points with completed decisions

upon movement start. The question was whether previously

observed eﬀects persist when only taking these latter move-

ments into account. Our classiﬁcation was implemented by

excluding all movements with x-values going below the low-

est x-value of the starting area, resulting in a vertical cutoﬀ

line touching the starting area on the left (see Fig.2). This

criterion classiﬁed more incompatible than compatible trials

as multi-step movements, which is consistent with response-

time studies reporting more commission errors with incom-

patible action-eﬀect mappings than with compatible map-

pings (e.g., Kunde, 2001).

Using one representative experiment, Fig.3 demonstrates

the impact of this cutoﬀ by showing how average trajecto-

ries – as commonly used to visualize experimental results

– change when multi-step movements are excluded.

Second, we show for each experiment how inferential

statistics change, that is, how the eﬀect evolves, when the

criterion is used and then relaxed from its original location

Attention, Perception, & Psychophysics

(i.e., on the left side of the starting area) up to the middle of

the wrong target area. In other words, we plot the standard-

ized eﬀect size of the compatibility eﬀect in the AUC as a

function of this cutoﬀ criterion.

As a further check for our spatial criterion, we pro-

vide corresponding velocity information for the two

diﬀerent movement types for every experiment via veloc-

ity proﬁle plots. To account for variability in the timing

of decision changes, we identiﬁed the point of maximum

absolute deviation within each trajectory and time-nor-

malized velocities from the start of the movement up to

this timepoint as well as from this timepoint to the end of

Fig. 2 Visualization of the cutoﬀ-criterion. Data from three example

participants. (A) Average trajectories over all trajectories (dashed,

dark gray lines), over trajectories excluded by the cutoﬀ criterion

(solid, light gray lines), and over trajectories surviving the cutoﬀ cri-

terion (solid, black lines). (B) Individual movements going into the

averages trajectories displayed in panel A. The vertical line visualizes

the cutoﬀ criterion

Fig. 3 Average trajectories for one exemplary experiment (Pﬁster

etal., 2014, Exp. 2). Average trajectories when using all movements

(left) and when excluding multi-step movements (right). Although

participant averages (thin lines) are smooth and do not cross our

exclusion criterion, the response-eﬀect compatibility eﬀect in spatial

measures completely vanishes when multi-step movement trials are

excluded: Compatible (blue) and incompatible (red) average trajecto-

ries overlap for single-step movements

Attention, Perception, & Psychophysics

the movement (see Fig.4 for an explanation of this novel

procedure).

Results

Table1 provides a summary over all re-analyzed experi-

ments, highlighting how the results change when multi-step

movements are excluded with the proposed cutoﬀ criterion.

Due to consistency in the pattern of results across all experi-

ments, we textually describe only one re-analysis in detail

in the main text. Detailed descriptions and visualizations

of the other experiments are available in the Appendix. We

focus on the Experiment 2 of Pﬁster etal. (2014) because

it served as the design template for all subsequent studies

investigating response-eﬀect compatibility eﬀects using

mouse-tracking.

Using all available data, a compatibility effect was

observed for all four measures in Experiment 2 of Pﬁs-

ter etal. (2014). Compatible actions had smaller AUCs

(-0.1 × 103 vs. 2.7 × 103 px2), t(19) = 3.59, p = .002, dz = 0.80,

smaller MADs (0.8 vs. 15.6 px), t(19) = 3.94, p = .001,

dz = 0.88, shorter ITs (639 vs. 693 ms), t(19) = 5.81, p < .001,

dz = 1.30, and shorter MTs (421 vs. 457 ms), t(19) = 3.12,

p = .006, dz = 0.70, than incompatible actions.

As expected, our cutoﬀ criterion excluded fewer com-

patible than incompatible movements (9.8% vs. 17.5%),

t(19) = 4.04, p = .001, dz = 0.90. When applying this cutoﬀ

criterion, the compatibility eﬀect vanished in the spatial

measures of AUC, |t| < 1, and MAD, |t|< 1. In the timing

measures, the test for the ITs remained signiﬁcant, with

compatible actions being initiated faster than incompatible

actions (634 vs. 706 ms), t(19) = 6.31, p < .001, dz = 1.41,

whereas the eﬀect in MTs vanished, |t|< 1.

Panel A of Fig.5 shows that the compatibility effect

remains non-signiﬁcant even when our criterion is relaxed to

permit movements to travel up to 40% of the horizontal dis-

tance towards the incorrect target area. Panel B of Fig.5 illus-

trates that this simple cutoﬀ criterion successfully classiﬁes the

movements into two distinct subgroups with markedly diﬀer-

ent velocity proﬁles: Single-step movements display a smooth

velocity around the time of reaching MAD, whereas multi-step

movements display a deceleration that is followed by a sub-

stantial acceleration around the time of reaching MAD.

Discussion

This paper had two diﬀerent aims. The ﬁrst aim was to sug-

gest an easy-to-implement method that separates two groups

of mouse trajectories with diﬀerent underlying processes.

The second aim was to apply this method to published

experiments within one exemplary ﬁeld and to examine how

the interpretation of previous data is aﬀected by these dif-

ferent groups of trials.

To distinguish between smooth single-step movements

and multi-step movements in which an initial, incomplete

decision is revised along the movement trajectory, a verti-

cal cutoﬀ criterion was implemented. This spatial criterion

is straightforward to implement and eﬀectively separates

both movement types, as evidenced by the velocity proﬁle

plots: While single-step movements exhibited rather smooth

velocity proﬁles with high speeds at the point of maximum

deviation, multi-step movements exhibited a pronounced

deceleration before and rapid acceleration after the point of

maximum deviation (Vogel etal., 2018). Thus, the binary

classiﬁcation (multistep: yes or no?) provided by our simple

criterion suﬃces to illustrate the presence of (at least) two

Fig. 4 Explanation of the velocity proﬁle plots. For all (time-nor-

malized) trajectories, the timepoint of maximal orthogonal deviation

(MAD) from the ideal line is computed (left). Trajectories are then

separated into pre- and post-MAD parts (middle). The resulting sub-

trajectories are time-normalized again before velocities can be aver-

aged (right). The solid and dashed lines illustrate two exemplary,

individual trajectories. Note that even if two movements exhibit their

MAD at a similar point on the ideal line (left), the timepoint of the

MAD might vary substantially (middle), necessitating a per-move-

ment, temporal alignment of the velocities (right)

Attention, Perception, & Psychophysics

Table 1 Overview of the re-analyzed experiments

Exp. Goal of the experiment Experimental

manipulations

Number of

trialsa

DV REC eﬀect without application of the cutoﬀ

criterionb

REC eﬀect with application of the cutoﬀ

criterionb

Pﬁster etal. (2014)

Exp. 1 First experiment that investigated REC

with mouse-tracking

REC 224 AUC t(19) = 2.75, p = .013, dz = 0.61 (15.8 × 103

vs. 16.9 × 103 px2)

t(19) = 1.89, p = .073, dz = 0.42

MAD t(19) = 2.58, p = .018, dz = 0.58 (64.1 vs.

