# Processing order in short-term memory is spatially biased in children

Maëliss Vivion, Morgane Ftaïta, Alessandro Guida, Fabien Mathy

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Maëliss Vivion, Morgane Ftaïta, Alessandro Guida, Fabien Mathy. Processing order in short-term memory is spatially biased in children. Journal of Experimental Child Psychology, 2025, 252, 10.1016/j.jecp.2024.106171. hal-05503968

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# Processing order in short-term memory is spatially biased in children

<figure><img src="image_4.png" /></figure>

Maëliss Vivion<sup>a,1,2</sup>, Morgane Ftaïta<sup>a,1,3</sup>, Alessandro Guida<sup>b,4</sup>, Fabien Mathy<sup>a,*,5</sup>

## ARTICLE INFO

### Article history:

Received 24 July 2024

Revised 29 November 2024

### Keywords:

Children

Development

Serial Order

Short-term Memory

Spatial Cognition

Spatialization

## ABSTRACT

When processing serial information, adults tend to map elements of a sequence onto a mental horizontal line, following the direction of their reading and writing system. For example, in a Western population, the beginning of a series is associated with the left-hand side of the mental line, while its end is preferentially associated with the right. To complete the few studies that have investigated the cultural vs. innate determinants of such a spatial bias, the current study used a rotation task of unlabeled serial information. Experiment 1 measured the presence of a left-oriented bias in children from toddlers to grade 5 (aged 2 to 12 years old) and in adults. Results only showed a bias in adults. Experiment 2 was designed to avoid potential confounds identified in Experiment 1, and Experiment 3 provided more explicit information to participants, but the results still did not show a clear left-oriented bias in children. By controlling the mental rotation of our material in Experiment 4, we finally observed a global left-to-right bias across age groups, in particular between the 2nd grade (7 years old) and the 4th grade (9 years old), and in adults. Overall, this study shows that spatial-ordinal associations observed in adults can also be observed in children as early as primary school. In addition, a weaker bias was observed in younger children, which suggests that

<footnote><sup>a</sup> BCL, CNRS, Université Côte d'Azur, Nice, France</footnote>

<footnote><sup>b</sup> LP3C, Université Rennes 2, Rennes, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: fabien.mathy@univ-cotedazur.fr (F. Mathy).</footnote>

<footnote n="1">¹ The first co-authors Maëliss Vivion and Morgane Ftaïta contributed equally to this work.</footnote>

<footnote n="2">² https://orcid.org/0000-0001-5040-7093.</footnote>

<footnote n="3">³ https://orcid.org/0000-0002-8616-5476.</footnote>

<footnote n="4">⁴ https://orcid.org/0000-0002-8733-4470.</footnote>

<footnote n="5">⁵ https://orcid.org/0000-0002-7705-5689.</footnote>
the effect could begin to emerge in preschool (4 years old) before
being reinforced later with expertise in literacy.

© 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Introduction

Humans have a tendency to map information onto space. It can be external space (as evidenced by the discovery of cave paintings created by humans 20,000 years ago, d'Errico & Nowell, 2001) or internal space (Worthen & Hunt, 2011). Internal spatial mapping is for instance a prominent aspect of temporal information (Tversky et al., 1991), which can be mapped in multiple ways (e.g., onto a horizontal line from left to right or from right to left, or onto a vertical line from top to bottom). This phenomenon depends on cultural differences and is especially influenced by the reading direction (see Boroditsky, 2001; Troadec & Zarhbouch, 2011). Such spatial mapping is embedded in our cognitive system, in particular when serial information is processed. In memory, a phenomenon known as *spatialization* consists in mentally organizing several elements of an ordered sequence onto a mental space.

Spatialization occurs when processing items from highly familiar sequences such as digits (referred to as the SNARC effect - Spatial Numerical Association of Response Codes - first studied by Dehaene et al., 1993), days of the week (Gevers et al., 2004), months of the year, and letters of the alphabet (Gevers et al., 2003). Spatialization of ordinal information is also observed with sequences of items presented in an unpredictable order, such as random sequences of digits (van Dijck & Fias, 2011), letters (de Belder et al., 2015), colors (Guida et al., 2018), and concrete shapes (Ginsburg et al., 2017). This specific phenomenon is referred to as the SPoARC (Spatial Positional Association of Response Codes, Guida & Lavielle-Guida, 2014), or OPE (Ordinal Position Effect, Ginsburg et al., 2014). The difference between the SNARC and the SPoARC is that spatialized items in the SNARC correspond to overlearned sequences pertaining to long-term memory. On the contrary, the spatialized items in the SPoARC correspond to sequences temporarily maintained in short-term memory (Guida & Campitelli, 2019). The present study focuses on the latter phenomenon.

While spatial-numerical associations in children are known to appear from the earliest stages of
life (see Bulf et al., 2016; de Hevia & Spelke, 2010; de Hevia et al., 2014; de Hevia et al., 2017), the ori-
gins of the SPoARC remain unknown and somehow debated. Several arguments lean towards a cultur-
ally determined spatial bias. Among these arguments is the fact that the direction in which
information is organized on a mental horizontal array follows reading and writing habits when com-
paring Western and Arabic readers (Guida et al., 2018). The absence of this bias in illiterate or early-
blind people (Bottini et al., 2016; Guida et al., 2018) also seems to indicate that this phenomenon
could be shaped by early visual experience, and later by reading and writing (Guida et al., 2018).

One way to further explore the origins of the SPoARC is to investigate its –putative– acquisition in children. As children grow up, they progressively become more familiar with spatial biases thanks to their daily life experiences (e.g., materials in schools such as timelines, or gestures of supervisors and relatives pointing to materials following the direction of reading; see Göbel et al., 2018; Troadec & Zarhbouch, 2011). Alphabetical and numerical knowledge can congruently influence the acquisition of spatial biases (McCrink et al., 2017; Guida et al., 2020). For example, McCrink et al. (2017) trained children aged 2–3 years old to locate an object that was hidden in a box among five boxes organized on a radial axis (or sagittal axis, i.e., an axis running horizontally from the back of the head to the front, thus dividing the body into a left and right part, see Fig. 1a). The five boxes were either labeled numerically, alphabetically, or were unlabeled. After the learning phase, the line of boxes was rotated 90°. Children had to retrieve the hidden object using the novel horizontal layout. Participants who were exposed to explicit ordinal information (boxes with numerical or alphabetical labels) exhibited a retrieval strategy consistent with a left-to-right mapping (e.g., they mapped the boxes from left to right, with Box #1 or Box A being associated with the first box on the left). Conversely, no evidence for a spatial bias was found for the children exposed to the unlabeled boxes. The absence of a spatial
bias in this unlabeled condition tends to favor the idea that the left-oriented spatial bias found in the other conditions was due to a cultural habit. However, the absence of a spatial bias using implicit serial information (i.e., using unlabeled material) in toddlers leaves uncertain its presence in older children.

