# Optimized experimental designs to best detect spatial positional association of response codes in working memory

Morgane Ftaïta, Maëliss Vivion, Emilie Banks, Alessandro Guida, Stephen Ramanoël, Michaël Fartoukh, Fabien Mathy

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## To cite this version:

Morgane Ftaïta, Maëliss Vivion, Emilie Banks, Alessandro Guida, Stephen Ramanoël, et al.. Optimized experimental designs to best detect spatial positional association of response codes in working memory. Attention, Perception, and Psychophysics, 2023, 85, pp.1661-1680. 10.3758/s13414-023-02666-9. hal-05503972

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OPTIMAL DESIGN FOR THE SPoARC EFFECT

Optimized experimental designs to best detect spatial positional association
of response codes in working memory

Morgane Ftaïta*¹, Maëliss Vivion¹, Emilie Banks¹, Alessandro Guida², Stephen Ramanoël³,

Michaël Fartoukh¹, and Fabien Mathy¹

¹Université Côte d'Azur and CNRS

²Université Rennes 2

³Université Côte d'Azur & Sorbonne Université INSERM CNRS

Author Note

Fabien Mathy https://orcid.org/0000-0002-7705-5689

* Correspondence should be addressed to Fabien Mathy, Université Côte d'Azur, CNRS, BCL, France, or by email to fabien.mathy@univ-cotedazur.fr. This research was supported in part by a grant from the Agence Nationale de la Recherche (ANR-17-CE28-0013-01) awarded to Fabien Mathy and a grant (Boost'Europe-21004278-00001052) from Region Bretagne awarded to Alessandro Guida. The first co-authors Morgane Ftaïta and Maëliss Vivion (by alphabetical order) contributed equally to this work. Conceptualization, all authors; Methodology, Morgane Ftaïta, Alessandro Guida, Fabien Mathy, Maëliss Vivion; Formal Analysis, Morgane Ftaïta, Alessandro Guida, Fabien Mathy, Maëliss Vivion; Writing, all authors. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
# OPTIMAL DESIGN FOR THE SPoARC EFFECT

## Abstract

The SPoARC (Spatial Positional Association of Response Codes) effect refers to spatialization of information in working memory. Among the potential factors that could influence how order is mapped onto a mental space during the recognition process, we selected the following two factors: i) the type of stimuli, in particular their verbal vs. visual aspects and ii) the number of probes. In this study, 137 participants memorized sequences of either words or pictures and subsequently performed a recognition test for which they responded using lateralized keys. For half of the participants, only one probe was presented after each sequence, whereas the other half were administered several probes. A significantly greater number of participants presented a SPoARC using a single probe. We discuss that spatialization is best detected when the sequence is scanned only once. Results also showed no difference between the two types of stimuli (i.e., verbal vs. visual). This finding raises the question of the respective roles of verbalization and visualization in the SPoARC.
# OPTIMAL DESIGN FOR THE SPoARC EFFECT

## Optimized experimental designs to best detect spatial positional association of response codes in working memory

Spatialization can be defined as the addition by the cognitive system of a spatial dimension that is not part of the actual input. Since ancient history, memory experts have been particularly familiar with spatialization (Yates, 1966). A vast majority of mnemonic experts still rely on the method of loci to memorize a countless quantity of information in a limited time. When practicing this method, one can use a mental palace (e.g., one's own house, as long as the place is known by heart) to support the memorizing process. Each to-be-remembered piece of information is linked to a spatial coordinate in the location (each coordinate can also be linked to a known object, such as the carpet), one must simply imagine themselves walking through the palace to retrieve the different items on their way.

Thanks to the method of loci, a memory expert voluntarily adds spatial processing to remember better. However, a similar process can be found at a more elementary level in the general population (Guida & Campitelli, 2019). Indeed, individuals can automatically and unconsciously carry-out spatial processing of non-spatial information when memorizing, a phenomenon highlighted by van Dijck and Fias (2011). The task used by the authors to detect spatialization consisted in the presentation of a sequence of stimuli during which each item was displayed sequentially in the center of a computer screen. After the presentation of the sequence, participants were asked to classify probes only if they belonged to the memorized sequence. Participants responded using lateralized computer keys. Spatialization was detected by faster responses for the first items of the sequence with the left hand while the last items elicited faster responses with the right hand. Overall, the results showed that the right-hand minus left-hand reaction times difference decreased when going through the positions being probed. This effect is known as SPoARC (Spatial Positional Association of Response Codes, Guida and Lavielle-Guida, 2014) or Ordinal Position Effect (Ginsburg et al., 2014).

Different hypotheses have been put forward to account for the SPoARC. Among them is the mental whiteboard hypothesis (Abrahamse et al., 2014). According to this theory, individuals would spontaneously use a mental whiteboard as a more rudimentary mental space
than the palace mentioned above. Items of a to-be-remembered list would be arranged on a
horizontal axis on the mental whiteboard in Westerners, beginning with the first element on
the far left, the second a little further to the right and so on, following left-to-right reading
habits. The observation that literacy can shape the phenomenon is supplemented by the fact
that this effect does not occur in illiterate individuals (Guida et al., 2018) and is not detected in
preschoolers (van Dijck et al., 2020). In addition, spatialization seems to arise only around 9
years of age (Guida, Fartoukh, et al., 2020).

In spite of this quite general description of the phenomenon in terms of a cultural
product, the numerous publications on the SPoARC effect (Guida & Campitelli, 2019)
comprise many variations. In addition to numbers, successful experimental paradigms have
comprised words as items (van Dijck & Fias, 2011), letters (Guida et al., 2016), concrete
shapes (Ginsburg et al., 2017), or even color patches (Guida et al., 2018). However when
focusing on the slopes of the SPoARC effect, results seemed to produce erratic patterns, as
shown by Figure 1, (see below for a description), and only a few studies lingered on
comparing those experimental conditions to determine the best way to detect spatialization.
Previtali et al. (2010) gave an insight by using in the same study both pictures and written
words as stimuli, indicating a stronger spatialization effect with imaged stimuli. An overview
of the diverse experimental designs has allowed us to summarize the different procedures and
analyze which ones elicited a stronger coefficient and effect size. The main differences across
procedures lie in the stimulus type (pictures, letters, words, color patches), the amount of
probes presented after the sequence to memorize, the amount of items in the memorized
sequence, the task performed after the memorization phase (recognition, classification), the
modality of response (bimanual, unimanual), and the presence of a task controlling the
encoding order or not.

Table 1 lists 21 studies on the SPoARC effect, based on a selection provided by Guida
and Campitelli (2019) that was enriched with eight additional studies<fnref n="1" /> (highlighted in bold in

<footnote n="1">¹ Among these additional studies, we selected six studies subsequent to the literature review conducted by Guida and Campitelli (2019), but also two other studies published before the synthesis of Guida & Campitelli that we still considered relevant. Conversely, within the list of Guida & Campitelli, studies conducted by Rinaldi et al. (2015), Martarelli et al. (2017) and Antoine et al. (2017) were excluded from our inventory because they did not measure spatialization using response times. The study carried out by Boiteau & Almor (2017, Experiment</footnote>
OPTIMAL DESIGN FOR THE SPoARC EFFECT

Table 1). Figure 1 shows how the 21 studies we selected could be categorized based on stimulus type and the amount of probes presented after the to-be-remembered sequence.

<figure><img src="image_3.png" /><figcaption>Figure 1</figcaption></figure>

SPoARC effect from previous studies listed in Table 1. The location of the data points on the Y axis corresponds to the average slope of the difference of response times between the two hands given the position of the test item in a to-be-remembered sequence. The size of each data point corresponds to the Eta Squared value associated with the spatialization slope of each experiment. Order of the conditions on the X axis is not alphabetical, but as a function of the spatialization slopes the experimental conditions produced on average across studies of the same kind.

* This study listed no explicit ANOVA values.