68.1 px)

t(19) = 1.17, p = .258, dz = 0.26

IT t(19) = 2.33, p = .031, dz = 0.52 (652 vs.

672 ms)

t(19) = 2.17, p = .043, dz = 0.49 (654 vs. 672 ms)

MT t(19) = 3.17, p = .005, dz = 0.71 (590 vs.

628 ms)

t(19) = 2.77, p = .012, dz = 0.62 (578 vs. 598 ms)

%CC t(19) = 3.19, p = .005, dz = 0.71 (5.9% vs.

10.3%)

Exp. 2 In contrast to Exp. 1, participants did not

have to start their movement upwards

and thus, were able to take the direct

path

REC 224 AUC t(19) = 3.59, p = .002, dz = 0.80 (-0.1 × 103

vs. 2.7 × 103 px2)

|t|< 1

MAD t(19) = 3.94, p = .001, dz = 0.88 (0.8 vs.

15.6 px)

|t|< 1

IT t(19) = 5.81, p < .001, dz = 1.30 (639 vs.

693 ms)

t(19) = 6.31, p < .001, dz = 1.41 (634 vs. 706 ms)

MT t(19) = 3.12, p = .006, dz = 0.70 (421 vs.

457 ms)

|t|< 1

%CC t(19) = 4.04, p = .001, dz = 0.90 (9.8% vs.

17.5%)

Wirth etal. (2015)

Exp. 1 Where is the locus of the mouse-tracking

REC eﬀect?

Dual tasking, “locus of slack” logic

Task 1: pitch discrimination

Task 2: REC with mouse-tracking

REC × stimulus

onset asynchrony

348 AUC F(1, 15) = 7.63, p = .015, ηp

2 = .34 (0.7 × 103

vs. 2.8 × 103 px2)

F < 1

MAD F(1, 15) = 8.19, p = .012, ηp

2 = .35 (4.2 vs.

15.0 px)

F < 1

IT F(1, 15) = 26.50, p < .001, ηp

2 = .64 (880 vs.

950 ms)

F(1, 15) = 27.17, p < .001, ηp

2 = .64 (879 vs.

950 ms)

MT F(1, 15) = 13.58, p = .002, ηp

2 = .48 (375 vs.

399 ms)

F(1, 15) = 1.70, p = .212, ηp

2 = .10

%CC t(15) = 4.30, p = .001, dz = 1.08 (9.4% vs.

17.1%)

Attention, Perception, & Psychophysics

Table 1 (continued)

Exp. Goal of the experiment Experimental

manipulations

Number of

trialsa

DV REC eﬀect without application of the cutoﬀ

criterionb

REC eﬀect with application of the cutoﬀ

criterionb

Exp. 2 Dual tasking, “eﬀect propagation” logic:

Task 1: REC with mouse-tracking

Task 2: pitch discrimination

REC × stimulus

onset asynchrony

348 AUC F(1, 15) = 4.53, p = .050, ηp

2 = .23 F < 1

MAD F(1, 15) = 6.40, p = .023, ηp

2 = .30 (22.8 vs.

27.9 px)

F(1, 15) = 1.00, p = .334, ηp

2 = .06

IT F(1, 15) = 3.55, p = .079, ηp

2 = .19 F(1, 15) = 3.87, p = .068, ηp

2 = .21

MT F(1, 15) = 9.78, p = .007, ηp

2 = .39 (1015 vs.

1091 ms)

F(1, 15) = 7.66, p = .014, ηp

2 = .34 (988 vs. 1053

ms)

%CC t(15) = 2.26, p = .039, dz = 0.56 (13.0% vs.

16.6%)

Hommel etal. (2017)

Exp. 1 Do REC eﬀects stem from sensory or

aﬀective compatibility? Is this diﬀeren-

tially aﬀected by whether actions are free

vs. forced choice?

sensory

RECc × aﬀective

RECc × free vs.

forced choice

240 AUC F(1, 34) = 10.41, p = .003, ηp

2 = .23

(3.2 × 103 vs. 5.3 × 103 px2)

F(1, 34) = 5.45, p = .026, ηp

2 = .14 (-0.7 × 103

vs. 0.3 × 103 px2)

MAD F(1, 34) = 9.77, p = .004, ηp

2 = .22 (17.7 vs.

27.6 px)

F(1, 34) = 4.76, p = .036, ηp

2 = .12 (-2.4 vs. 1.5

px)

IT F(1, 34) = 7.19, p = .011, ηp

2 = .17 (496 vs.

507 ms)

F(1, 34) = 5.38, p = .027, ηp

2 = .14 (497 vs. 507

ms)

MT F(1, 34) = 5.69, p = .023, ηp

2 = .14 (339 vs.

347 ms)

F(1, 34) = 5.24, p = .028, ηp

2 = .13 (317 vs. 324

ms)

%CC t(34) = 4.82, p < .001, dz = 0.81 (16.5% vs.

22.3%)

Schonard etal. (2021)

Exp. 1 Can mouse-tracking REC eﬀects be repli-

cated in a simpliﬁed setting?

REC × free vs.

forced choice

240 AUC F(1, 19) = 23.22, p < .001, ηp

2 = .55

(22.7 × 103 vs. 33.7 × 103 px2)

F(1, 19) = 3.05, p = .097, ηp

2 = .14

MAD F(1, 19) = 23.00, p < .001, ηp

2 = .55 (32.4

vs. 51.7 px)

F(1, 19) = 3.02, p = .098, ηp

2 = .14

IT F(1, 19) = 3.77, p = .067, ηp

2 = .17 F(1, 19) = 3.50, p = .077, ηp

2 = .16

MT F(1, 19) = 30.65, p < .001, ηp

2 = .62 (544 vs.

572 ms)

F(1, 19) = 6.43, p = .020, ηp

2 = .25 (535 vs. 552

ms)

%CC t(19) = 5.52, p < .001, dz = 1.23 (7.1% vs.