In addition, other studies have shown a left-oriented bias in younger children, which contradicts the hypothesis of an exclusive cultural origin. For example, newborns show a preference for small quantities when presented on the left side of a screen and an opposite preference for large quantities when presented on the right side of a screen (de Hevia et al., 2017; Di Giorgio et al., 2019). Infants aged 7 months old also exhibit a preference for looking at increasing numerical sequences presented from left to right (de Hevia et al., 2014). A left-oriented bias is even present in non-human species such as monkeys (Drucker & Brannon, 2014), bees (Giurfa et al., 2022), and chicks (Rugani et al., 2010). Chicks that are trained to peck at a specific position among an array of 16 items oriented radially<fnref n="6" /> tend to peck at the same position starting from the left after the array is rotated 90° (i.e., to a horizontal position). Thus, an innate bias would be present in human and non-human species. In humans, this bias would spontaneously extinct at an early age (McCrink & de Hevia, 2018; McCrink et al., 2017), followed later on by the emergence of a cultural bias that would develop with schooling (but for an alternative hypothesis see Patro et al. (2016), who showed that spatial biases could be shaped by visuo-motor activities, leading to the implicit learning of cultural habits before the acquisition of reading and writing). Alternatively, the cultural bias could cause the extinction of the innate bias. Evidence of the fading of this innate bias has been shown using eye-tracking in a study in which children from 1 to 5 years old and adults were tested for a left-to-right visual preference after a rotation from a vertical presentation to a horizontal one (West & McCrink, 2021). A layout of five boxes was presented vertically on a screen. An object was always hidden in the same box during the first four trials (Box #2 for 50% of participants and Box #4 for the other 50%). The layout was then rotated to a horizontal axis in the last trial. The bias was characterized by the time spent searching on the part of the screen corresponding to a left-to-right mapping. The results showed that the 1-year-old children exhibited a preference for a left-to-right mapping. This preference then disappeared before reappearing at 4 years old, but was no longer present in 5-year-old children and in adults. Still, it is not excluded that a spatial bias can preferentially occur when participants are required to select locations instead of simply looking at the most plausible location.

## The present study

In this study, we used a paradigm inspired by the methodologies of McCrink et al. (2017) and West and McCrink (2021) to explore the developmental trajectory of a spatial bias in children from 2 to 12 years old and in adults. To do so, we used a rotation task in which a line of six unlabeled boxes was surreptitiously transposed from a radial to a horizontal layout. Children were first habituated to find an object in a specific box on the radial layout before being asked to retrieve this particular box on the horizontal layout. We chose not to use any label for the boxes that were presented to participants. This approach allowed to reproduce the condition in which McCrink et al. (2017) did not observe any spatial bias in their youngest group of 2–3 years old, thus enabling to investigate whether this bias would be detected in older participants. We also thought that an unlabeled condition, which reduces cultural aspects, could offer better comparisons with the original navigational paradigm of Rugani et al. (2010), first devised to study non-human animals.

Under the hypothesis that a left-to-right cultural bias preferentially appears with schooling, we hypothesized that the bias would emerge at the earliest in grade 1, when children receive extensive formal teaching of reading and writing. Because numbers and the alphabet are already learned early in preschool, such knowledge could help children spatialize information when numerical or alphabetical information is explicitly stated. However, since no numerical or alphabetical information was used in our experiment, we expected a deeper (i.e., more abstract) process to take place to bootstrap spatialization in our task. Such a process would require a more extensive enculturation of the left-to-right

<footnote n="6">⁶ We use the radial vs. horizontal terminology rather than sagittal vs. transversal.</footnote>
direction. We thus expected that children would need to get more expert with reading and writing for a left-to-right spatial bias to apply implicitly.

For the same reason, we expected that adults would show a clear spatial bias from left to right due to a longer cultural exposure, allowing serial information to be bound to a left-to-right mental line. As such, the population of adults was thought to offer a baseline.

# Experiment 1

## Method

### Participants

This study was approved by Université Côte d'Azur's ethic committee (CERN #2018-009)<fnref n="7" />. A sample of 216 participants took part in this experiment, divided in eight age groups. Sample size and mean age are reported for each group in Table 1. Data from children in grades 4 and 5 were analyzed as one group, since only two children in grade 5 could participate in this experiment. Our sample size was based on McCrink et al. (2017) who tested 48 children per condition, comprising two age groups. We decided to target a similar sample size (i.e., 24 per age group), allowing us to analyze the data in each group separately and also to investigate the bias by grouping age groups of children (for instance, 53 participants by grouping the toddlers and preschool children, etc; see Table 1).

### Material

The stimuli consisted of six 3.5×3.5 cm cards representing colored drawings of six animals: "Abeille" (bee), "Cochon" (pig), "Fourmi" (ant), "Grenouille" (frog), "Mouton" (sheep), and "Tortue" (turtle). An additional card of the same size but representing a gift was used for the test phase (see Fig. A in Appendix). For each animal name, the frequency, number of syllables, and age of acquisition were controlled using the OpenLexicon app, as presented in Table A in Appendix. All animal names were bisyllabic in French. A tray of 70×12 cm was used with six opaque cups (with a radius of 8 cm) glued on it. The distance between each cup was 4.5 cm and each cup was closed by removable opaque paper lids (see Fig. B in Appendix).

### Procedure

Each participant sat in front of the experimenter with the material placed between them, positioned approximately 30 cm away from the child. They were instructed that the experimenter was playing a game of hide and seek with the animals represented on the cards, and that the experimenter needed their help to find the animals. It was explained that each box was a hiding place, and that animals could only hide in one of those boxes. Children were asked to name each animal before the beginning of the experiment to ensure their knowledge of those animals.

For the adult group, the procedure was similar except that it was underlined that the experiment was originally implemented for young children. The adults were instructed that the task would seem overly simple, and that participants were just requested to give the first most intuitive response. This clarification was made in order to prevent adults from overthinking, for instance by thinking of a trick question.