One can visually notice from Figure 1 that a larger negative slope seems to be triggered by visual objects or objects for which a visual mental image can be formed (food, drawings, colors). A second obvious feature is that most studies used a multi-probe design (i.e., when

number two) was also discarded because of a protocol essentially focusing on the spatialization of syntax (the so-called Syntax-Space Effect). This study was replaced by a study conducted by Boiteau (2015, Experiment number four) which had a more standard design and which allowed us to consider the effect of a new type of stimulus in our analysis. Finally, the study conducted by Wang et al. (2018) does not appear in our selection, as no regression coefficient was explicitly provided by the authors. Among the 21 studies listed in Table 1, study 1.c was discarded because the authors did not use a standard SPoARC paradigm to detect spatialization. Experiment 4.3, 4.4 and 5.1 were also discarded because they involved a SNARC effect (see Dehaene et al., 1993). In Boiteau (2015), we only selected Experiment number four because all other experiments involved the Syntax-Space effect. Study 9.1 was also discarded because spatialization was measured through whole-hand and precision grip instead of a standard key-pressing procedure commonly used to detect the SPoARC. Study 13.5 was excluded due to its use of articulatory suppression and tapping. Study 16.2 and 16.3 were excluded due to a vertical response mapping. Finally, 19.2 and 19.3 were not included due to their non central spatial coordinates.
OPTIMAL DESIGN FOR THE SPoARC EFFECT

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<caption>**Table 1**</caption>

Summary table of the different studies presented in Figure 1

<table><thead><tr><th>Study number</th><th>Study Name</th><th>Regression coefficient</th><th>Effect size of the ANOVA (η<sup>2</sup>)</th></tr></thead><tbody><tr><td>1.a*</td><td>Previtali et al. (2010)</td><td>-8.71</td><td>-</td></tr><tr><td>1.b*</td><td>Previtali et al. (2010)</td><td>-51.97</td><td>-</td></tr><tr><td>2.1</td><td>Van Dijck et Fias (2011)</td><td>-13.35</td><td>0.14</td></tr><tr><td>2.2</td><td>Van Dijck et Fias (2011)</td><td>-29.04</td><td>0.23</td></tr><tr><td>3.1</td><td>Van Dijck et al. (2013)</td><td>-4.99</td><td>0.12</td></tr><tr><td>3.2</td><td>Van Dijck et al. (2013)</td><td>-5.94</td><td>0.18</td></tr><tr><td>3.3</td><td>Van Dijck et al. (2013)</td><td>-4.12</td><td>0.13</td></tr><tr><td>4.1</td><td>Ginsburg et al. (2014)</td><td>-18.09</td><td>0.21</td></tr><tr><td>4.2</td><td>Ginsburg et al. (2014)</td><td>-15.61</td><td>0.14</td></tr><tr><td>5.2</td><td>Van Dijck et al. (2014)</td><td>-4.73</td><td>0.11</td></tr><tr><td>5.3*</td><td>Van Dijck et al. (2014)</td><td>-8.3</td><td>-</td></tr><tr><td>6*</td><td>Boiteau (2015)</td><td>0</td><td>-</td></tr><tr><td>7.1</td><td>De Belder et al. (2015)</td><td>-26</td><td>0.74</td></tr><tr><td>7.2</td><td>De Belder et al. (2015)</td><td>-17</td><td>0.58</td></tr><tr><td>8.1</td><td>Ginsburg et Gevers (2015)</td><td>-16.18</td><td>0.11</td></tr><tr><td>8.2</td><td>Ginsburg et Gevers (2015)</td><td>-12.46</td><td>0.1</td></tr><tr><td>9.2</td><td>Van Dijck et al. (2015)</td><td>-33</td><td>0.31</td></tr><tr><td>10</td><td>Bottini, et al. (2016)</td><td>-20</td><td>0.18</td></tr><tr><td>11*</td><td>Guida et al. (2016)</td><td>-30</td><td>-</td></tr><tr><td>12*</td><td>Huber et al. (2016)</td><td>-9.35</td><td>-</td></tr><tr><td>13.1</td><td>Ginsburg et al. (2017)</td><td>-16.22</td><td>0.1</td></tr><tr><td>13.2</td><td>Ginsburg et al. (2017)</td><td>-16.99</td><td>0.01</td></tr><tr><td>13.3</td><td>Ginsburg et al. (2017)</td><td>-13.95</td><td>0.1</td></tr><tr><td>13.4a</td><td>Ginsburg et al. (2017)</td><td>-27.5</td><td>0.16</td></tr><tr><td>13.4b</td><td>Ginsburg et al. (2017)</td><td>-27.24</td><td>0.18</td></tr><tr><td>13.4c*</td><td>Ginsburg et al. (2017)</td><td>-20.77</td><td>-</td></tr><tr><td>13.6a</td><td>Ginsburg et al. (2017)</td><td>-38.33</td><td>0.31</td></tr><tr><td>13.6b</td><td>Ginsburg et al. (2017)</td><td>-16.91</td><td>0.14</td></tr><tr><td>14.1</td><td>Guida, Carnet, et al. (2018)</td><td>0</td><td>-</td></tr><tr><td>14.2</td><td>Guida, Carnet, et al. (2018)</td><td>-6.25</td><td>0.1</td></tr><tr><td>15</td><td>Guida, Megreya, et al. (2018)</td><td>-27.92</td><td>0.08</td></tr><tr><td>16.1</td><td>Zhou et al. (2019)</td><td>-40.58</td><td>0.33</td></tr><tr><td>17.a*</td><td>Guida, Abrahamse et al. (2020)</td><td>-21.5</td><td>0.005</td></tr><tr><td>17.b*</td><td>Guida, Abrahamse et al. (2020)</td><td>-50.5</td><td>0.04</td></tr><tr><td>18*</td><td>Guida, Mosinski, et al. (2020)</td><td>-23.9</td><td>-</td></tr><tr><td>19.1</td><td>Shi et al. (2020)</td><td>-48.81</td><td>0.18</td></tr><tr><td>20*</td><td>Van Dijck et al. (2020)</td><td>0</td><td>-</td></tr><tr><td>21</td><td>Zhou et al. (2021)</td><td>-47.83</td><td>0.49</td></tr></tbody></table>

Note: the symbol of the regression coefficient illustrates the trend for the difference in response times. A negative value indicates faster response times for the first items with the left hand and for the last items with the right hand (as expected in westerners).

Note: For all the studies that have integrated ANOVA in their statistical processing, the eta squared was listed or calculated with the F value and the df, using the following formula:

$$ \eta_2 = \frac{F(k - 1)}{F(k - 1) + F(N - k)} $$

This formula has been found at http://www.statistika.ca/2014/05/calcul-dun-eta-carre-a-laide-du-f-seulement/
several probes are used to test memory after the presentation of a sequence), leaving the effect of mono-probe designs quite uncertain (i.e., when a unique probe is presented to test memory after the presentation of a sequence). However, mono-probe designs could be more efficient for instance with children as mono-probing a priori limits output interference in memory. Moreover, although not common, the mono-probe design produced quite large spatialization slopes for two studies. Regarding the theoretical and practical implications, we then thought that increasing the number of probes should increase output interference (i.e., a gradual decrease in memory performance due to adding lures in the task as well as probing different positions randomly), which we hypothesized should impact the SPoARC effect. In addition, the mental whiteboard hypothesis implies that items are spatialized visually. Therefore we thought that manipulating the type of stimuli appeared relevant to confirm this view.

**The present study.** In order to improve the way spatialization can be detected, we manipulated these two factors (visual aspect of the objects and number of probes). We predicted that the effect would be larger using visual objects. Based on the whiteboard hypothesis, we reasoned that visual objects should facilitate mental imagery if spatialization is by nature visual. We also predicted a larger effect using a single probe. Due to the limitation of output interference, the response times should be more straightforward using a mono-probe design.

We now further detail how we derived these two predictions. One can note that although the multi-probe method is most often used in the literature (De Belder et al., 2015; Zhou et al., 2021; Zhou et al., 2019), it is unsure whether this design produces greater spatialization slopes, as some other studies have found that using a single probe could elicit a strong SPoARC effect as well (Guida, Abrahamse, et al., 2020; Guida, Mosinski, et al., 2020; Shi et al., 2020). Since the latter method is more rarely used, the size effects associated to the phenomenon remain uncertain. On one hand the multi-probe method has the advantage of collecting a larger number of observations (and faster) than using a mono-probe design (just because responding to probes is faster than presenting a sequence before each probe). On the other hand, one could think that the multi-probe design should induce a stronger spatialization effect, because scanning the sequence several times could reinforce its spatial coding. But as
OPTIMAL DESIGN FOR THE SPoARC EFFECT

mentioned earlier, the data might also contain noise precisely because the numerous probes
can interfere with the memorization of the sequence (i.e., via a phenomenon called output
interference; Criss et al., 2011). Second, a visual condition was expected to induce larger
effect than a verbal condition. Images are still little used in experimental methods intended to
analyze spatialization. However, studies comparing these two types of stimulus (word
vs. image) have been able to highlight stronger spatialization slopes when presenting images
rather than when presenting words (Ginsburg et al., 2017; Previtali et al., 2010). We also
predicted that these two effects would simply be additive (i.e., that they would not involve an
interaction).