16.1%)

Attention, Perception, & Psychophysics

Table 1 (continued)

Exp. Goal of the experiment Experimental

manipulations

Number of

trialsa

DV REC eﬀect without application of the cutoﬀ

criterionb

REC eﬀect with application of the cutoﬀ

criterionb

Exp. 2 Is the mouse-tracking REC eﬀect subject

to sequential modulation?

REC × previous

RECd

240 AUC t(39) = 4.37, p < .001, dz = 0.69 (63.2 × 103

vs. 72.7 × 103 px2)

t(39) = 1.02, p = .312, dz = 0.16

MAD t(39) = 4.22, p < .001, dz = 0.67 (92.5 vs.

108.1 px)

|t|< 1

IT t(39) = 5.15, p < .001, dz = 0.81 (602 vs.

645 ms)

t(39) = 5.80, p < .001, dz = 0.92 (604 vs. 658 ms)

MT t(39) = 4.75, p < .001, dz = 0.75 (633 vs.

661 ms)

t(39) = 3.14, p = .003, dz = 0.50 (613 vs. 628 ms)

%CC t(39) = 5.11, p < .001, dz = 0.81 (11.1% vs.

17.4%)

Exp. 3 Excludes dimensional overlap between

stimuli and eﬀects

REC × free vs.

forced choice

240 AUC F(1, 39) = 8.89, p = .005, ηp

2 = .19

(13.8 × 103 vs. 19.3 × 103 px2)

F(1, 39) = 5.42, p = .025, ηp

2 =.12(7.2 × 103 vs.

9.7 × 103 px2)

MAD F(1, 39) = 8.63, p = .006, ηp

2 = .18 (20.7 vs.

30.3 px)

F(1, 39) = 4.94, p = .032, ηp

2 = .11 (9.5 vs. 13.0

px)

IT F(1, 39) = 10.66, p = .002, ηp

2 = .21 (633 vs.

653 ms)

F(1, 39) = 11.69, p = .001, ηp

2 = .23 (634 vs.

657 ms)

MT F(1, 39) = 2.90, p = .097, ηp

2 = .07 F < 1

%CC t(39) = 2.78, p = .008, dz = 0.44 (8.6% vs.

11.8%)

Tonn etal. (2023)

Exp. 1 Can REC eﬀects be observed for actions

that prevent (instead of produce) sensory

eﬀects? Typical actions that produce sen-

sory eﬀects serve as baseline condition

REC × eﬀect-

preventing vs.

eﬀect-producing

actions

312 AUC F(1, 42) = 13.98, p = .001, ηp

2 = .25

(3.5 × 103 vs. 6.2 × 103 px2)

F < 1

MAD F(1, 42) = 17.48, p < .001, ηp

2 = .29 (16.5

vs. 30.6 px)

F < 1

IT F(1, 42) = 34.62, p < .001, ηp

2 = .45 (632 vs.

673 ms)

F(1, 42) = 48.99, p < .001, ηp

2 = .54 (634 vs.

683 ms)

MT F(1, 42) = 47.93, p < .001, ηp

2 = .53 (506 vs.

562 ms)

F(1, 42) = 30.12, p < .001, ηp

2 = .42 (481 vs.

524 ms)

%CC t(42) = 5.01, p < .001, dz = 0.76 (13.7% vs.

21.2%)

Attention, Perception, & Psychophysics

Exp. Goal of the experiment Experimental

manipulations

Number of

trialsa

DV REC eﬀect without application of the cutoﬀ

criterionb

REC eﬀect with application of the cutoﬀ

criterionb

Exp. S1 In contrast to Exp. 1, to-be-produced and

to-be-prevented eﬀects were no longer

associated with monetary gains/losses

REC × eﬀect-

preventing vs.

eﬀect-producing

actions

312 AUC F(1, 40) = 14.91, p < .001, ηp

2 = .27

(3.7 × 103 vs. 6.5 × 103 px2)

F < 1

MAD F(1, 40) = 17.08, p < .001, ηp

2 = .30 (16.9

vs. 30.9 px)

F < 1

IT F(1, 40) = 40.36, p < .001, ηp

2 = .50 (588 vs.

635 ms)

F(1, 40) = 52.36, p < .001, ηp

2 = .57 (591 vs.

646 ms)

MT F(1, 40) = 31.24, p < .001, ηp

2 = .44 (423 vs.

461 ms)

F(1, 40) = 9.30, p = .004, ηp

2 = .19 (401 vs. 422

ms)

%CC t(40) = 6.14, p < .001, dz = 0.96 (12.7% vs.

21.9%)

Exp. S2 In contrast to Exp. 2, unsuccessful eﬀect-

preventing actions were no longer associ-

ated with unpleasant auditive eﬀects

REC × eﬀect-

preventing vs.

eﬀect-producing

actions

312 AUC F(1, 40) = 28.88, p < .001, ηp

2 = .42

(3.6 × 103 vs. 7.1 × 103 px2)

F < 1

MAD F(1, 40) = 30.86, p < .001, ηp

2 = .44 (18.0

vs. 35.4 px)

F < 1

IT F(1, 40) = 96.42, p < .001, ηp

2 = .71 (538 vs.

579 ms)

F(1, 40) = 72.79, p < .001, ηp

2 = .65 (541 vs.

589 ms)

MT F(1, 40) = 85.02, p < .001, ηp

2 = .68 (449 vs.

491 ms)

F(1, 40) = 28.89, p < .001, ηp

2 = .42 (423 vs.

448 ms)

%CC t(40) = 8.55, p < .001, dz = 1.34 (15.9% vs.

25.3%)

Exp. S3 Eﬀect-producing actions only REC 156 AUC t(45) = 3.84, p < .001, dz = 0.57 (6.1 × 103

vs. 9.1 × 103 px2)

t(45) = 1.44, p = .156, dz = 0.21

MAD t(45) = 4.12, p < .001, dz = 0.61 (26.8 vs.

43.0 px)

t(45) = 1.62, p = .111, dz = 0.24

IT t(45) = 5.56, p < .001, dz = 0.82 (573 vs.

609 ms)

t(45) = 5.23, p < .001, dz = 0.77 (580 vs. 621 ms)

MT t(45) = 7.06, p < .001, dz = 1.04 (506 vs.

561 ms)

t(45) = 4.16, p < .001, dz = 0.61 (475 vs. 515 ms)

%CC t(45) = 5.88, p < .001, dz = 0.87 (17.3% vs.