Training phase (radial trials). Conditioning was implemented as follows: a set of six boxes arranged on a radial axis was presented on the table in front of the participants (see Fig. 1a). The experimenter first showed a card representing an animal to the participants and asked them to name the animal ("Who is going to hide now?"). Then, the experimenter placed the card in the second box starting from the participants<fnref n="8" />. Participants had their eyes open and could see where the card was hidden. They were then asked to point to the hiding box in order to retrieve the card. Once the animal was found, the same pro-

<footnote n="7">⁷ Experiments 2 and 3 were also approved by this committee, under the same file number.</footnote>

<footnote n="8">⁸ The choice of hiding the cards in the second box was made based on the study conducted by Rugani et al. (2010) involving a similar protocol. In their study, the item to be found was placed (on average) in the fifth position out of the 16 possible locations. This approximates the second position out of the six locations that we used in the current study.</footnote>
<table><caption>**Table 1**
Sample size and mean age per group in Experiment 1.</caption><thead><tr><td>Group</td><td>Sample Size</td><td>Mean Age (SD)</td></tr></thead><tbody><tr><td>Toddlers</td><td>26</td><td>2.5 (0.58)</td></tr><tr><td>Preschool</td><td>27</td><td>3.6 (0.49)</td></tr><tr><td>Kindergarten</td><td>38</td><td>4.9 (0.72)</td></tr><tr><td>Grade 1</td><td>29</td><td>7.1 (0.34)</td></tr><tr><td>Grade 2</td><td>15</td><td>8.2 (0.44)</td></tr><tr><td>Grade 3</td><td>27</td><td>9.0 (0.38)</td></tr><tr><td>Grades 4 & 5</td><td>26</td><td>10.2 (0.31)</td></tr><tr><td>Adults</td><td>28</td><td>32.2 (14.54)</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>**Fig. 1.** Spatial configurations of the practice and test trials in Experiment 1.</figcaption></figure>

procedure was repeated for four other animals (presented in a random order for each participant), with the card always being hidden in the second box. For the last animal (sixth trial), following the procedure of McCrink et al. (2017), the experimenter asked participants to look away while the last card was hidden in the second box ("This time, the animal will hide without you seeing it, but you can know where it will hide"). Participants were then requested to point to the hiding box to find the animal. They could look into the box to check their response and the right box was pointed to them if they were wrong. The first five trials lasted approximately 15 s each (comprising 3 s of stimulus presentation, 2 s hiding the card in the box, 5 s
s for the search phase, and 5 s for the verification phase). The last radial trial lasted 17 s (the hiding phase lasting 4 s instead of 2).

*Testing phase (horizontal trial).* In the last trial (Trial 7, see Fig. 1b), participants were instructed that all animals had been successfully found but that there was a final gift card to be found. To ensure that they could associate this final trial to the six previous ones, they were reminded that all of the animals had always been found in the same box (see McCrink et al., 2017). Then, participants had to turn away and the experimenter made sure they had their eyes closed while hiding the gift card in the second box. Unlike the preceding trials, the series of boxes was rotated 90° unbeknownst to the participants. Particular attention was paid not to make any noise during the rotation in order to prevent participants from relying on auditory cues to estimate the location. When participants opened their eyes again, the boxes were arranged horizontally in front of them. Participants were then requested to point to the box in which they believed the card was hidden. They could then look inside the selected box to verify whether their guess was correct. If not, participants were invited to point to another location. This horizontal trial lasted 19 s (including the hiding phase lasting 6 s while rotating the layout). Only the first response given during the seventh trial was recorded to determine whether participants spontaneously exhibited a spatialization from left to right (i.e., when participants searched in the second box starting from the left after the rotation), from right to left (i.e., when they searched in the second box starting from the right), or when they searched in any of the remaining boxes. The collected data and R scripts that were used for the following analyses are available at https://osf.io/5sg87/.

## Results

We used the *stats* package (R Core Team, 2023) in R to analyze our data. Responses were coded as “Congruent” when matching the expected left-to-right spatial mapping (i.e., Box #2). Responses that corresponded to an inverted spatial mapping (Box #5, matching a right-to-left spatial mapping) were coded as “Reversed”. All other responses were coded as “Incongruous”. To assess the presence of a spatial bias, we first conducted a set of goodness-of-fit $\chi^2$ tests. This test allowed us to evaluate whether the distribution of responses between the six boxes differed from a random distribution. Then, we conducted a set of binomial tests to assess whether a given box (e.g., Box #2) was chosen significantly more than chance level. Under the hypothesis of a leftward bias, we expected Box #2 to be preferentially selected by participants.

## Analysis combining age groups

We first analyzed data by grouping the toddlers and preschool children (age range: 2.5–4 years old), children in kindergarten and grade 1 (age range: 5–7 years old), and children in grades 2 to 5 (age range: 8–12 years old). This approach enabled to assess the presence of a spatial bias given a sample size that approached the one used in McCrink et al. (2017), as the authors detected an effect with a minimum of 48 participants by grouping two age groups. Our results showed that these distributions (see Table 2 for the details of the responses, see also Fig. C in Appendix) differed from a uniform distribution as goodness-of-fit $\chi^2$ tests were significant for each group (all $\chi^2 \ge 16.85$, all *p* values $\le .005$, and all Cohen's W $\ge 0.56$).

Across all samples, participants chose the second box from the left significantly more than chance level (87 congruent responses over the 216 responses, *p* < .001, Cohen's *h* = 0.38). The significance of the result was calculated using a two-tailed binomial test with the probability to choose a specific box set at $\pi = \frac{1}{6}$. The same analysis conducted within each group, using a critical *p*-value threshold of $\frac{0.05}{4} = .0125$ after Bonferroni correction, showed that the test was significant for children in kindergarten and grade 1 (30 congruent responses over 67 responses, *p* < .001, Cohen's *h* = 0.44); grade 2 to grade 5 (23 congruent responses over 68 responses, *p* < .001, Cohen's *h* = 0.28); and adults (21 congruent responses over 28 responses, *p* < .001, Cohen's *h* = 0.89). The same test was however not significant for toddlers and preschool children (13 congruent responses over 53 responses, *p* = .138). These results could indicate that a spatial bias was present for children from kindergarten to grade 5 and for adults. However, we observed that children in grades 2 to 5 also chose Box #5 more than
<table><caption>**Table 2**
Distribution of responses across the six boxes for each age group in Experiment 1.</caption><thead><tr><th>Group</th><th>N</th><th>Box #1</th><th>Box #2 (%)</th><th>Box #3</th><th>Box #4</th><th>Box #5</th><th>Box #6</th><th>Box #2 or Box #5</th><th>p value #2 vs. #5</th><th>Pwr</th></tr></thead><tbody><tr><td colspan="11" style="text-align:center; font-weight:bold;">Grouped Analysis</td></tr><tr><td>Toddlers & Preschool</td><td>53</td><td>3</td><td>13 (25%)</td><td>11</td><td>14</td><td>11</td><td>1</td><td>24 (45%)</td><td>p = .42</td><td>/</td></tr><tr><td>Kindergarten & Grade 1</td><td>67</td><td>9</td><td><strong>30 (45%)*</strong></td><td>3</td><td>4</td><td>17</td><td>4</td><td><strong>47 (70%)*</strong></td><td>p = .04</td><td>/</td></tr><tr><td>Grade 2-5</td><td>68</td><td>2</td><td><strong>23 (34%)*</strong></td><td>2</td><td>2</td><td><strong>36*</strong></td><td>3</td><td><strong>59 (87%)*</strong></td><td>p = .06</td><td>/</td></tr><tr><td colspan="11" style="text-align:center; font-weight:bold;">Ungrouped Analysis</td></tr><tr><td>Toddlers</td><td>26</td><td>0</td><td>7 (27%)</td><td>6</td><td>10</td><td>2</td><td>1</td><td>9 (35%)</td><td>p = .09</td><td>.71</td></tr><tr><td>Preschool</td><td>27</td><td>3</td><td>6 (22%)</td><td>5</td><td>4</td><td>9</td><td>0</td><td>15 (55%)</td><td>p = .30</td><td>.57</td></tr><tr><td>Kindergarten</td><td>38</td><td>5</td><td><strong>17 (45%)*</strong></td><td>2</td><td>2</td><td>9</td><td>3</td><td><strong>26 (68%)*</strong></td><td>p = .08</td><td>.99</td></tr><tr><td>Grade 1</td><td>29</td><td>4</td><td><strong>13 (45%)*</strong></td><td>1</td><td>2</td><td>8</td><td>1</td><td><strong>21 (72%)*</strong></td><td>p = .19</td><td>.98</td></tr><tr><td>Grade 2</td><td>15</td><td>0</td><td>6 (40%)</td><td>1</td><td>0</td><td>7</td><td>1</td><td><strong>13 (87%)*</strong></td><td>p = .71</td><td>.99</td></tr><tr><td>Grade 3</td><td>27</td><td>1</td><td>10 (37%)</td><td>1</td><td>2</td><td><strong>13*</strong></td><td>0</td><td><strong>23 (85%)*</strong></td><td>p = .80</td><td>.99</td></tr><tr><td>Grades 4 & 5</td><td>26</td><td>1</td><td>7 (27%)</td><td>0</td><td>0</td><td><strong>16*</strong></td><td>2</td><td><strong>23 (88%)*</strong></td><td>p = .046</td><td>.99</td></tr><tr><td>Adults</td><td>28</td><td>0</td><td><strong>21 (75%)*</strong></td><td>1</td><td>0</td><td>5</td><td>1</td><td><strong>26 (93%)*</strong></td><td>p = .001*</td><td>.99</td></tr></tbody></table>