To collect response times, we chose a recognition task with a bimanual response (this
design was for instance used in the original study of the SPoARC by van Dijck and Fias,
2011). More specifically, participants had to perform a probe detection task adapted from
Guida et al. (2016) and Ginsburg et al. (2017). Each trial began with a memorization phase of
a sequence of four items. Four fruits were presented sequentially to the participants in the
center of a computer screen. These fruits were presented in the form of color drawings for half
of the sample (“Image” condition), and in the form of written words for the other half of the
sample (“Word” condition). Once the memorization phase was completed, the participants
moved on to a recognition phase. During this phase, participants had to judge whether a new
item displayed in the center of the screen was part of the previously presented sequence by
answering “Yes” or “No” using the “S” and “L” keys on the keyboard. For half of participants,
a single target was presented after the sequence (“Mono-probe” condition). The other half of
the participants were asked to perform the recognition task on a series of eight successive
probes (“Multi-probe” condition) before moving on to the next trial. The four experimental
conditions were crossed in the experimental design to obtain “Image” with Mono-probe,
“Image” with Multi-probe, “Word” with Mono-probe and “Word” with Multi-probe. The
participants were distributed equally among the four experimental conditions.

Memory for order<fnref n="2" /> was not verified after the recognition process as several studies that

<footnote n="2">² Some studies on the SPoARC effect allocated time to verify that the order of the different items was correctly memorized by participants, for example by asking participants to identify the memorized sequence among several ones at the end of each trial (for instance, the distractive sequences contained the same items organized in</footnote>
# OPTIMAL DESIGN FOR THE SPoARC EFFECT

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did not include this step in their procedure still successfully identified a SPoARC effect (Guida, Abrahamse, et al., 2020; Guida et al., 2016; also see Guida and Campitelli, 2019).

This allowed us to keep each trial as short as possible to get the greatest number of trials in the time allocated to the task. The number of items in the sequence was set to 4, because this list length has been the most disseminated in the literature (De Belder et al., 2015; Ginsburg et al., 2017; Guida et al., 2018; Van Dijck et al., 2014; van Dijck et al., 2013; Zhou et al., 2021; Zhou et al., 2019).

## Method

### Participants

A sample of 137 second-year Psychology students<fnref n="3" /> (126 women and 11 men, mean age = 19.9 years, *SD* = 1.4) took part in this study. Each participant received a bonus in exchange for their participation. To the best of our knowledge, the SPoARC effect is not taught in class for undergraduate students. However, the ingenuity of all participants concerning this effect was still checked during the debriefing of the experiment. The sample included 120 right-handed participants, 14 left-handed and 3 ambidextrous, and among all of these participants, 125 were native French speakers<fnref n="4" />.

### Material

All the programs used for this study were developed using the PsychoPy (Peirce et al., 2019) software. Participants were seated in front of a computer screen that was approximately 50cm away from them. Responses were collected through keys of the computer keyboard.

Stimuli from the fruit category were used because of their familiarity and concreteness. This category of stimuli (associated with vegetables) is one of the most widely used in previous studies that have demonstrated the SPoARC effect (after digits, that were excluded here not to interfere with the SNARC effect) (Bottini et al., 2016; van Dijck & Fias,

a different order; see van Dijck and Fias, 2011 or Ginsburg et al., 2014).

<footnote n="3">³ One participant was excluded from the analyses due to poor understanding of the instructions.</footnote>

<footnote n="4">⁴ Out of the 12 participants who were not native French speakers, four of them were native Arabic speaker, three native Spanish speaker, one native English speaker, one native Bulgarian speaker, one native Portuguese speaker, one native Albanian speaker and one native Tagalog speaker.</footnote>
OPTIMAL DESIGN FOR THE SPoARC EFFECT

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2011; Zhou et al., 2019). When considering previous studies, this category of stimuli has elicited a strong effect size, but using pictures or written words indistinctly. Comparing the two would allow to validate using images, which could be useful in particular to study the SPoARC effect with preliterate children or dyslexic participants. A list of ten fruit names ("banane" (banana), "cerise" (cherry), "citron" (lemon), "framboise" (raspberry), "grenade" (pomegranate), "kiwi" (kiwi), "myrtille" (blueberry), "orange" (orange), "pastèque" (watermelon) and "raisin" (grape)) was created. These words were selected on the basis of four lexical criteria: the number of syllables (the study only contains bi-syllabic words), frequency, imageability and age of acquisition. This information was collected from several databases within the OpenLexicon platform.

From this list of ten fruits, sequences of four items were created for each trial. The total number of sequences presented to the participants was different depending on the experimental condition (Mono-probe or Multi-probe), in order to guarantee a constant duration of the experiment between the two samples. In the Mono-probe condition, the participants had to memorize a set of 60 sequences divided into two homogeneous subgroups ("Test 1" and "Test 2") of 30 trials each. The value associated with the response hand ("yes" for the right hand and "no" for the left hand or vice versa) being inverted between the two sub-groups. In the Multi-probe condition, 32 sequences were presented to the participants, equally divided into two subgroups of 16 trials each. Each participant performed two experimental sessions, during which they carried out one test per session, the order of presentation between Test 1 and Test 2 being counterbalanced between the participants. The value associated with the response hand between the first and second session was also counterbalanced between participants.

For each sequence presented in the memorization phase, a series of probes was developed. In the Mono-probe condition, the series contained only one item, versus eight items in the Multi-probe condition. In both condition, 50% of the items presented for recognition corresponded to a fruit that was part of the sequence to be memorized. For the remaining 50%, the item presented was a lure that was not presented in the sequence. In the Mono-probe condition, a participant had to identify 15 lures (a.k.a. negative probes) and 15
items presented in the memorized sequence (a.k.a. positive probes) per session. In the Multi-probe condition, each set of probes contained four lures and the four items presented in the sequence. The participant therefore had to respond to 64 negative probes and 64 positive probes per session. The order in which the different positions of the probes to be detected were presented was counterbalanced over the trials, by randomly choosing 16 orders among the 24 possible permutations of the four items to be detected. Therefore, in total each participant saw 30 negative probes and 30 positive probes in the Mono-probe condition, whereas the participants of the Multi-probe condition saw in total 128 negative probes and 128 positive probes.

The stimuli were presented for half of the participants in the form of colored drawings representing the ten fruit names previously mentioned. These drawings were selected from the IMABASE database of Bonin et al. (2020) for the words “banana”, “cherry”, “lemon”, “orange”, “watermelon” and “grape”. The drawings used for the words “raspberry”, “pomegranate”, “kiwi” and “blueberry” were royalty-free images taken from the internet <fnref n="5" />. For the other half of the participants, the material used consisted of the fruit names written in full, in Arial font, size 60 and black color.

## Procedure

The experiment took place in a quiet room and lasted approximately one hour. The experimenter faced the participant and watched the task through an additional screen, which allowed him to oversee the smooth running of the task. The experimenter manually moved from one trial to another by clicking the mouse, making sure beforehand that the participant was sufficiently focused. Otherwise, the latter was invited to refocus his/her attention before starting the memorization.

Each participant took part in two experimental sessions, for one session the value “yes” was being associated with one response hand, and for the second session with the other hand. Each of these sessions included a training phase, consisting of four sequences to be

<footnote n="5">⁵ https://www.freepik.com/free-vector/vector-illustration-juicy-raspberry-isolated-white_1215960.htm#page=1&query=raspberry&position=0&from_view=searchhttps:// for raspberry, https://icones8.fricons/set/kiwi for kiwi, https://www.vecteezy.com/vector-art/3486476-doodle-freehand-sketch-drawing-of-blueberry-fruit for blueberry and https://fr.freepik.com/vectors-libre/fond-grenade-dessine-main_3885171.htm#page=1&query=grenade&position=20&from_view=search for the pomegranate.</footnote>
OPTIMAL DESIGN FOR THE SPoARC EFFECT

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memorized, followed by a test phase containing 30 sequences (Mono-probe condition) or 16 sequences (Multi-probe condition) presented in random order. Each phase began with the presentation of the instructions, reminding the participants to always keep their hands on the response keys in order to be able to answer as quickly as possible. Before starting the test phase, participants in the Image condition were systematically asked if they were able to recognize all the fruits on the list.