25.4%)

DVdependent variable; REC response eﬀect compatibility; ITinitiation time, MTmovement time; AUCarea under the curve; MADmaximum absolute distance; %CCpercentage of trials that

were classiﬁed by the cutoﬀ criterion and excluded as multistep movements. For signiﬁcant diﬀerences, descriptive values for the compatible (ﬁrst descriptive value) and incompatible (second

descriptive value) condition are provided

a Number of trials denotes the total number of trials for each participant, prior to any exclusions. In all experiments, participants worked through an equal amount of compatible and incompatible

trials

b For brevity, only the eﬀect of compatibility is reported, and inﬂuences of all other experimental factors are omitted. Thus, in multifactorial designs, F-statistics for the main eﬀect of compatibil-

ity are reported, whereas in unifactorial designs, t-statistics are reported

c Sensory compatibility denotes whether the location of an eﬀects corresponds to the movement direction (i.e., “typical” spatial dimensional overlap as in the other experiments). Aﬀective com-

patibility denotes whether a positive or negative event must be approached by the movement

d We omitted the factor “REC in the previous trial”’ and treated the data like a unifactorial design

Table 1 (continued)

Attention, Perception, & Psychophysics

markedly diﬀerent trajectory types that are mixed up when

relying solely on average statistics.

In fact, the re-analyses of previous experiments revealed

that a major proportion of the systematic variance in spatial

measures resulted from multi-step movements, which con-

stituted only a minor portion of the trials. In 10 out of 12

experiments, the compatibility eﬀect in AUCs and MADs

completely vanished after excluding movements starting

in the wrong direction. This supports a recent speculation

suggesting that these initial movements towards the wrong

location may be the driving factor for inﬂuences on spatial

trajectory markers in response-eﬀect compatibility setups

(Tonn etal., 2023), and therefore speaks against previous

interpretations which ascribed these inﬂuences to a continu-

ous activation of the anticipated perceptual eﬀects (Hommel

etal., 2017; Pﬁster etal., 2014). It is important to note that

across all experiments, the response-eﬀect compatibility

eﬀect for initiation times remained signiﬁcant (and some-

times even increased in magnitude) after excluding trials

with initial decision errors. Thus, while our analyses yielded

no evidence for an inﬂuence on motor execution, temporal

measures indicated a strong inﬂuence of response-eﬀect

compatibility on decision making.

But why diﬀerentiate between diﬀerent types of move-

ments and investigate where the compatibility eﬀect origi-

nates from? The question of whether an anticipated action

eﬀect is represented is indeed not aﬀected by this distinction.

However, in the ideomotor framework, mouse-tracking was

speciﬁcally employed to make precise inferences on when

and how the anticipated action eﬀect inﬂuences movements

(Hommel etal., 2017; Pﬁster etal., 2014), that is, which

action stages are aﬀected by eﬀect anticipations. In other

words, observed inﬂuences were ascribed to a speciﬁc phase

within a movement, to action execution, which in this con-

text referred to the eﬀerent activity that follows a completed

decision. Thus, identifying the impact of movements ini-

tially starting into the wrong direction is critical because,

in these trials, the decision phase was not completed before

movement start. From our analyses we can conclude that the

eﬀects in the average trajectories do not primarily originate

from movements starting with a completed decision towards

the correct location. Therefore, the observed deviations in

incompatible trajectories do not yield evidence for a continu-

ous activation of the anticipated perceptual eﬀects of the

movement during its execution: This pattern mainly reﬂects

decision errors during action selection instead.

Consequently, we suggest that researchers implement

design features that hamper decision changes within the

mouse-tracking paradigm or, alternatively, cross-validate

results through other approaches when aiming to make infer-

ences on movement execution rather than action selection.

However, is it even possible to unequivocally separate action

execution from decision making? At a broad level, one might

argue that movements without changes-of-mind represent

“pure” motor execution. On a more nuanced level, how-

ever, movements inherently involve a decision-making and

planning component, as the system continuously “decides”

whether (and how) to adjust the execution of an action. Con-

sequently, a movement may contain decisional inﬂuences

even when excluding all initial decision errors. Conversely,

not all discontinuities (e.g., rapid speed or direction changes)

necessarily indicate an erroneous initial decision but could

likewise result from a correct decision where the execution

failed at any point (e.g., due to muscle twitches). Neverthe-

less, in either scenario it can be argued that discontinui-

ties in the movements reﬂect decision making while acting

(Netick & Klapp, 1994; Vogel etal., 2024), irrespective of

whether an erroneous decision or an erroneous execution is

corrected.

Of course, mouse-tracking is not always utilized to make

inferences on “pure” motor execution without leakage of

decisional processes. Rather, various ﬁelds of research

employ methods that aim at increasing (instead of decreas-

ing) the temporal overlap of action selection and action

execution to tightly couple cognitive and motor processes.

Such approaches may include instructing participants to

start moving swiftly (Freeman & Ambady, 2011; Hehman

etal., 2015; Stolier & Freeman, 2016) or displaying

imperative stimuli only after movement onset (e.g., Kies-

lich etal., 2020; Scherbaum & Kieslich, 2018; Schoemann

etal., 2019). Thus, movements with incomplete or erro-

neous decisions are the primary research target there and

should not be excluded from the analyses. However, as

many studies are based on the assumption that cognitive

processes manifest in the movement at the point in time

where they occur (Dshemuchadse etal., 2013; Stillman

etal., 2018), analyzing velocity proﬁles, as demonstrated

here, provides vital new insights: It has recently been stated

that interruptions in the form of pauses in the movement

decouple the cognition-movement connection (Schoemann

etal., 2021). Consequently, there are eﬀorts to exclude

such trials by eliminating the respective data points (e.g.,

Schonard etal., 2021) or by introducing design features

that make pauses less likely, for example, by reducing

the overall time limit (e.g., Boschet etal., 2022; Garcia-

Guerrero etal., 2022). While this is a promising start-

ing point towards more straightforward interpretations,

it might only exclude a fraction of the movements where

the cognition-movement connection is decoupled: Error

research suggests that neural correlates of error processing

can start even before the erroneous response is initiated

(Yeung etal., 2004). Consequently, errors can be canceled

extremely quickly or are even corrected on the ﬂy (Foer-

ster etal., 2022a, b). As error correction times are very

short (e.g., Cooke & Diggles, 1984), the time until the

corrective movement is initiated might be shorter than the

Attention, Perception, & Psychophysics

time required to overcome the mass-inertia of the hand

executing the erroneous movement. Therefore, the phases

of decelerating the movement in the direction of the wrong

response and accelerating the movement in the direction

of the correct response might overlap, raising the ques-

tion whether the two components are indeed always sepa-

rated by a complete stop. Consequently, researchers are

well advised to explicitly check not only for pauses, but

also for dips in the velocity proﬁles because any kind of

velocity change (e.g., a notable deceleration of the move-

ment) might indicate a decoupling of the cognition-move-

ment connection and thereby hide processes taking place.