Note. Box #2 was considered the congruent response. Box #5 was considered the reversed response. Box #2 or Box #5 were considered undirectional “correct” responses. Values in bold* represent significant values above chance level. The significance was calculated using a two-tailed binomial test with a probability set at $\pi = \frac{1}{6}$. Significance for choosing either Box #2 or #5 was based on $\pi = \frac{2}{6}$. Significance for choosing Box #2 more than Box #5 (or Box #5 more than Box #2) was based on $\pi = \frac{1}{2}$. Using a Bonferroni correction, the p-value threshold was set at $0.05/4 = 0.0125$ for the grouped analysis and to $0.05/8 = 0.006$ for the ungrouped analysis. A post hoc power analysis conducted using G*Power 3.1 (Faul et al., 2009) revealed that our sample sizes in the ungrouped analysis enabled to reach sufficient power (Pwr > .80) for our binomial tests for each age group, except for preschool children and toddlers. The last column (Pwr) indicates the power we obtained for the binomial test that was based on the largest difference observed for one group. For instance, power reached .99 in the kindergarten group for the Box #2 or Box #5 test against other boxes (i.e., 26 vs. 12). Presence of a power superior to .80 for a given age group thus indicates that we observed at least one sufficiently large difference between frequencies, thus showing that insufficient power in some other tests could only be due to a lesser difference between a pair of frequencies, rather than the size of the sample itself. The reasoning applies between groups: for instance, since the sample size of the preschool group matched another group (grade 3) for which we detected enough power (.99), we can conclude that there were enough participants in the preschool group and in toddlers to detect the putative effect.
chance level (36 responses over 68 responses, *p* < .001, Cohen's *h* = 0.56, see Table 2). We thus cannot conclude that these children showed a preferential left-to-right mapping bias.

Additional binomial tests were thus conducted for each group to compare the choices for Box #2 and Box #5 with the probability of choosing the most often selected box (Box #2 or Box #5) being greater than choosing the other one set at $\pi = \frac{1}{2}$. The results of these tests (see Table 2) indicated that only adults chose Box #2 significantly more often than Box #5 (21 responses over 26 responses, *p* = .001, Cohen's *h* = 0.47). It should be noted that the result for children in kindergarten and grade 1 was statistically significant based on *p* < .05, but not after Bonferroni correction (i.e., using a *p*-value threshold set at $\frac{0.05}{4} = .0125$).

Because our findings show that many children (and a few adults) chose Box #5, a choice corresponding to a right-to-left spatialization, responses were also analyzed by regrouping congruent and reversed responses. We thus investigated whether Box #2 and Box #5 were chosen more than any other box, allowing us to observe whether participants could at least generalize that the correct box was the second regardless of the starting point. We refer to these responses as “undirectional correct responses”. This test was significant for children in kindergarten and grade 1 (*p* < .001, Cohen’s *h* = 0.53); grade 2 to grade 5 (*p* < .001, Cohen’s *h* = 0.83), but not for toddlers and children in preschool (*p* = .079). The non-significant result for this last group indicates that younger children were not able to infer which boxes were the most plausible.

## Analysis per age group

In order to achieve a finer developmental analysis, we then analyzed our data using the initial age groups instead of combining age groups. Our first analysis showed that the distribution of responses (see Table 2, see also Fig. D in Appendix) differed from a uniform distribution in all groups except in preschool ($\chi^2(5) = 10.11, p = .072$ in preschool; all other $\chi^2 \ge 17.85$, with *p* values $\le .003$ and Cohen's *W* $\ge 0.83$).

To assess the understanding of the task for each group separately, binomial tests were then applied to investigate whether Box #2 and Box #5 taken together were selected above chance level. The tests were significant for all age groups except for toddlers and preschool children (see Table 2). Note that although the result for preschool children was significant based on *p* < .05, it was not the case anymore after Bonferroni correction (using a critical *p*-value threshold of $\frac{0.05}{8} = .006$)<fnref n="9" />.

Subsequently, we assessed whether Box #2 was chosen above chance level for each group. Analyses showed a significant result for children in kindergarten, grade 1, and in adults (all *p* < .001, all Cohen's *h* ≥ 0.44). Note that the result of this test was also significant for children in grades 2 and 3 when considering a more liberal *p*-value threshold (i.e., using *p* = .05 instead of the corrected threshold of *p* = .006; *p* = .027, Cohen's *h* = 0.37 for children in grade 2, and *p* = .009, Cohen's *h* = 0.33 for children in grade 3). The same test was however not significant for toddlers, children in preschool, and children in grades 4 and 5 (all *p* ≥ .183).

To investigate the presence of a left oriented bias, binomial tests were then conducted within each group. These tests assessed whether the choice for Box #2 was greater than for Box #5 (or conversely when Box #5 was chosen more than Box #2), with the probability set at $\pi = \frac{1}{2}$. Results showed that only the adults chose Box #2 significantly more often than Box #5 (21 congruent responses over 26 responses, *p* = .001, Cohen's *h* = 0.47, see Table 2 for the results of this test for all age groups). On the contrary, children in grade 4 and 5 tended to select Box #5 more than Box #2, although this result was not significant using a lower *p*-value threshold based on a Bonferroni correction (i.e., *p* = .006).