As shown in Figure 2, a trial consisted of a presentation of a sequence of four fruits in the center of the screen (Step 1: memorization), followed by the presentation of a probe (Mono-probe condition) or eight probes (Multi-probe condition) also in the center of the screen. When the probe was displayed the participant had to indicate whether it belonged to the memorized sequence or not (Step 2: recognition) by responding with the “S” and “L” keys of the keyboard. For half of the participants, the answer “Yes” was assigned to the left hand during the first session and to the right hand during the second, and vice versa for the other half of the participants. Each participant completed two sessions in a single sitting, and a five minutes break was systematically offered between the two sessions.

<figure><img src="image_4.png" /><figcaption>**Figure 2**

Spatialization task used in the Image condition.</figcaption></figure>

Each sequence began with the sentence “Attention, début de l'essai” (Be careful, the
# OPTIMAL DESIGN FOR THE SPoARC EFFECT

trial is about to start) presented in the center of the screen. During the memorization phase, each item was presented for 4000 milliseconds in the center of the screen, with a 1000 millisecond interval between each item. After the presentation of the sequence, a fixation cross appeared on the screen for 2000 milliseconds. A probe was then displayed for a maximum of 3500 milliseconds, during which the participants had to indicate their answer. These rather long presentation times tend to favor the emergence of the spatialization effect when the presentation of items is central (Guida, Abrahamse, et al., 2020). No response (or a response made after 3500 milliseconds) was coded as incorrect. Red and green stickers were placed on the “S” and “L” keys to facilitate the use of response keys. The fixation cross and the probe were displayed on a background with question marks to remind the participant that an answer was expected. After recording a response, or after 3500 milliseconds in the absence of a response, the program automatically moved on to the next sequence for the Mono-probe condition. In the Multi-probe condition the presentation of the items to be identified continued automatically, always starting with a fixation cross presented for 2000 milliseconds followed by a probe presented for 3500 milliseconds (or until the participant responded). For each probe that elicited a response from the participant, a reaction time expressed in milliseconds was recorded. No feedback was given to the participants concerning the accuracy of their answers and they were not asked to recall the sequence at the end of the recognition phase.

## Results

### Preliminary Analysis

Over the task, the participants had a proportion of correct answers of 0.96 (SD = 0.20). The 4% of incorrect data corresponded to wrong answers, non-responses or responses made after 3500 ms. The data of two participants were excluded from the analysis because of a too low percentage of correct answers over the course of the experiment (40% and 48%). Subsequently, the analyses were conducted solely on the correct responses carried out for probes present in the memorized sequences (positive probes). All of the response times collected during the recognition of lures were therefore excluded from the analyses. Focusing only on the correct answers for the to-be-detected probes, the results showed a success rate of
0.94 (SD = 0.24).

A first step of data harmonization was carried out through the winsorizing procedure (Reifman & Keyton, 2010; Rivest, 1994). This approach minimizes the impact of extreme values while keeping a maximal and constant number of observations (which is important for the subsequent bootstrapping analysis). For each participant, a mean reaction time was first calculated and a lower and upper limit was determined by taking the values within plus or minus two standard deviations of this mean. All response times between these two limits were kept. On the other hand, the response times located beyond these limits have been replaced by the lower and upper limits. This operation was performed on 4.6% of the responses. The average response time over the entire experiment was 734 ms (SD = 276 ms). The correlation between response time and response accuracy did not indicate a higher error rate when responses were faster ($\rho$ = -0.099, $p$ < .001). However, the results showed that response times tended to increase with the trial number, but with a relatively small effect ($\rho$ = 0.065, $p$ < .001).

## Spatialization Effect through Generalized Linear Mixed Models

To analyze our data, we used generalized linear mixed models to follow a method proposed by Lo and Andrews (2015) considered more suitable for the study of reaction times. This analysis was carried out on the non-aggregated data collected (after winsorizing, as explained above) in order to assess more precisely the presence of the effect as a function of the experimental conditions. Generalized linear mixed models are particularly suited for non-normal distributions. Using this method avoided the transformation of our raw data to satisfy the normality assumption. Indeed, an analysis of the distribution of the collected response times showed that the raw data was distributed in a positively asymmetric manner (see Figure A in Supplementary Material). The results of the fitDist test (gamlss library) performed on the Rstudio software (Team et al., 2013) indicated that an inverse-Gaussian distribution (also called Wald distribution, Heathcote, 2004) fitted well enough the collected data. As suggested by Lo and Andrews (2015) (but see also Ratcliff, 1993), an inverse Gaussian distribution was therefore taken as a reference distribution in our analysis. Such an approach has already been used in the past in this particular domain (Guida et al., 2016).
OPTIMAL DESIGN FOR THE SPoARC EFFECT

15

The four independent variables used in this analysis were as follows: two within-subject independent variables, that is, Position of the item in the sequence (four levels: 1, 2, 3, 4) and Hand of response (two levels: Right and Left); two between-subjects independent variables, that is, Stimulus type (two levels: Image and Word) and Probe amount (two levels: Mono and Multi). Under the hypothesis of a variation in response times over the course of the task, Trial number was also integrated as a factor for this analysis. Concerning this fifth variable, each memorized sequence was coded from 1 to 60 for the Mono-probe condition, and from 1 to 32 for the Multi-probe condition, for each participant. Two random factors were systematically integrated into the models: the Subject factor, allowing the variation between the different trials for the same participant to be taken into account; and the Item factor which corresponded to the fruits presented as probes during recognition. The integration of the Item factor into the models enabled to take into account a potential difference in recognition time between fruits.

The complexity of our mixed models gradually increased, by initially only taking into account the effects of the random factors on the dependent variable (see Guida et al., 2013; Guida et al., 2016). A very first degenerate model including only the effect of the random factor Subject (M0), was therefore developed and considered as a starting point. This model was then enriched, first with the random factor Item (M1), followed by the various factors of interest, also included successively (from M2 to M6). For these first models, only the main effects of the different variables were tested.

In more complex models, all possible interactions between the factors Position, Hand, Probe Amount and Stimulus Type were gradually integrated, starting with two-way interactions (from M7 to M12), then by simulating three-way interactions (M13 to M16). The most complex model (M17) simulates the interactions between the 4 factors. For all of the models, the Trial number factor was kept out of the interactions in order to relieve the sum of calculations, even if an hypothesis related to Trial number would have been justified (i.e., an interaction could gradually appear as the tests progress). For a summary of the models that were created for this analysis and details about the Akaike criterion (AIC) that we used to rank the models, see Table 2.
<caption>**Table 2**</caption>

Presentation of the generalized linear mixed models

<table><tr><td>M0</td><td>RT~ (1|Subject)</td></tr><tr><td>M1</td><td>RT~ (1|Item) + (1|Subject)</td></tr><tr><td>M2</td><td>RT~ Trial + (1|Item) + (1|Subject)</td></tr><tr><td>M3</td><td>RT~ Position + Trial + (1|Item) + (1|Subject)</td></tr><tr><td>M4</td><td>RT~ Position + Hand + Trial + (1|Item) + (1|Subject)</td></tr><tr><td>M5</td><td>RT~ Position + Hand + Stimulus Type + Trial + (1|Item) + (1|Subject)</td></tr><tr><td>M6</td><td>RT~ Position + Hand + Stimulus Type + Probe Amount + Trial + (1|Item) + (1|Subject)</td></tr><tr><td>M7</td><td>RT~ Position * Hand + Stimulus Type + Probe Amount + Trial + (1|Item) + (1|Subject)</td></tr><tr><td>M8</td><td>RT~ Position * Stimulus Type + Hand + Probe Amount + Trial + (1|Item) + (1|Subject)</td></tr><tr><td>M9</td><td>RT~ Position * Probe Amount + Hand + Stimulus Type + Trial + (1|Item) + (1|Subject)</td></tr><tr><td>M10</td><td>RT~ Hand * Stimulus Type + Probe Amount + Trial + Position + (1|Item) + (1|Subject)</td></tr><tr><td>M11</td><td>RT~ Hand * Probe Amount + Stimulus Type + Trial + Position + (1|Item) + (1|Subject)</td></tr><tr><td>M12</td><td>RT~ Stimulus Type * Probe Amount + Hand + Trial + Position + (1|Item) + (1|Subject)</td></tr><tr><td>M13</td><td>RT~ Position * Hand * Stimulus Type + Probe Amount + Trial + (1|Item) + (1|Subject)</td></tr><tr><td>M14</td><td>RT~ Position * Hand * Probe Amount + Stimulus Type + Trial + (1|Item) + (1|Subject)</td></tr><tr><td>M15</td><td>RT~ Position * Probe Amount * Stimulus Type + Hand + Trial + (1|Item) + (1|Subject)</td></tr><tr><td>M16</td><td>RT~ Hand * Stimulus Type * Probe Amount + Trial + Position + (1|Item) + (1|Subject)</td></tr><tr><td>M17</td><td>RT~ Position * Hand * Stimulus Type * Probe Amount + Trial + (1|Item) + (1|Subject)</td></tr></table>

Note: RT = Reaction Time, Position = Position of the item in the sequence, Hand = Hand of response and Trial = Trial Number

We created 17 models for our mixed model analysis. Each model was classified using the aictab function of R (Team et al., 2013) (AICcmodvag library), allowing to compare their Akaike Information Criterion (AIC). This criterion enables to choose the most parsimonious model according to the likelihood of the model and the number of parameters to be estimated, the best model being the one with the lowest AIC value. This index was preferred to the BIC index (Bayesian Information Criterion) because the latter tends to choose models that are too parsimonious for data relating to a small sample. Although it is strongly recommended to aim for parsimony, a model too parsimonious is not necessarily the one that generalizes best at the scale of the population (Burnham & Anderson, 2004; Pitt & Myung, 2002).