A more detailed look into the origin of observed eﬀects

regarding velocities within a movement, trajectories on

a by-participant and by-trial level, and a speciﬁcation of

whether these eﬀects depict errors or a deliberate strategy

to postpone a decision (Wong & Haith, 2017), can advance

the interpretations drawn from mouse-tracking experiments

in various ﬁelds.

How do the current methodological considerations inform

ideomotor theorizing? Inﬂuences of eﬀect anticipations on

action execution have not only been investigated by evidently

metric movement trajectories, but also by metric aspects of

seemingly discrete keypress movements such as duration

or force of the executed keypress. This raises the question

of whether the current results also have implications for

the interpretation of these experiments. In other words, do

experimental setups in which anticipated eﬀects manifest

in the parameters of executed actions generally reﬂect only

decisional inﬂuences? We believe that this is not the case.

In mouse-tracking setups, participants have ample time to

correct an incorrect response during its execution. Most

keypress experiments, however, do not provide this oppor-

tunity (notable exceptions are mainly found in literature

on error processing; e.g., Crump & Logan, 2013; Rabbitt,

1966). Instead, participants usually know that the onset of a

keypress immediately categorizes their movement as either

correct or wrong. If an initially incorrect response exceeds

the key’s activation threshold, the trial is directly classiﬁed

as error, regardless of whether the correct key is pressed

afterwards. In these designs, the onset of a keypress serves

as a natural barrier beyond which a change of mind can no

longer be implemented. Therefore, if anticipated eﬀects still

inﬂuence action execution after the onset of the keypress,

this suggests that the observed inﬂuences go beyond a deci-

sional component.

We recently investigated keypress durations (i.e., the time

between pressing and releasing a key; Pﬁster etal., 2023;

Shin etal., 2023) in such a design and indeed found the

duration of keypresses to be biased towards the duration of

irrelevant auditory eﬀects (Tonn etal., 2023). Similarly, in

a study investigating motor sequences, execution times (i.e.,

the time between the onsets of the ﬁrst and the last keypress)

showed assimilative inﬂuences of temporal eﬀect anticipa-

tions (Brown etal., 2022). Together, these results suggest

that response-eﬀect compatibility eﬀects in action execution

Fig. 5 Results from Pﬁster etal. (2014), Experiment 2. (A) Compat-

ibility eﬀect in area under the curve (AUC) as a function of the used

cutoﬀ criterion. The x-axis indicates the allowed horizontal move-

ment between the center of starting area and the center of the wrong

target area, normalized to percentage. The y-axis indicates the stand-

ardized eﬀect size. The dashed vertical line indicates the cutoﬀ used

in the text. (B) Velocity proﬁles for all movements (left), and move-

ments classiﬁed with the cutoﬀ criterion. The light-gray line depicts

movements excluded from the analysis while the black line depicts

movements remaining in the analysis. The solid vertical lines mark

the point of maximal deviation from an ideal trajectory, with times on

the x-axis normalized to percentage from start up this point to as well

as from this point to reaching the target

Attention, Perception, & Psychophysics

are not generally driven by categorical decision making.

Interestingly, actions have not only been reported to align

with features of the ensuing eﬀects, but also to diverge from

them. For instance, contrast eﬀects were observed when par-

ticipants were speciﬁcally instructed to press a key for either

a short or a long duration (Kunde, 2003), or with low or high

force (Kunde etal., 2004; Thébault etal., 2020), resulting in

tones of varying lengths or intensities. Unlike experiments

that found assimilation eﬀects, these experiments involved

task-relevant action features. Thus, it is conceivable that for

task-relevant features, participants intuitively counteracted

the natural tendency to align their actions with the antici-

pated eﬀect to prevent errors.

Conclusion

Decision errors are pervasive in mouse-tracking studies.

Understood in the context of a single response, such decision

errors relate to a response that is initiated in a wrong direc-

tion but might be corrected later during the movement. If an

experiment seeks to measure any inﬂuence of an experimen-

tal condition, such decision errors do not pose a concern.

They are of substantial concern, however, if researchers

intend to speciﬁcally investigate how completed decisions

are put into motion: Not accounting for changes of mind

during the execution of an action leads to erroneous inter-

pretation of aggregate statistics. Thus, when investigating

what movement kinematics reveal about human cognition,

researchers are well advised to take full advantage of the

rich information inherent in every single trajectory instead

of interpreting the shape of average trajectories.

Appendix

This appendix discusses the usage of an additional velocity

criterion and provides the complete results and visualiza-

tions for all experiments which were not described in detail

in the main body.

Velocities asadditional criterion

Although spatial information is an important characteristic

of the multi-step movements we aim to exclude (i.e., trials

that initially start into the wrong direction), a spatial cut-

oﬀ-criterion might fail to identify some multi-step move-

ments and conversely, might classify some smooth move-

ments as multi-step. To address this, we supplemented our

analyses with velocity proﬁle plots and visualizations of

the empirical eﬀect as function of diﬀerent cutoﬀ values.

The velocity proﬁle plots demonstrate that our criterion

can partition the movements into two disjunct sets, each

displaying the acceleration characteristics expected of

either multi-step or single-step movements. Additionally,

the visualizations of the adjusted cutoﬀ-values show that

the pattern of results remains stable regardless of whether

the cutoﬀ is positioned exactly at the border of the start-

ing area. Although such adjustments do not enhance the

inherent accuracy of the classiﬁer itself, making the cut-

oﬀ more lenient or more stringent can alter the balance

between false-positives and false-negatives. Improving

overall accuracy could be possible by, for example, using

the velocity around the point of reaching MAD as an addi-

tional criterion.

In the current re-analyses, however, this approach comes

with a substantial drawback: Because the velocities around

the point of reaching the MAD were used as means to vali-

date the spatial criterion, using them as additional quantita-

tive criterion would undermine the validation process. Yet,

if another validation method is available – such as manual

labeling of movements – or if validation is not a major

concern, then velocity proﬁles could indeed serve as sup-

plementary quantitative criterion to enhance classiﬁcation

accuracy. Speciﬁcally, we propose using the velocity at the

point of reaching MAD, relative to some characteristic of

the trial’s velocity distribution, such as maximum or median

speed. Similarly, exploring other movement characteristics

around the point of reaching MAD, for example the rate

of change in movement direction (angular velocity), could

also be beneﬁcial. Incorporating multiple criteria into an

ensemble classiﬁer might improve overall categorization

performance, potentially oﬀering a more accurate approach

for distinguishing between multi-step and single-step move-

ments. For researchers particularly interested in the meth-

odology of mouse tracking per se, velocity-based classiﬁca-

tions could be of substantial beneﬁt. We added an exemplary

script to the OSF repository that, for the main experiment of

this article, compares our spatial criterion with a criterion

taking velocity around MAD into account.