<footnote n="9">⁹ To refine these results, a correlational analysis was conducted between the undirectional correct responses and the age of the participants. This correlation was significant when including both adults and children (Spearman's $\rho = .38, p < .001$), but also when including only children (Spearman's $\rho = .35, p < .001$, see Fig. E in Appendix). This result reflects a developmental trajectory towards a correct recall of the undirectional location of the items, meaning that the associations between items and their ordinal position (regardless of the starting point) were more obvious as children grew older.</footnote>
Discussion

This experiment investigated the emergence of a leftward spatial bias in children and adults after a rotation from a radial to a horizontal axis. As expected in our hypotheses, we found that toddlers and preschool children did not exhibit a spatial bias corresponding to a left-to-right mapping. On the contrary, toddlers rather searched the card in the central area in front of them after the rotation (e.g., Box #4 was chosen most often). Boxes that were the furthest from them (Box #1 or Box #6) were chosen the least. In addition, no spatial bias from left to right was found in school-aged children either, as no group selected Box #2 more than Box #5. This result contradicts our hypotheses as we expected the bias to appear around grade 1 and to consolidate in older children due to the acquisition of reading and writing. Still, we observed a leftward bias in adults, as predicted.

Contrary to our findings, West and McCrink (2021) did not observe a left-to-right spatial bias in adults using an eye-tracking paradigm. However, consistent with our findings, both West and McCrink (2021) and McCrink et al. (2017) reported no bias in children aged 2 to 3 years old. In contrast, West and McCrink (2021) identified a bias in 4-year-olds (i.e., preschool children), which was not observed in our experiment.

We do not think that the absence of a spatial bias in children could be due to a misunderstanding of our task, because participants from kindergarten onward did choose Box #2 or Box #5 above chance level. Our analysis regarding the choice of these congruent and reversed responses revealed that, as they grow up, children progressively chose more either Box #2 or Box #5. We can thus conclude that the older children who did not exhibit a spatial bias still understood on average which locations were the most plausible. It is only the toddlers and children in preschool who did not seem to understand which were the correct locations.

Overall, the high proportion of reversed responses observed in most of our age groups could indicate that participants indiscriminately mapped serial information from left to right or from right to left. However, this right-to-left mapping seems incompatible with the leftward cultural habits of our participants. Therefore, it is possible that these reversed responses could rather be due to a pitfall produced by our experimental design. Upon a more detailed examination of our methodology, it became apparent that the position of the experimenter during the task may have influenced children's responses, as it was shown for instance in a study conducted by Rugani et al. (2022). Because the experimenter was facing the child in our protocol (with the material between them, see Fig. 1a), some participants could have used an allocentric reference instead of an egocentric reference to complete the task (i.e., by considering the experimenter as the agent). In doing so, the child would have potentially taken the experimenter as a reference to retrieve the card. That is, when hiding the card in Box #2, the perceived location would correspond to the fifth box from the experimenter's point of view. Said otherwise, the large movement made by the experimenter to reach Box #2 would have induced participants to choose Box #5 when the axis was rotated to a horizontal layout (again, as if the card was hidden in the fifth box from the experimenter's point of view on the radial layout). Participants could thus have picked Box #5 in spite of considering the left side of the layout as the starting point. This might potentially explain why children in grades 4 and 5 tended to select preferentially Box #5 rather than Box #2. Experiment 2 was thus conducted with the aim of investigating whether changing the position of the experimenter would enable to observe a left-to-right bias in children.

Experiment 2

Experiment 1 might have induced a confound between allocentric and egocentric reference frames. By adapting the procedure to remove this confound in Experiment 2, we hypothesized that a left-to-right bias would be detected. In this experiment, we only selected a sample of children in kindergarten and grade 5. Children in kindergarten were selected because they were the youngest group to choose Box #2 above chance level. The task in Experiment 1 was indeed found too difficult for toddlers and preschool children, as they did not make undirectional correct responses (i.e., choosing either Box #2 or Box #5) above chance level. Their lack of task comprehension thus undermines the ability to detect a putative spatial bias in this population.
Children in grade 5 were also selected because they were the oldest children in Experiment 1 to be
compared with. We had two reasons to choose the oldest children to maximize our chance to observe
a left-to-right bias: i) Since the bias should consolidate with expertise in reading and writing (and in
particular because the bias was observed in adults in Experiment 1), the effect should be present in
this group using a simpler procedure. ii) Comparing children in kindergarten with children in grade
5 would allow us to show a clear statistical difference between the respective results of the two
groups. The bias should be stronger in fifth graders because it should be more consolidated as children
grow up and gain expertise in literacy. If successful, we could infer that the bias develops between
kindergarten and grade 5, and we thought that future studies could then attempt to determine more
precisely at which age a change operates.

Method

Participants

A sample of 58 children took part in this study: 31 children from kindergarten (mean age = 6 years, SD = 0.34) and 27 children from grade 5 (mean age = 11 years, SD = 0.31); 50 children were right-handed and the sample included an equal number of girls and boys. In Experiment 1, a sample of 26 participants enabled us to achieve sufficient power for our binomial tests. Thus, a minimal sample of 26 participants in the current experiment was thought to provide enough statistical power to detect a putative effect. We used slightly larger samples because of over-recruitment.

Material

The material was the same as in Experiment 1.

Procedure

The procedure was identical to the one used in Experiment 1, except that the experimenter was sitting to the left of the participants (see Fig. 2). This modification was thought to ensure that children would use the same reference frame as the experimenter to search the card after the rotation. Again, because the experimenter was far away from Box #2 in the previous experiment, participants could have chosen Box #5 after the rotation based on a left spatial bias, by encoding a third-person perspective in the practice trials (and then they could have merged these third-person and first-person perspectives to guess the location).

Another difference with Experiment 1 lies in our attempt to avoid guessing strategies by instructing participants that the task was easy and that it would not involve any tricks. Participants were told that they were going to play a very easy game that was originally designed for toddlers, and hence that the task would not be deceitful whatsoever. Moreover, a blindfold was used during the trials in which children had to have their eyes closed.

To ensure that children understood the task, we also recorded the box participants selected in the
final radial trial prior to the rotation. This information allowed to restrict the analysis to children who
selected the correct box in the last radial trial (i.e., the “good seekers” as labeled by McCrink et al.,
2017). Doing so enabled us to investigate the presence of a bias only when children fully understood
the task, which was not possible in Experiment 1 since this measure was missing. All other features of
the procedure remained identical to those of Experiment 1.