The results of this operation are available in Table 3 using the AICc as a reference value. This advanced criterion corresponds to a correction of the AIC carried out in the case of small samples, or when many parameters are to be taken into account. The Table 3 also lists the delta AICc of each model, calculated with the following formula:

$$ \Delta AICc = AICc_i - AICc_{min} $$
This value indicates for each model its difference in AICc with the model ranked first (AICc<sub>min</sub>; Burnham and Anderson, 2004). The AICcWt, which is also referenced in Table 3, refers to the weight of the model and also corresponds to its probability (Burnham et al., 2011).

*Summary of the ranking of the models implemented, according to the number of parameters present in each model (K), the AICc, the delta AIC and the weight of each model*

<table><thead><tr><th>Model</th><th>K</th><th>AICc</th><th>ΔAICc</th><th>AICcWt</th></tr></thead><tbody><tr><td>M14</td><td>13</td><td>133290.770</td><td>0</td><td>0.817</td></tr><tr><td>M9</td><td>10</td><td>133295.192</td><td>4.421</td><td>0.090</td></tr><tr><td>M17</td><td>20</td><td>133296.076</td><td>5.306</td><td>0.058</td></tr><tr><td>M15</td><td>13</td><td>133297.010</td><td>6.240</td><td>0.036</td></tr><tr><td>M7</td><td>10</td><td>133308.902</td><td>18.132</td><td>0.000</td></tr><tr><td>M13</td><td>13</td><td>133311.005</td><td>20.234</td><td>0.000</td></tr><tr><td>M8</td><td>10</td><td>133316.257</td><td>25.487</td><td>0.000</td></tr><tr><td>M6</td><td>9</td><td>133316.416</td><td>25.645</td><td>0.000</td></tr><tr><td>M10</td><td>10</td><td>133316.940</td><td>26.170</td><td>0.000</td></tr><tr><td>M12</td><td>10</td><td>133318.065</td><td>27.294</td><td>0.000</td></tr><tr><td>M11</td><td>10</td><td>133318.396</td><td>27.626</td><td>0.000</td></tr><tr><td>M16</td><td>13</td><td>133319.710</td><td>28.940</td><td>0.000</td></tr><tr><td>M4</td><td>7</td><td>133321.742</td><td>30.972</td><td>0.000</td></tr><tr><td>M5</td><td>8</td><td>133322.183</td><td>31.413</td><td>0.000</td></tr><tr><td>M3</td><td>6</td><td>133325.247</td><td>34.477</td><td>0.000</td></tr><tr><td>M2</td><td>5</td><td>133336.483</td><td>45.713</td><td>0.000</td></tr><tr><td>M1</td><td>4</td><td>133339.157</td><td>48.387</td><td>0.000</td></tr><tr><td>M0</td><td>3</td><td>133386.598</td><td>95.827</td><td>0.000</td></tr></tbody></table>

*Note: The details of all models are specified in Table 2*

The model ranked first (model M14) using AIC (see Table 3) was the one retained as best fitting the data. This model accounted for an interaction of primary interest for this study, namely the signature of spatialization (Position in the sequence * Hand of response). This model also considered the influence of the probe amount presented after the memorization on the spatialization effect. A Chi-square test was conducted between this model and the model ranked second in the AIC table (M9 model, simulating an interaction between the Position factor and the Probe Amount factor only), in order to estimate their likelihood ratio. The results indicated a significant difference between the two models (χ²(3) = 10.44, p = .015).

In the finer analysis of the M14 model, a significant effect of the position in the
sequence on participants' reaction times was observed, with faster response times for the first items in the sequence: 783 ms (SD = 209 ms) on average for position 1, against 802 ms (SD = 228 ms) for position 2, 775 ms (SD = 202 ms) for position 3 and 792 ms (SD = 222 ms) for position 4. An effect of the probe amount was also observed<fnref n="6" /> sequence in the multi-probe condition. This restricted analysis still showed slower reaction times in the mono-probe condition than in the multi-probe condition for the first probe (t(2801) = -9.22, p < .001), indicating significantly slower response times in the Mono-probe condition than in the Multi-probe condition: 874 ms (SD = 231 ms) vs. 704 ms (SD = 149 ms). Participants also had significantly slower response times in the Image condition, compared to the Word condition: 816 ms (SD = 222 ms) vs. 756 ms (SD = 194 ms). Finally, participants tended to respond faster overall with the left hand (785 ms, SD = 223 ms), than with the right hand (791 ms, SD = 208 ms).

A significant interaction effect between the position of the item in the sequence and the response hand was then observed, supporting the existence of a spatialization effect. This interaction, shown in Figure 3, reported faster response times with the left hand for the first item of the sequence: 757 ms (SD = 197 ms) on average for position 1, 812 ms (SD = 245 ms) for position 2, 777 ms (SD = 210 ms) for position 3, and 795 ms (SD = 235 ms) for position 4; and faster response times with the right hand for the last items of the sequence: the average response time for position 1 was 809 ms (SD = 218 ms), against 793 ms for position 2 (SD = 210 ms), 772 ms for position 3 (SD = 195 ms), and 790 ms for position 4 (SD = 210 ms). All of these results are reported in Table 4.

Finally, a significant three-way interaction between the position of the item, the response hand and the probe amount after the sequence was observed. The results, shown in Figure 4, suggest that spatialization is modulated by the number of probes presented to participants during the recognition phase. A primacy effect in the Multi-probe condition was observed, with globally faster response times for the first positions, while a recency effect was more marked in the Mono-probe condition (which was also marked by a primacy effect). The combined primacy and recency effects seems to produce a better balance of the spatialization

<footnote n="6">⁶ This effect was also significant when considering only the first probe presented after the to-be-recalled</footnote>
OPTIMAL DESIGN FOR THE SPoARC EFFECT

<table><caption>**Table 4**

*Summary of M14 model results.*</caption><thead><tr><th>Effect</th><th>SD</th><th>t</th><th>p</th></tr></thead><tbody><tr><td>Position</td><td>4.098</td><td>-6.828</td><td>&lt;.001</td></tr><tr><td>Hand</td><td>7.224</td><td>-9.196</td><td>&lt;.001</td></tr><tr><td>Probe Amount</td><td>10.460</td><td>-20.630</td><td>&lt;.001</td></tr><tr><td>Stimulus Type</td><td>10.613</td><td>-4.656</td><td>&lt;.001</td></tr><tr><td>Trial</td><td>0.183</td><td>-2.179</td><td>0.029</td></tr><tr><td>Position × Hand</td><td>4.081</td><td>5.296</td><td>&lt;.001</td></tr><tr><td>Position × Probe Amount</td><td>4.472</td><td>7.325</td><td>&lt;.001</td></tr><tr><td>Hand × Probe Amount</td><td>7.363</td><td>4.799</td><td>&lt;.001</td></tr><tr><td>Position × Hand × Probe Amount</td><td>4.422</td><td>-2.853</td><td>0.004</td></tr></tbody></table>

*Note: SD = Standard Deviation, Position = Position in the sequence, Hand = Hand of response and Trial = Trial Number.*

effect in the Mono-probe condition. **Indeed, the spatialization effect was more symmetrical in this condition, in which we observed a clear difference between the left hand and the right hand for the first position, and a difference of the same nature but opposite for the last position.**

The generalized linear mixed model analysis was also conducted to compare the mono-probe condition to the case where participants were administered the first probe in the multi-probe condition. Among the 17 models created, the model that best fitted the data was similar to that of the previous more general analysis –that included all probes– (M14<sub>Probe 1</sub> ← RT~ Position * Hand * Probe Amount + Stimulus Type + Trial + (1|Item) + (1|Subject), see Table A in Supplementary Material). Although the best models between the two analyses matched, one difference between the two analyses was that the interaction between the spatialization (Position × Hand) and the Amount of probe was no longer significant in the new analysis. Because restricting the analysis to the first probe in the multi-probe condition reduced the data set (16 true probes per participant, vs. 30 in the mono-probe condition), we might have lacked power to best detect this interaction. However, the comparison between the global analysis and this new restricted analysis allows us to conclude that the significantly different pattern of responses between the two conditions (in the global comparison) most probably emerged due to the succession of probes.
<figure><img src="image_5.png" /><figcaption>Figure 3</figcaption></figure>

Mean and linear trend of response times (ms) depending on the position of the item in the sequence and the response hand. Note. In blue, the response times obtained with the left hand; in yellow, the response times obtained with the right hand; the black slope corresponds to the regression line of the $d_{RT}$ (RT right hand - RT left hand). All of the linear regressions were calculated on the aggregated data including a $d_{RT}$ per position and per subject, and the error bars correspond to a standard error.