Nonetheless, we believe that the main strength and unique

advantage of our current criterion lies in its simplicity,

especially when compared to other methods that are more

advanced and thus more diﬃcult to implement. In our view,

its performance is quite satisfying, and the additional eﬀort

required for more complex methods may pose a signiﬁcant

barrier for researchers that consider mouse tracking to be

just one part of a broader toolkit for investigating other

research areas. For such researchers, our criterion likely

provides a good balance of eﬃciency and eﬀectiveness.

Pﬁster etal. (2014)

Using all available data, a compatibility eﬀect was observed

for all four measures. Compatible actions had smaller AUCs

(15.8 × 103 vs. 16.9 × 103 px2), t(19) = 2.75, p = .013, dz

Attention, Perception, & Psychophysics

= 0.61, smaller MADs (64.1 vs. 68.1 px), t(19) = 2.58, p =

.018, dz = 0.58, shorter ITs (652 vs. 672 ms), t(19) = 2.33, p

= .031, dz = 0.52, and shorter MTs (590 vs. 628 ms), t(19) =

3.17, p = .005, dz = 0.71, than incompatible actions.

As expected, our cutoﬀ criterion excluded fewer compat-

ible than incompatible movements (5.9% vs. 10.3%), t(19)

= 3.19, p = .005, dz = 0.71. When applying our cutoﬀ crite-

rion, the compatibility eﬀect vanished in the spatial meas-

ures of AUC, t(19) = 1.89, p = .073, dz = 0.42, and MAD,

t(19) = 1.17, p = .258, dz = 0.26. In contrast, it remained

present only in the timing measures: Compatible actions had

shorter ITs (654 vs. 672 ms), t(19) = 2.17, p = .043, dz =

0.49, and shorter MTs (578 vs. 598 ms), t(19) = 2.77, p =

.012, dz = 0.62, than incompatible actions.

Figure6 shows the results for Experiment 1 in Pﬁster

etal. (2014).

Wirth etal. (2015)

Using all available data of Experiment 1, a compatibil-

ity eﬀect was observed for all four measures. Compatible

actions had smaller AUCs (0.7 × 103 vs. 2.8 × 103 px2),

F(1, 15) = 7.63, p = .015, ηp

2 = .34, smaller MADs (4.2 vs.

15.0 px), F(1, 15) = 8.19, p = .012, ηp

2 = .35, shorter ITs

(880 vs. 950 ms), F(1, 15) = 26.50, p < .001, ηp

2 = .64, and

shorter MTs (375 vs. 399 ms), F(1, 15) = 13.58, p = .002,

ηp

2 = .48, than incompatible actions. Note that the original

paper did not analyze MAD.

As expected, our cutoﬀ criterion excluded fewer compat-

ible than incompatible movements (9.4% vs. 17.1%), t(15) =

4.30, p = .001, dz = 1.08. When applying our cutoﬀ criterion,

the compatibility eﬀect vanished in the spatial measures of

AUC, F < 1, and MAD, F < 1. In the timing measures, the

test for the ITs remained signiﬁcant, with compatible actions

initiated faster than incompatible actions (879 vs. 950 ms),

F(1, 15) = 27.17, p < .001, ηp

2 = .64, whereas the eﬀect in

MTs vanished, F(1, 15) = 1.70, p = .212, ηp

2 = .10.

Using all available data of Experiment 2, no eﬀect was

observed for AUCs, F(1, 15) = 4.53, p = .050, ηp

2 = .23,

but compatible actions had smaller MADs than incompat-

ible actions (22.8 vs. 27.9 px), F(1, 15) = 6.40, p = .023,

ηp

2 = .30. In the timing measures, ITs did not diﬀer, F(1,

15) = 3.55, p = .079, ηp

2 = .19, but MTs were shorter with

compatible than with incompatible actions (1015 vs. 1091

ms), F(1, 15) = 9.78, p = .007, ηp

2 = .39.

As expected, our cutoﬀ criterion excluded fewer compat-

ible than incompatible movements (13.0% vs. 16.6%), t(15)

= 2.26, p = .039, dz = 0.56. When applying our cutoﬀ crite-

rion, the compatibility eﬀect vanished in the spatial meas-

ures of AUC, F < 1, and MAD, F(1, 15) = 1.00, p = .334,

Fig. 6 Results from Pﬁster etal. (2014), Experiment 1. (A) Compat-

ibility eﬀect in AUC as a function of the used cutoﬀ criterion. The

x-axis indicates the allowed horizontal movement between the center

of starting area and the center of the wrong target area, normalized

to percentage. The y-axis indicates the standardized eﬀect size. The

dashed vertical line indicates the cutoﬀ used in the text. (B) Velocity

proﬁles for all movements (left), and movements classiﬁed with the

cutoﬀ criterion. The light-grey line depicts movements excluded from

the analysis while the black line depicts movements remaining in the

analysis. The solid vertical lines mark the point of maximal deviation

from an ideal trajectory, with times on the x-axis normalized to per-

centage from start up this point to as well as from this point to reach-

ing the target

Attention, Perception, & Psychophysics

ηp

2 = .06. In the timing measures, ITs did not diﬀer, F(1,

15) = 3.87, p = .068, ηp

2 = .21, but MTs were shorter with

compatible than with incompatible actions (988 vs. 1053

ms), F(1, 15) = 7.66, p = .014, ηp

2 = .34.

Figure7 shows the results for Experiment 1 and Experi-

ment 2 in Wirth etal. (2015).

Hommel etal. (2017)

Using all available data, a compatibility eﬀect was observed

for all four measures. Compatible actions had smaller AUCs

(3.2 × 103 vs. 5.3 × 103 px2), F(1, 34) = 10.41, p = .003, ηp

= .23, smaller MADs (17.7 vs. 27.6 px), F(1, 34) = 9.77, p =

Fig. 7 Results from Wirth et al. (2015), Experiment 1 and 2. (A)

Compatibility eﬀect in AUC as a function of the used cutoﬀ criterion.

The x-axis indicates the allowed horizontal movement between the

center of starting area and the center of the wrong target area, nor-

malized to percentage. The y-axis indicates the standardized eﬀect

size. The dashed vertical line indicates the cutoﬀ used in the text.