Data Analysis

As in Experiment 1, responses were coded as “Congruent”, “Reversed”, or “Incongruous”. To determine whether children showed a spatial bias, χ² tests were first conducted to ascertain whether the distribution of responses between the different boxes differed from a random distribution. We then applied a binomial test to evaluate whether Box #2 and Box #5 (undirectional correct responses) were selected above chance level, thus ensuring task comprehension. A second binomial test comparing the preference for Box #2 over chance level was also used to test a specific preference for the congruent response. Finally, a third binomial test directly comparing the preference for Box #2 over Box #5 was used to assess the left-to-right bias within these two most chosen responses. This final analysis was conducted not only on the entire sample, but also specifically on the children identified as good seekers.
<figure><img src="image_6.png" /><figcaption>Fig. 2. Spatial configurations of the practice and test trials in Experiment 2.</figcaption></figure>

ers. This approach allowed to control the potential influence of participants who did not correctly encoded the spatial position in the vertical trials.

## Results

The distribution of participants' responses across the six boxes is reported in Table 3 (and shown in Fig. F in Appendix). Goodness-of-fit $\chi^2$ tests were run for both age groups, indicating a distribution of the frequencies among the six boxes significantly different from a uniform distribution ($\chi^2(5) = 24.16, p < .001$, Cohen's W = 0.88 for kindergarten; and $\chi^2(5) = 59.44, p < .001$, Cohen's W = 1.43 for grade 5). We then tested whether the two undirectional correct responses were chosen above chance level (with the probability of choosing either Box #2 or Box #5 set at $\pi = \frac{2}{6}$). The results indicated that both children in kindergarten and grade 5 selected either Box #2 or Box #5 above chance level (71% and 100% of responses respectively, both $p < .001$, Cohen's $h \ge 0.55$).

Subsequently, binomial tests were performed to assess whether children exhibited a preference for Box #2 only (with the probability of choosing Box #2 set at $\pi = \frac{1}{6}$). This test was significant for both children in kindergarten ($p = .003$, Cohen's $h = 0.36$) and grade 5 ($p < .001$, Cohen's $h = 0.70$). We finally conducted binomial tests to estimate whether Box #2 was chosen more than Box #5 (with the probability of choosing Box #2 being greater than choosing Box #5 set at $\pi = \frac{1}{2}$). The results did not indicate that Box #2 was chosen more often than Box #5 for either groups (see Table 3 for the results of this test)<fnref n="10" />.

<footnote n="10">¹⁰ The binomial tests were also conducted on the good seekers only (i.e., children who selected the congruent box during the last radial trial before the rotation). Using this procedure, four participants were excluded in kindergarten, which however did not change the pattern of results ($p = .5$, Cohen's $h = 0.04$). Children in grade 5 were all good seekers.</footnote>
<table><caption>**Table 3**
Distribution of responses across the six boxes by age group in Experiments 1 and 2.</caption><thead><tr><th></th><th>Box #1</th><th>Box #2 (%)</th><th>Box #3</th><th>Box #4</th><th>Box #5</th><th>Box #6</th><th>Box #2 or Box #5</th><th>p value #2 vs. #5</th></tr></thead><tbody><tr><td></td><td></td><td></td><td></td><td colspan="3">Kindergarten</td><td></td><td></td></tr><tr><td>Experiment 1</td><td>5</td><td><strong>17 (45%)*</strong></td><td>2</td><td>2</td><td>9</td><td>3</td><td><strong>26 (68%)*</strong></td><td>p = .08</td></tr><tr><td>Experiment 2</td><td>1</td><td><strong>12 (39%)*</strong></td><td>2</td><td>6</td><td>10</td><td>0</td><td><strong>22 (71%)*</strong></td><td>p = .42</td></tr><tr><td></td><td></td><td></td><td></td><td colspan="3">Grade 5</td><td></td><td></td></tr><tr><td>Experiment 1</td><td>1</td><td>7 (27%)</td><td>0</td><td>0</td><td><strong>16*</strong></td><td>2</td><td><strong>23 (88%)*</strong></td><td>p = .046</td></tr><tr><td>Experiment 2</td><td>0</td><td><strong>17 (63%)*</strong></td><td>0</td><td>0</td><td><strong>10*</strong></td><td>0</td><td><strong>27 (100%)*</strong></td><td>p = .12</td></tr></tbody></table>

Note. Values in bold* represent significant values above chance level. The significance was calculated using a two-tailed binomial test with a probability set at $\pi = \frac{1}{6}$. Significance for choosing either Box #2 or #5 was based on $\pi = \frac{1}{6}$. Significance for choosing Box #2 more than Box #5 (or Box #5 more than Box #2) was based on $\pi = \frac{1}{2}$. Using a Bonferroni correction, the p-value threshold was set at $0.05/2 = 0.025$. We do not indicate power in this table since Experiment 2 was carried out with a larger number of participants than the smallest group for which we detected enough power in Experiment 1 (see Table 2 in which numbers are provided).

To investigate a potential difference between the two age groups overall, a $\chi^2$ test for independence was conducted on the responses of participants reported in the contingency Table 3. This test highlighted a significant difference between age groups ($\chi^2(4) = 9.63, p = .047$, Cramer's V = 0.41). This analysis thus showed that older children simply better understood the task, as they did not choose any incongruous box, unlike younger children in kindergarten.

### Comparison with Experiment 1

The results of Experiment 2 were then compared to those of Experiment 1 (see Table 3). Results were compared by group (children in fifth grade in Experiment 2 were compared to children who were either in fourth or fifth grade in Experiment 1, as these children had been grouped to achieve a reasonable sample size). For children in kindergarten, a $\chi^2$ test for independence did not show any significant difference in the distribution of responses across all boxes between the two experiments ($\chi^2(5) = 7.95, p = .159$). Concerning the results of children in grade 5, a $\chi^2$ test for independence performed on the distribution of responses showed a difference in the response pattern ($\chi^2(3) = 8.53, p = .036$, Cramer's V = 0.40), driven by a larger choice of Box #2 in Experiment 2.

Overall our findings suggest that changing the position of the experimenter only had an influence on children in grade 5, which was confirmed by a logistic regression showing a significant interaction between experiments (Experiment 1 vs. Experiment 2) and age groups (kindergarten vs. grade 5) on the congruency of responses ($z = -2.3, p = .021, \text{Std.}\beta = -1.78$). However, the manipulation in our paradigm was not sufficient to induce a clear left-to-right bias.

### Discussion

The aim of the present experiment was to attempt to better detect a putative leftward bias by changing the position of the experimenter in comparison to Experiment 1. The position was changed to prevent children from using an allocentric reference frame when performing the task.

Based on the results of Experiment 1, we here only selected two age groups (kindergarten and grade 5). However, we still did not observe a preferential response that would have typically been induced by a left bias, as children in kindergarten and grade 5 significantly selected Box #2 (39% for kindergarten and 63% for grade 5) and Box #5 (31% for kindergarten –although not significant after Bonferroni correction– and 37% for grade 5) indiscriminately. We therefore did not find any significant left-oriented bias in this second experiment, which can be surprising since the presence of the experimenter on the left could have induced a left bias simply because her position constituted a cue.