Spatialization effect through linear regression

A linear regression involving the independent variables Position of the item in the sequence and Hand of response was then calculated. This linear regression was calculated using the difference of response times between the right hand and the left hand ($d_{RT} = RT_{right hand} - RT_{left hand}$) depending on the position of the item in the memorized sequence. A positive $d_{RT}$ indicated a faster response time with the left hand, while a negative $d_{RT}$ indicated a faster response time with the right hand. A linear regression on the difference in response times between right and left hands was performed for each participant. The regression coefficient then quantified the weight of this regression for each increase of one unit of the Position variable (considered a predictive variable). When it was negative, the
OPTIMAL DESIGN FOR THE SPoARC EFFECT

<figure><img src="image_6.png" /><figcaption>Figure 4</figcaption></figure>

Mean and linear trend of response times (in ms) depending on the position of the item in the sequence and the response hand. The blue curve corresponds to the response times obtained with the left hand and the yellow curve to the response times obtained with the right hand. The black curve corresponds to the general linear trend of $d_{RT}$

(RT right hand – RT left hand). These results are obtained on the aggregated data and the error bars correspond to a standard error.

regression coefficient indicated a so-called “Western” spatialization, going from left to right.

A significant effect of the position of the item on the $d_{RT}$ of all participants was found, with a decrease in $d_{RT}$ of 16.37 ms on average per position ($t(523) = -2.747, p = .006$). The average $d_{RT}$ for position 1 was 48.1 ms ($SD = 156$ ms), against -11.6 ms ($SD = 159$ ms) for position 2, -2.9 ms ($SD = 134$ ms) for position 3, and -9.4 ms ($SD = 156$ ms) for position 4.

This analysis therefore indicated a faster response time with the left hand for the first items in the sequence and a faster response time with the right hand for the last items in the sequence, as highlighted in Figure 5 which shows the general trend for all participants. One sample t-tests were conducted for each position in the sequence to determine if the mean $d_{RT}$ significantly differed from 0. Results were significant only for the first position

$(t(130) = 3.524, p < .001 \text{ against } t(130) = -0.836, p = 0.404 \text{ for position 2,}$
$t(130) = -0.249, p = 0.804$ for position 3, and $t(130) = -0.687, p = 0.493$ for position 4).

<figure><img src="image_7.png" /><figcaption>Figure 5</figcaption></figure>

Linear regression showing the decrease in the difference of mean response times between right and left hands (denoted $d_{RT}$, in milliseconds) as a function of the position of the item in the memorized sequence. Note. A positive $d_{RT}$, found for example in position 1, indicates faster response times with the left hand. A negative $d_{RT}$, observed for example in position 4, indicates faster response times with the right hand. The figure was made with aggregated data, with a $d_{RT}$ by position and by subject. Each $d_{RT}$ was obtained by calculating the difference between the mean RT obtained with the right hand and the mean RT obtained with the left hand, for each position.

## Bootstrap and log-linear analysis

The analysis described previously does not account for the effect of spatialization for each participant. However, individual analysis is important because effects observed at the group level may be due to a minority of participants producing a particularly large effect. Analyses were therefore carried out at the individual level with the Bootstrap method, which was implemented by Cipora et al. (2019) to investigate the SNARC effect (for the SPoARC effect see van Dijck et al., 2020 or Guida, Mosinski, et al., 2020). This method enables to obtain results which are not influenced by the characteristics of the sample by determining a confidence interval of the spatialization slope for each participant. This interval which is
defined by taking into account only the answers of a given participant solely depends on the stability of the answers for this participant. The confidence interval is calculated by selecting from the raw data of the participant *n* random answers by replacement, by hand of response and by position of the item in the sequence. This process is repeated 5000 times and for each random sample of *n* answers created, an individual spatialization slope is calculated.

Repeating this process thousands of times enables to gain precision and stability in the estimation of the spatialization slopes. The confidence interval of the effect is then determined by removing from the set of estimates the lower and upper $\alpha/2$ of the distribution. For an 80% confidence interval, $\alpha = .20$. The confidence interval contains the middle range of the $1 - \alpha$ percentages of the slope estimates. If this confidence interval does not contain 0, the participant is a spatializer. On the other hand, if the confidence interval contains 0, the participant is a non-spatializer.

The analysis carried out revealed that 66% of the participants presented a SPoARC effect (86 participants out of 131), as the confidence interval of their spatialization slope excluded 0. Among these 66% of spatializers, 46% showed a left-to-right spatialization (expected result for Westerners) against 20% who showed a right-to-left spatialization. These results are shown in Figure 6. An adjustment $\chi^2$ test showed that this distribution of participants among the different types of spatialization (Positive slope, No effect, Negative slope) differed from a random distribution ($\chi^2(2) = 13.30, p = .001$), the number of Western spatializers being higher than expected by a theoretical random distribution.

Then, comparisons of the distribution of individuals results between the different experimental conditions were carried out, with the objective of determining whether a condition induced a greater number of spatializers. These analyses are shown in Figure 7 and Figure 8. Concerning the Probe amount variable, in the Mono-probe condition, 57% of the participants obtained a negative slope, 18% did not present any spatialization effect, and 25% obtained a positive slope. Concerning the Multi-probe condition, 35% of the participants obtained a negative slope, 50% did not present a spatialization effect, and 15% obtained a positive slope. Concerning the variable Stimulus Type, 46% of the participants obtained a negative slope, 30% did not present a spatialization effect, and 24% obtained a positive slope
<figure><img src="image_8.png" /><figcaption>Figure 6</figcaption></figure>

Results of the individual analysis for each participant using the Bootstrap method with 5000 repetitions. Each point represents a participant's regression slope, with an 80% confidence interval. Participants exhibit a left-to-right SPoARC effect when their slope is negative and when their confidence interval does not contain 0. Participants exhibit a right-to-left SPoARC effect when their slope is positive and when the confidence interval does not contain 0. If the confidence interval contains 0, the participant does not show any significant SPoARC effect. Note. The entire sample comprises 46% of western spatializers, 34% of non-spatializers and 20% of participants spatializing information from right to left.

in the Image condition. In the Word condition, 46% of the participants obtained a negative slope, 39% did not present a spatialization effect, and 15% obtained a positive slope. In order to detect a difference of distribution between these groups, independence $\chi^2$ tests were carried out. These indicated a significant difference in terms of distribution of participants between the Mono-probe and Multi-probe conditions ($\chi^2(1) = 5.44, p = .019$). The same test was not significant between the Word and Image conditions ($\chi^2(1) = 8.41 e^{-31}, p = 1$).