(B) Velocity proﬁles for all movements (left), and movements clas-

siﬁed with the cutoﬀ criterion. The light-grey line depicts movements

excluded from the analysis while the black line depicts movements

remaining in the analysis. The solid vertical lines mark the point of

maximal deviation from an ideal trajectory, with times on the x-axis

normalized to percentage from start up this point to as well as from

this point to reaching the target

Attention, Perception, & Psychophysics

.004, ηp

2 = .22, shorter ITs (496 vs. 507 ms), F(1, 34) = 7.19,

p = .011, ηp

2 = .17, and shorter MTs (339 vs. 347 ms), F(1,

34) = 5.69, p = .023, ηp

2 = .14, than incompatible actions.

As expected, our cutoﬀ criterion excluded fewer compat-

ible than incompatible movements (16.5% vs. 22.3%), t(34)

= 4.82, p < .001, dz = 0.81. In this experiment, the pattern

of signiﬁcance remained the same after applying our cutoﬀ

criterion: Compatible actions still had smaller AUCs (-0.7 ×

103 vs. 0.3× 103 px2), F(1, 34) = 5.45, p = .026, ηp

2 = .14,

smaller MADs (-2.4 vs. 1.5 px), F(1, 34) = 4.76, p = .036,

ηp

2 = .12, shorter ITs (497 vs. 507 ms), F(1, 34) = 5.38, p

= .027, ηp

2 = .14, and shorter MTs (317 vs. 324 ms), F(1,

34) = 5.24, p = .028, ηp

2 = .13, than incompatible actions.

Figure8 shows the results for Hommel etal. (2017).

Schonard etal. (2021)

Using all available data of Experiment 1, a compatibility

eﬀect was found for spatial measures. Compatible actions

had smaller AUCs (22.7 × 103 vs. 33.7 × 103 px2), F(1,

19) = 23.22, p < .001, ηp

2 = .55, and smaller MADs (32.4

vs. 51.7 px), F(1, 19) = 23.00, p < .001, ηp

2 = .55, than

incompatible actions. In the timing measures, ITs did not

diﬀer, F(1, 19) = 3.77, p = .067, ηp

2 = .17, but MTs were

shorter with compatible than with incompatible actions (544

vs. 572 ms), F(1, 19) = 30.65, p < .001, ηp

2 = .62.

As expected, our cutoﬀ criterion excluded fewer com-

patible than incompatible movements (7.1% vs. 16.1%),

t(19) = 5.52, p < .001, dz = 1.23. When applying our cutoﬀ

criterion, the compatibility eﬀect vanished for the spatial

measures of AUC, F(1, 19) = 3.05, p = .097, ηp

2 = .14,

and MAD, F(1, 19) = 3.02, p = .098, ηp

2 = .14. In the tim-

ing measures, ITs did not diﬀer, F(1, 19) = 3.50, p = .077,

ηp

2 = .16, but MTs were shorter with compatible than with

incompatible actions (535 vs. 552 ms), F(1, 19) = 6.43, p

= .020, ηp

2 = .25.

Using all available data of Experiment 2, a compatibility

eﬀect was found for all four measures. Compatible actions

had smaller AUCs (63.2 × 103 vs. 72.7 × 103 px2), t(39) =

4.37, p < .001, dz = 0.69, smaller MADs (92.5 vs. 108.1

px), t(39) = 4.22, p < .001, dz = 0.67, shorter ITs (602 vs.

645 ms), t(39) = 5.15, p < .001, dz = 0.81, and shorter MTs

(633 vs. 661 ms), t(39) = 4.75, p < .001, dz = 0.75, than

incompatible movements.

Fig. 8 Results from Hommel etal. (2017). (A) Compatibility eﬀect in

AUC as a function of the used cutoﬀ criterion. The x-axis indicates

the allowed horizontal movement between the center of starting area

and the center of the wrong target area, normalized to percentage.

The y-axis indicates the standardized eﬀect size. The dashed vertical

line indicates the cutoﬀ used in the text. (B) Velocity proﬁles for all

movements (left), and movements classiﬁed with the cutoﬀ criterion.

The light-grey line depicts movements excluded from the analysis

while the black line depicts movements remaining in the analysis.

The solid vertical lines mark the point of maximal deviation from an

ideal trajectory, with times on the x-axis normalized to percentage

from start up this point to as well as from this point to reaching the

target. Note that in this experiment, the data logging rate was substan-

tially higher than the polling rate of the mouse. To prevent edge arti-

facts, data without updated position information had to be excluded

via a custom script prior to time-normalization (for details see https://

osf. io/ hrpk6)

Attention, Perception, & Psychophysics

As expected, our cutoﬀ criterion excluded fewer compat-

ible than incompatible movements (11.1% vs. 17.4%), t(39) =

5.11, p < .001, dz = 0.81. When applying our cutoﬀ criterion,

the compatibility eﬀect vanished in the spatial measures of

AUC, t(39) = 1.02, p = .312, dz = 0.16, and MAD, |t| < 1. In

contrast, it remained present in the timing measures: Compat-

ible actions had shorter ITs (604 vs. 658 ms), t(39) = 5.80, p

< .001, dz = 0.92, and shorter MTs (613 vs. 628 ms), t(39) =

3.14, p = .003, dz = 0.50, than incompatible actions.

Using all available data of Experiment 3, a compatibil-

ity eﬀect was found for the spatial measures. Compatible

actions had smaller AUCs (13.8 × 103 vs. 19.3 × 103 px2),

F(1, 39) = 8.89, p = .005, ηp

2 = .19, and smaller MADs

(20.7 vs. 30.3 px), F(1, 39) = 8.63, p = .006, ηp

2 = .18,

than incompatible actions. In the timing measures, ITs were

shorter for compatible actions than for incompatible actions

(633 vs. 653 ms), F(1, 39) = 10.66, p = .002, ηp

2 = .21, but

MTs did not diﬀer, F(1, 39) = 2.90, p = .097, ηp

2 = .07.

As expected, our cutoﬀ criterion excluded fewer compat-

ible than incompatible movements (8.6% vs. 11.8%), t(39)

= 2.78, p = .008, dz = 0.44. In this experiment, the pattern

of signiﬁcance remained the same after applying our cutoﬀ

criterion: Compatible actions still had smaller AUCs (7.2

× 103 vs. 9.7 × 103 px2), F(1, 39) = 5.42, p = .025, ηp

2 =

.12, smaller MADs (9.5 vs. 13.0 px), F(1, 39) = 4.94, p =

.032, ηp

2 = .11, and shorter ITs (634 vs. 657 ms), F(1, 39)

= 11.69, p = .001, ηp

2 = .23, than incompatible actions, and

MTs again did not diﬀer, F < 1.