We could argue that children in the present experiment tended to choose Box #5 because the leftward bias would not have been fully consolidated yet at this age. Over time, this preferential direction would become firmly established through increased expertise in reading and writing, resulting in a specific left-oriented bias in adults (as found in Experiment 1). However, another confound could
be at stake here. An additional plausible explanation for choosing Box #5 is the “page” analogy that stems from the mental whiteboard hypothesis (Abrahamse et al., 2014). This analogy, in relation to the vertical SPoARC found by Hartmann et al. (2021), states that the first items of a sequence are preferentially spatialized at the top of the mental space and the last ones at the bottom, by analogy to how one reads text on a sheet of paper (i.e., starting at the top of the page). Children in our experiment (or some of the children) could thus have associated the locations that were the furthest to them in the radial trials to the top of a sheet of paper. Box #2 would then correspond to the end of the sheet of paper. For the children who would have imagined the top of the virtual page on the left after the rotation of the series, choosing Box #5 would then logically reflect a left bias. As such, we believe that our experimental design did not provide a clear starting point to help children encode serial information, which we aimed to improve in a third experiment.

## Experiment 3

In Experiment 2, although the experimenter was placed next to the children, the task itself did not strongly induced a direction from a clear starting point, meaning that the reference frame could still be ambiguous for participants. The two most frequent responses could correspond to two different reference frames. Children with an egocentric reference frame might preferentially choose Box #2 using their own body as the starting point. On the contrary, children using a page as a reference frame would choose Box #5 when scanning their mental representation starting from the left after the rotation, because they would have encoded the starting point at the top of the virtual page.

To clarify this point, Experiment 3 offers a novel attempt, this time simulating the path taken by the animal to reach its hiding place in order to make the starting point clearer. The target box was also counterbalanced between Box #2 and Box #5 across children to better generalize the results. We restricted even further the range of ages by only selecting fifth graders. We opted for a sequential test, hoping to add more age groups (by decreasing age) after we obtained a positive result. By limiting the potential reference frames that could have caused noise in the data, we expected to observe a left bias in this third experiment.

### Method

#### Participants

Fifth graders were selected based on our hypothesis that the bias would manifest due to extensive enculturation. We thought this group was the most likely to exhibit the effect, given that it was the oldest age group of children in our previous experiments. A sample of 32 children in grade 5 (mean age = 10.3 years, SD = 0.5) participated in this experiment; 29 participants were right-handed and the sample included 21 girls and 11 boys. The number of participants matched the sample size of the two previous experiments.

#### Material

The material was similar to the preceding experiments.

#### Procedure

The procedure was overall similar to Experiment 2, with a few exceptions. First, the position of the experimenter was counterbalanced between and within each participant. For the five trials in which participants had their eyes open, the experimenter was alternately placed to the left and to the right of the child. The side where the experimenter was placed first was counterbalanced between participants. Note that for these five trials, the experimenter was not placed behind the children as it was not convenient. However, for Trials 6 and 7, the experimenter was placed behind the participants while they had their eyes open (see Fig. 3).

Second, to counterbalance the position of the hiding box, the animals were hidden either in the second box from the child for half of the participants, or in the fifth box for the other half. Finally, for each of the first five trials, the experimenter simulated the path of the animal by making it go from one box
<figure><img src="image_7.png" /><figcaption>**Fig. 3.** Spatial configurations of the practice and test trials in Experiment 3. Note. The same procedure was used for the participants probed with Box #5, except that items were hidden in the fifth box.</figcaption></figure>

to the next, starting with the box closest to the participants. A little noise that lasted for about three seconds was produced by the experimenter along the path (the duration of the noise remained the same regardless of the box in which the card was hidden, Box #2 or Box #5). The same noise was applied to Trials 6 and 7 to allow a concordance between the first five trials and the trials when children had their eyes closed. This concordance between time and space was thought to let children infer that the path taken by the animals was always the same.

Additional steps were added after the test trial. Once the rotation was made, children were asked to point to the box where they thought the gift card was hidden, but without opening it. Then, participants were requested to count the boxes one by one. The side where they started counting (left or right) was recorded by the experimenter. Then, children had to close their eyes again while the experimenter rotated the boxes 90° to put them back in their initial position. Once more, participants were asked to count the boxes. The starting point for the counting (bottom or top) was recorded as well. Finally, the experimenter asked participants to put back the boxes horizontally to observe how they performed the rotation. The experimenter recorded whether the rotation was clockwise or counter-clockwise. Finally, participants were asked to open the box where they thought the gift card had been hidden.
## Results

Responses were coded as “Congruent” when matching the expected left-to-right spatial mapping, that is Box #2 or Box #5 depending on the target box. Responses were considered reversed if they cor- responded to a right-to-left mapping. All other responses were considered incongruous. Results showed that 47% of participants (i.e., 15 participants) produced a congruent response in the final trial after the rotation, against 50% (16 participants) producing a reversed response. The remaining 3% (1 participant) produced an incongruous response (Box #3, see Fig. G in Appendix for the distribution of responses).

The distribution of congruent, reversed, and incongruous responses differed from a uniform distri- bution ($\chi^2(2) = 13.19, p < .001$, Cohen's W = 0.64). Participants properly understood the task as they selected undirectional correct responses (i.e., congruent or reversed responses) well above chance level (97% undirectional correct responses, $p < .001$, Cohen's *h* = 1.1, with the probability of selecting an undirectional correct response above chance level set at $\pi = \frac{2}{6}$). In addition, results showed that congruent responses were selected above chance level ($p < .001$, Cohen's *h* = 0.47, with $\pi = \frac{1}{6}$). How- ever, when comparing participants who made congruent (15) vs. reversed responses (16), a binomial test based on chance level ($\pi = \frac{1}{2}$) did not turn significant ($p = .11$). Results thus matched those of the previous experiments, that is, participants did not show any preference for either the congruent or reversed option over the other.

Regarding counting, 81% of participants started counting from the left of the horizontal layout (i.e., 19% started from the right-hand side). On the radial layout, 91% of participants started from the bot- tom of the series (i.e., using the box closest to them). Regarding the rotation task, 69% of participants executed a counterclockwise rotation, while the remaining 31% rotated the series in a clockwise direc- tion. Goodness-of-fit $\chi^2$ tests revealed that each of the three distributions (regarding the direction of horizontal counting, radial counting, and rotation) differed from a uniform distribution ($\chi^2(1) = 12.5, p < .001$, Cohen's W = 0.62 for the horizontal counting; $\chi^2(1) = 21.13, p < .001$, Cohen's W = 0.81 for the radial counting; and $\chi^2(1) = 4.5, p = .034$, Cohen's W = 0.38 for the rotation task). Participants preferentially started counting from the left of the horizontal layout and from the bottom of the radial layout, and preferentially executed a counterclockwise rotation. The two behav- iors (the direction of their rotation and the side where they started counting – horizontally or radially) were not correlated as participants tended to start counting from the left and from the bottom regard- less of how they executed the rotation (contingency coefficient = .15 and .21 respectively).