Finally, a last comparison of individuals from the different experimental conditions was carried out, with the aim of specifying whether one of these combined conditions could enable to obtain a greater number of spatializers. This analysis, shown in Figure 9, indicated
OPTIMAL DESIGN FOR THE SPoARC EFFECT

<figure><img src="image_9.png" /><figcaption>Figure 7</figcaption></figure>

Comparison of the distribution of the results of the individual analysis for each participant depending on the probe amount presented, using the Bootstrap method with 5000 repetitions. Note. Western spatializers are 57% and 35% in the Mono-probe and the Multi-probe conditions, respectively. Non-spatializers are 18% and 50% respectively in Mono-probe and Multi-probe conditions. The right-to-left spatializers are 25% and 15% respectively in the Mono-probe and Multi-probe conditions.

that in the Mono-Image condition, 53% of participants had a negative slope, compared to 61% in the Mono-Word condition, 38% in the Multi-Image condition, and 32% in the Multi-Word condition. Concerning the participants not presenting any spatialization effect, they were 16% in the Mono-Image condition, 19.5% in the Mono-Word condition, 44% in the Multi-Image condition, and 56% in the Multi-Word condition. Finally, in the Mono-Image condition, 31% of participants obtained a positive slope, against 19.5% in the Mono-Word condition, 18% in the Multi-Image condition and 12% in the Multi-Word condition. Intending to further investigate the interaction between the probe amount and the stimulus type, a log-linear analysis was conducted using JASP (JASP Team, 2022) on the contingency Table 5 summarizing the results of individual analysis by experimental condition. The results (see Table 6) showed a
OPTIMAL DESIGN FOR THE SPoARC EFFECT

26

<figure><img src="image_10.png" /><figcaption>Figure 8</figcaption></figure>

Comparison of the distribution of the results of the individual analysis for each participant depending on the stimulus type presented, using the Bootstrap method with 5000 repetitions. Note. Western spatializers are 46% and 46% in the Image and the Word conditions, respectively. Non-spatializers are 30% and 39% respectively in Image and Word conditions. The right-to-left spatializers are 24% and 15% respectively in the Image and Word conditions.

significant effect of the type of spatialization (negative slope, absence of effect, positive slope), indicating a non-random distribution of the participants across the conditions ($L^2(2) = 13.88, p < .001$). A significant effect of the interaction between the probe amount and the type of spatialization was also produced ($L^2(2) = 15.95, p < .001$), indicating a significantly higher number of spatializers with a Western direction in the Mono-probe condition compared to the Multi-probe condition. On the other hand, no effect of the stimulus type and no effect of interaction with Stimulus type was found.

Discussion

For the very first time, this study conjointly manipulated the number of probes in a SPoARC experiment (single vs. multiple) and the stimulus type (image vs. word) comparing
OPTIMAL DESIGN FOR THE SPoARC EFFECT

<figure><img src="image_11.png" /><figcaption>**Figure 9**</figcaption></figure>

Comparison of the distribution of the results of the individual analysis for each participant depending on the four experimental conditions, using the Bootstrap method with 5000 repetitions.

**Table 5**

Contingency table characterizing the number of participants (and the corresponding percentage) having a significantly positive regression slope, significantly negative regression slope or showing no effect depending on the four experimental conditions.

<table><thead><tr><th rowspan="2">Condition</th><th colspan="3">Mono-probe</th><th colspan="3">Multi-probe</th></tr><tr><th>Negative</th><th>No effect</th><th>Positive</th><th>Negative</th><th>No effect</th><th>Positive</th></tr></thead><tbody><tr><td>Image</td><td>17 (53%)</td><td>5 (16%)</td><td>10 (31%)</td><td>13 (38%)</td><td>15 (44%)</td><td>6 (18%)</td></tr><tr><td>Word</td><td>19 (61%)</td><td>6 (19.5%)</td><td>6 (19.5%)</td><td>11 (32%)</td><td>19 (56%)</td><td>4 (12%)</td></tr></tbody></table>

four experimental designs used in the investigation of the spatialization phenomenon in order to determine which method allows a better detection of the effect. We expected to observe a stronger spatialization in participants having to detect only one probe after each sequence, compared to participants having to detect several ones. Our second prediction was that the use of pictorial stimuli would allow a better demonstration of the SPoARC effect than the use of
<caption>**Table 6**</caption>

*Summary of the results of the log-linear analysis.*

<table><thead><tr><th></th><th>ddl</th><th>L</th><th>p</th></tr></thead><tbody><tr><td>Spatialization Type</td><td>2</td><td>13.877</td><td>&lt; .001</td></tr><tr><td>Probe Amount</td><td>1</td><td>0.191</td><td>0.662</td></tr><tr><td>Stimulus Type</td><td>1</td><td>0.008</td><td>0.930</td></tr><tr><td>Spatialization Type × Probe Amount</td><td>2</td><td>15.952</td><td>&lt; .001</td></tr><tr><td>Spatialization Type × Stimulus Type</td><td>2</td><td>1.946</td><td>0.378</td></tr><tr><td>Probe Amount × Stimulus Type</td><td>1</td><td>0.076</td><td>0.783</td></tr><tr><td>Spatialization Type × Probe Amount × Stimulus Type</td><td>2</td><td>0.224</td><td>0.894</td></tr></tbody></table>

written words. Our findings only confirmed the hypothesized effect of the amount of probes. We found no significant effect of the stimulus type.

We first discuss the fact that 20% of the participants showed a significant reversed SPoARC effect in our results. A right-to-left spatialization is expected to be found in individuals that have a right-to-left reading and writing direction (Guida et al., 2018). However, this is not the case in our study, as no participant that exhibited a reversed effect have reported having such reading direction. This right-to-left spatial mapping can be due to the analysis we used to process our results at an individual level. Cipora et al. (2019) observed a significant reversed SNARC effect in some of their participants when using the Bootstrap analysis. The authors stated that a larger number of repetition of the sampling process in the bootstrapping analysis can lead to the detection of a greater number of participant showing a spatialization effect (a SNARC effect in their case). However, the greater sensitivity of the test is also more likely to detect a greater number of participant showing a reversed effect. This is due to the confidence intervals that become narrower as the number of repetitions increases. The authors also showed that the choice of the confidence interval matters. In our study, we chose a quite liberal level of confidence interval equal to 80%, which could produce a greater detection of the reversed effect. We believe that both of these factors are at stake here in the detection of inverse spatializations. But regarding the inverse effect per se, although we obtained a larger proportion than in previous studies using the same parameters for the bootstrap (van Dijck et al., 2020), no clear explanation has been provided so far for either the reversed SNARC or SPoARC effect in adults (to the best of our knowledge).

Regardless of the stimulus type, our experiment let us observe a greater number of
Western spatializers than chance would expect. These findings are consistent with various studies that have extended the SPoARC effect to the memorization of different stimuli such as letters, colors, words or images (Guida, Mosinski, et al., 2020; Shi et al., 2020; van Dijck et al., 2020; Zhou et al., 2019). However, our results do not favor one stimulus type over the other in the detection of the SPoARC effect. Using words or images hence does not seem to influence spatialization in an adult population. This is in contrast with the results of Previtali et al. (2010) who showed that the intensity of the spatialization effect varied according to the type of stimulus presented to the participant. However when comparing our results with those of Previtali et al. (2010) it is important to keep in mind that although they used random sequences of items (i.e., bow, tent, apple, train, chair, rose, lighthouse, cat, and palm), their sequences had to be over-learned during a training session, so by the time of the test these sequences were memorized in long-term memory (LTM). It is unsure whether this could explain the discrepancy of the results, but this potential confound has to be kept in mind for future study. Overall, images could be easier to visualize due to their diverse features (shape, color, ...). However, words can also feel more natural to organize from left to right because reading or writing words impels a movement in the expected direction. The role of visualization in the process of spatialization is then questioned here.

The lack of facilitation of spatialization by imaged stimulus may also indicate that it is
only the positions that are coded from left to right and not the image of the items themselves.
This last interpretation suggests that the SPoARC effect could reflect the recruitment of an
ordered recall structure allowing the spatial encoding of positions, with each position referring
indirectly to the successive to-be-remembered items (Guida & Campitelli, 2019). Instead of
being triggered differently by stimulus type (word, image, etc.), a SPoARC effect could
simply depend on a common feature of these two types of stimuli. Indeed, Ginsburg et al.
(2017) showed a difference in spatialization by presenting concrete and abstract drawings in
their study. Specifically, a difference was observed between participants who verbalized the
material and participants who did not use a verbalization strategy when presented with
abstract drawings. Participants using a verbalization strategy showed a strong spatialization
slope with both types of drawings, while participants not using verbalization had a strong
spatialization slope only with concrete drawings. Highly semantic stimuli thus appear to be
spatialized regardless of their form (word or image). This therefore questions the role of
verbalization in the phenomenon of spatialization.

The lack of difference in spatialization between the two types of stimulus also supports
the idea that the use of visual material is suitable for studying spatialization in a population of
children for whom reading skills are not acquired or not consolidated yet. Although testing
participants with auditory presentations is a potential solution (Bottini et al., 2016; Guida
et al., 2016), the use of images could also open the possibility to investigate the effect with
participants having a written language disorder. Using written words with such participants
could bias the measure of spatialization due to slower word processing during memorization
or recall. Using images would therefore provide a solid basis to compare such populations and
a general population of adults.