Figure9 shows the results for Experiment 1, Experiment

2, and Experiment 3 in Schonard etal. (2021).

Tonn etal. (2023)

Using all available data of Experiment 1, a compatibility

eﬀect was found for all four measures. Compatible actions

had smaller AUCs (3.5 × 103 vs. 6.2 × 103 px2), F(1, 42) =

13.98, p = .001, ηp

2 = .25, smaller MADs (16.5 vs. 30.6 px),

F(1, 42) = 17.48, p < .001, ηp

2 = .29, shorter ITs (632 vs.

673 ms), F(1, 42) = 34.62, p < .001, ηp

2= .45, and shorter

MTs (506 vs. 562 ms), F(1, 42) = 47.93, p < .001, ηp

2 = .53,

than incompatible actions.

As expected, our cutoﬀ criterion excluded fewer com-

patible than incompatible movements (13.7% vs. 21.2%),

t(42) = 5.01, p < .001, dz = 0.76. When applying our cut-

oﬀ criterion, the compatibility eﬀect vanished in the spatial

measures of AUCs, F < 1, and MAD, F < 1. In contrast,

it remained present in the timing measures: Compatible

actions had shorter ITs (634 vs. 683 ms), F(1, 42) = 48.99,

p < .001, ηp

2 = .54, and shorter MTs (481 vs. 524 ms), F(1,

42) = 30.12, p < .001, ηp

2 = .42, than incompatible actions.

Using all available data of Experiment S1, a compatibility

eﬀect was found for all four measures. Compatible actions

had smaller AUCs (3.7 × 103 vs. 6.5 × 103 px2), F(1, 40) =

14.91, p < .001, ηp

2 = .27, smaller MADs (16.9 vs. 30.9 px),

F(1, 40) = 17.08, p < .001, ηp

2 = .30, shorter ITs (588 vs.

635 ms), F(1, 40) = 40.36, p < .001, ηp

2 = .50, and shorter

MTs (423 vs. 461 ms), F(1, 40) = 31.24, p < .001, ηp

2 = .44,

than incompatible actions.

As expected, our cutoﬀ criterion excluded fewer com-

patible than incompatible movements (12.7% vs. 21.9%),

t(40) = 6.14, p < .001, dz = 0.96. When applying our cutoﬀ

criterion, the compatibility eﬀect vanished in the spatial

measures of AUC, F < 1, and MAD, F < 1. In contrast,

it remained present in the timing measures: Compatible

actions had shorter ITs (591 vs. 646 ms), F(1, 40) = 52.36,

p < .001, ηp

2 = .57, and shorter MTs (401 vs. 422 ms), F(1,

40) = 9.30, p = .004, ηp

2 = .19, than incompatible actions.

Using all available data of Experiment 2, a compatibility

eﬀect was found for all four measures. Compatible actions

had smaller AUCs (3.6 × 103 vs. 7.1 × 103 px2), F(1, 40) =

28.88, p < .001, ηp

2 = .42, smaller MADs (18.0 vs. 35.4 px),

F(1, 40) = 30.86, p < .001, ηp

2 = .44, shorter ITs (538 vs.

579 ms), F(1, 40) = 96.42, p < .001, ηp

2 = .71, and shorter

MTs (449 vs. 491 ms), F(1, 40) = 85.02, p < .001, ηp

2 = .68,

than incompatible trials.

As expected, our cutoﬀ criterion excluded fewer com-

patible than incompatible movements (15.9% vs. 25.3%),

t(40) = 8.55, p < .001, dz = 1.34. When applying our cut-

oﬀ criterion, the compatibility eﬀect vanished in the spatial

measures of AUC, F < 1, and MAD, F < 1. In contrast,

it remained present in the timing measures: Compatible

actions had shorter ITs (541 vs. 589 ms), F(1, 40) = 72.79,

p < .001, ηp

2 = .65, and shorter MTs (423 vs. 448 ms), F(1,

40) = 28.89, p < .001, ηp

2 = .42, than incompatible actions.

Using all available data of Experiment S3, a compatibility

eﬀect was found for all four measures. Compatible actions

had smaller AUCs (6.1 × 103 vs. 9.1 × 103 px2), t(45) =

3.84, p < .001, dz = 0.57, smaller MADs (26.8 vs. 43.0 px),

t(45) = 4.12, p < .001, dz = 0.61, shorter ITs (573 vs. 609

ms), t(45) = 5.56, p < .001, dz = 0.82, and shorter MTs (506

vs. 561 ms), t(45) = 7.06, p < .001, dz = 1.04, than incom-

patible movements.

As expected, our cutoﬀ criterion excluded fewer compat-

ible than incompatible movements (17.3% vs. 25.4%), t(45)

Fig. 9 Results from Schonard etal. (2021), Experiment 1, 2, and 3.

(A) Compatibility eﬀect in AUC as a function of the used cutoﬀ crite-

rion. The x-axis indicates the allowed horizontal movement between

the center of starting area and the center of the wrong target area,

normalized to percentage. The y-axis indicates the standardized eﬀect

size. The dashed vertical line indicates the cutoﬀ used in the text.

(B) Velocity proﬁles for all movements (left), and movements clas-

siﬁed with the cutoﬀ criterion. The light-grey line depicts movements

excluded from the analysis while the black line depicts movements

remaining in the analysis. The solid vertical lines mark the point of

maximal deviation from an ideal trajectory, with times on the x-axis

normalized to percentage from start up this point to as well as from

this point to reaching the target

◂

Attention, Perception, & Psychophysics

= 5.88, p < .001, dz = 0.87. When applying our cutoﬀ crite-

rion, the compatibility eﬀect vanished in the spatial meas-

ures of AUC, t(45) = 1.44, p = .156, dz = 0.21, and MAD,

t(45) = 1.62, p = .111, dz = 0.24. In contrast, it remained

present in the timing measures: Compatible actions had

shorter ITs (580 vs. 621 ms), t(45) = 5.23, p < .001, dz =

0.77, and shorter MTs (475 vs. 515 ms), t(45) = 4.16, p <

.001, dz = 0.61, than incompatible actions.

Figure10 shows the results for Experiment 1 and Experi-

ment S1 in Tonn etal. (2023).

Figure11 shows the results for Experiment S2 and Exper-

iment S3 in Tonn etal. (2023).

Fig 10 Results from Tonn etal. (2023), Experiment 1, S1. (A) Com-

patibility eﬀect in AUC as a function of the used cutoﬀ criterion. The