Finally, the absence of difference between images and words may highlight a
difference between spatialization in working memory and spatialization as used in the method
of loci. As we explained in the introduction, the method of loci is used by mnemonists to
increase their mnemonic capacities. They encode items to be remembered by mentally linking
them to known locations (e.g., linking a “swan” to their front door). During this process, they
usually create a visual mental image of each association (e.g., the swan is dandling in the air
with its beak on the handle of the door) to favor the integration of the memoranda into the
locations. Given these elements, one could have imagined that the images in our experiment
would have favored an integration of the memoranda into the horizontal mental line increasing
the SPoARC effect, but it does not seem to be the case. We believe that this highlights an
important difference, which derives from the simple and maybe abstract nature of the
horizontal mental line in comparison to how semantics and locations can be associated in the
method of loci.

Our main result concerns the number of probes presented after each sequence. Our
experiment shows a benefit of presenting a single probe rather than multiple probes to detect a
greater number of spatializers, as expected in the hypotheses. A possible explanation might be
that during a multi-probe recognition task, participants mentally scan the memorized sequence
for each presented probe. On one hand, this successive scanning of the sequence could reinforce the memorization of the sequence. This putative reinforcement could indicate a potential stronger encoding of the position of the items, thus supporting a stronger spatialization effect. In terms of mnemonic performance, this is what occurs in the testing effect where successive retrievals are known to be beneficial (e.g., Roediger III and Karpicke, 2006). On the other hand, the consolidation of the sequence could result in chunking. The positional information of each item would then vanish as several items or the whole sequence could be grouped and having only one positional code, eventually alleviating spatialization.

The chunking hypothesis seems to agree with our results which indicate that the more the participant is asked to scan the memorized sequence, the less the spatialization is detected. Our results could inspire the investigation of spatialization when chunks are formed. In light of our results, one could then postulate that the more the sequence is repeated (and consequently chunked in LTM due to progressive learning), the less items would be spatialized in memory. We thus believe that such an experimental design could be of interest for further studies to come.

However, here what we believe to be the main culprit of the weakened spatialization in the Multi-probe condition is that presenting different probes after the same sequence produces output interference. This process would compromise the measure of spatialization as positional information could be less well marked in the progressively decaying memory traces. Output interference is the gradual decrease in memory performance as a function of the position of items in a testing sequence (e.g., Annis et al., 2013; Clark and Gronlund, 1996; Criss et al., 2011; Humphreys et al., 1989). In this phenomenon, two sources of interference have been highlighted. The first type is what Criss et al. (2011) call “item interference”. In our design item interference corresponds to the proactive interference between successive probes. The second element is what they call “context interference”, which could correspond in our task to the spatial values that are linked to the successive probes. Therefore, in the Multi-probe condition, not only the accumulation of the probes (of one sequence) could create interference but the fact that the participants will convoke the spatial values of each probe could also cause spatial interference. This accumulation of probes and spatial context
interference at each sequence does not exist in the Mono-probe condition where each sequence is only tested using a single probe.

The output interference account seems consistent with the decrease in the accuracy of responses as the position of probes in the probing sequence increased in the multi-probe condition (as shown in our results by a significant negative correlation between accuracy and the rank of the probe during the test phase, $\rho = -.05, p < .001$; the mean accuracy for each position of the probe in the probing sequence is reported in Table B in Supplementary Material). Participant tended to commit more errors as probes accumulated after a to-be-recalled sequence. Another hint for this phenomenon could be slower reaction times in the multi-probe condition. Participants would require more time to take a decision as a function of interference. On the contrary, the reaction times tended to be faster as the position of the probe in the probing sequence increased ($\rho = -.09, p < .001$; see the mean response times for each position of the probe in the probing sequence in Table B in Supplementary Material). This could rather favor the chunking account that we previously mentioned, as one could have expected a reversed pattern of response times if output interference had indeed been at stake here. However, this negative correlation between response times and the position of the probe in the probing sequence was actually mainly due to a difference between the first probe and the following probes. The negative correlation was no longer significant for the probes between the second and eighth position ($\rho = -.01, p = .34$). We argue here that faster response times could reflect that participants might have been able to respond at a faster pace because of the repetitive successive tasks of the same nature in the multi-probe condition, in comparison to the mono-probe condition that involved more frequent switching (from observing sequences, to responding to probes).

Consistent with this hypothesized output interference is the phenomenon of spatial expansion that is thought to occur with spatialization (Guida, Abrahamse, et al., 2020). In their study of the SPoARC effect, Guida, Abrahamse, et al., 2020 asked participants to remember sequences of 5 consonants presented in the center of the screen like in our study. However unlike our study, they manipulated (among other factors) the presentation rate of the consonants (1 second per item vs. 5 seconds per item). Their results showed that the SPoARC
effect became larger with slower presentation rates, which was interpreted as follows. When given more time, the cognitive system increases the spatialization of the memoranda. In other words, the horizontal mental line is expanded increasing the space between the memoranda. Conversely, once the probe is displayed and its processing takes place, it is thought that the horizontal mental line will start shrinking given that the participant cannot focus on the whole sequence. Going back to our results, this should mean that when comparing Mono- with Multi-probe conditions, the horizontal mental line should be similar right after the sequence is displayed (i.e., for the first probe, as it is shown by the absence of difference in spatialization between the mono-probe condition and when considering only the responses to the first probe in the multi-probe condition). However, as the number of probes increases in the Multi-probe condition, participants will not be able to focus their attention on the horizontal mental line which will shrink over time, which could explain why the SPoARC effect is smaller in this condition.

Conclusion

Our experimental manipulation of the number of probes influences the way spatialization can be detected. The presentation of a single probe after each memorized sequence produces larger negative slopes than presenting multiple probes after each sequence. It is therefore preferable to use a mono-probe organization in future experiments, despite a much smaller number of measurements (30 single probes against 128 multiple probes).

Finally, the absence of difference between written and visual stimuli indicates that it is possible to investigate the SPoARC with specific populations (atypical readers or non-readers, such as young children or dyslexic people for example), as we intend to do in the future.

Open Practices Statement

The experiments were not preregistered. The data for the experiment and the R scripts are available at https://osf.io/fam6q/.
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OPTIMAL DESIGN FOR THE SPoARC EFFECT

**Supplementary Material**

<figure><img src="image_12.png" /><figcaption>**Figure A**
Distribution of response times</figcaption></figure>

<table><caption>**Table A**
Summary of model M14. Note. The data was limited to the first probe presented after the to-be-memorized sequence of the multi-probe condition.</caption><thead><tr><th>Effect</th><th>SD</th><th>t</th><th>p</th></tr></thead><tbody><tr><td>Position</td><td>4.99</td><td>-5.12</td><td>&lt;.001</td></tr><tr><td>Hand</td><td>18.30</td><td>-3.60</td><td>&lt;.001</td></tr><tr><td>Probe Amount</td><td>21.84</td><td>-9.22</td><td>&lt;.001</td></tr><tr><td>Stimulus Type</td><td>20.60</td><td>-2.89</td><td>&lt;.001</td></tr><tr><td>Trial</td><td>0.23</td><td>-1.51</td><td>0.13</td></tr><tr><td>Position × Hand</td><td>6.44</td><td>3.35</td><td>&lt;.001</td></tr><tr><td>Position × Probe Amount</td><td>8.02</td><td>5.94</td><td>&lt;.001</td></tr><tr><td>Hand × Probe Amount</td><td>26.79</td><td>0.08</td><td>0.94</td></tr><tr><td>Position × Hand × Probe Amount</td><td>10.69</td><td>-0.25</td><td>0.81</td></tr></tbody></table>
OPTIMAL DESIGN FOR THE SPoARC EFFECT

40

**Table B**

*Mean reaction times and mean accuracy for each probe position presented during the recognition phase in the multi-probe condition.*

<table><thead><tr><td>Probe position</td><td>Reaction time (ms)</td><td>Accuracy (%)</td></tr></thead><tbody><tr><td>1</td><td>860</td><td>0.972</td></tr><tr><td>2</td><td>729</td><td>0.966</td></tr><tr><td>3</td><td>705</td><td>0.963</td></tr><tr><td>4</td><td>721</td><td>0.953</td></tr><tr><td>5</td><td>717</td><td>0.959</td></tr><tr><td>6</td><td>707</td><td>0.964</td></tr><tr><td>7</td><td>716</td><td>0.949</td></tr><tr><td>8</td><td>709</td><td>0.948</td></tr></tbody></table>

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