Further analysis showed that the distribution of congruent, reversed, and incongruous responses differed as a function of the side where participants began counting on the horizontal layout ($\chi^2(2) = 6.18, p = .045$, Cramer's V = 0.44, see Table 4). However, no significant difference was found when focusing only on the congruent vs. reversed responses within each counting side ($p = .42$ for participants who started counting from the left and $p = .19$ for participants who started counting from the right, when performing a one-tailed binomial test based on chance level, i.e., $\pi = \frac{1}{2}$). Participants thus did not produce more congruent responses as a function of where they began counting on the horizontal layout. Concerning the radial layout, the distribution of congruent, reversed, and incongru- ous responses did not significantly differ as a function of the side where the counting began ($\chi^2(2) = 0.42, p = .81$, also in Table 4).

In addition, we found a significant difference in the distribution of responses as a function of the direction of the rotation ($\chi^2(2) = 10.88, p = .004$, Cramer's V = 0.58; see Table 5). Participants who executed a clockwise rotation tended to produce more congruent responses than reversed responses ($p = .01$, Cohen's *h* = 0.66), while participants who executed a counterclockwise rotation tended to produce more reversed responses than congruent responses ($p = .039$, Cohen's *h* = 0.31). Responses of participants were also more dependent of the direction of the rotation (contingency coefficient =

<footnote n="11">¹¹ The pattern of results did not change when considering only good seekers (i.e., participants selecting the congruent box on the last radial trial before the rotation, with one participant not being a good seeker over the sample), *p* = 1.</footnote>
<caption>**Table 4**</caption>

Contingency table of the distribution of congruent, reversed, and incongruous responses depending on the side where participants began counting in Experiment 3.

<table><caption>**Table 5**</caption><thead><tr><th>Counting side</th><th>Congruent Responses (%)</th><th>Incongruous Responses (%)</th><th>Reversed Responses (%)</th></tr></thead><tbody><tr><td></td><td colspan="3" style="text-align: center;">Horizontal</td></tr><tr><td>Left</td><td>14 (54%)</td><td>0 (0%)</td><td>12 (46%)</td></tr><tr><td>Right</td><td>1 (16.5%)</td><td>1 (16.5%)</td><td>4 (67%)</td></tr><tr><td></td><td colspan="3" style="text-align: center;">Radial</td></tr><tr><td>Bottom</td><td>14 (48%)</td><td>1 (4%)</td><td>14 (48%)</td></tr><tr><td>Top</td><td>1 (33.5%)</td><td>0 (0%)</td><td>2 (66.5%)</td></tr></tbody></table>

Contingency table of the distribution of congruent, reversed, and incongruous responses depending on the direction of the rotation participants performed (clockwise vs. counterclockwise) in Experiment 3.

<table><caption>**Table 6**</caption><thead><tr><th>Rotation direction</th><th>Congruent Responses (%)</th><th>Incongruous Responses (%)</th><th>Reversed Responses (%)</th></tr></thead><tbody><tr><td>Clockwise</td><td>9 (90%)</td><td>0 (0%)</td><td>1 (10%)</td></tr><tr><td>Counterclockwise</td><td>6 (27%)</td><td>1 (5%)</td><td>15 (68%)</td></tr></tbody></table>

Contingency table of the distribution of congruent, incongruous, and reversed responses between Experiment 1, 2, and 3 (age group: grades 4 & 5).

<table><thead><tr><th></th><th>Congruent Responses (%)</th><th>Incongruous Responses (%)</th><th>Reversed Responses (%)</th></tr></thead><tbody><tr><td>Experiment 1</td><td>7 (27%)</td><td>3 (11%)</td><td>16 (62%)</td></tr><tr><td>Experiment 2</td><td>17 (63%)</td><td>0 (0%)</td><td>10 (37%)</td></tr><tr><td>Experiment 3</td><td>15 (47%)</td><td>1 (3%)</td><td>16 (50%)</td></tr></tbody></table>

.5) than of the counting side (the contingency coefficient was equal to .4 for the horizontal counting vs. .11 for the radial counting).

Finally, we carried out a comparison between experiments. A $\chi^2$ test for independence was run on the contingency Table 6 to determine whether the responses made by children in grades 4 and 5 varied between Experiment 1, 2, and 3. The result showed no significant difference ($\chi^2(4) = 9.39, p = .052$).

## Discussion

In Experiment 3, we simulated the path of the animal during the task to induce a clearer direction in view of limiting the noise in our data. The rationale was that a leftward bias should be best detected when children are prompted to rely on a single frame of reference (i.e., encoding serial information from bottom to top). Contrary to our hypothesis, the results did not indicate a left-oriented bias since children still selected both congruent and reversed boxes indiscriminately.

The task used in our third experiment still highlighted a left bias and a bottom bias when participants were asked to count the boxes. Almost all participants (81%) started counting from the left-hand side, showing a clear spatial bias towards the left for the numerical series they had in mind. Also, when asked to count the boxes on a radial layout, almost all participants (91%) started from the bottom (contrary to the “page hypothesis”), thus following the direction that we induced in the task using the path of the animal. The reversed responses observed in this experiment might thus not be due to a particular flaw in the design of our tasks but rather to an absence of a specific bias when ordinal information is more implicit. Children would tend to use a more biased strategy when the task requires a more explicit processing of serial information (for instance when they are required to count), as suggested by the findings of McCrink et al. (2017). Indeed, the authors showed that participants exposed
to explicit ordinal information (boxes with numerical or alphabetical labels) exhibited a retrieval
strategy consistent with a left-to-right mapping contrary to those exposed to unlabeled boxes. When
no explicit information is given during the experiment (e.g., no alphabetical or numerical label), par-
ticipants would then tend to use internal cues instead of external cues to solve the task. We believe the
main internal cue available in our task to be the direction of the rotation that participants would imag-
ine when being presented with an unexpected horizontal layout.

The observed reversed bias found in the current experiment could thus originate from this mental rotation. This hypothesis is supported by our results, which showed a large contingency coefficient between participants' responses and the direction of the rotation performed. As most participants started counting from the bottom of the array, we can posit that they considered the box closest to them as the starting point of the layout. After a clockwise rotation, this starting point would have been the far-left box, which is congruent with most participants starting counting from the left of the hor- izontal layout. Their starting point being the far-left box, participants produced the expected congru- ent responses as shown by the 90% of congruent responses given by participants who performed a clockwise rotation. On the contrary, performing a counterclockwise rotation associates the starting point of the layout (i.e., originally the bottom) with the far-right box. Starting from the right side of the layout, participants produced more reversed responses (68%). However, 27% of participants still produced a congruent response while performing a counterclockwise rotation. This could be due to the two representations interfering. The right-oriented bias induced by the counterclockwise rotation could compete with the left-to-right direction of the counting process (as shown with the horizontal counting task). This could explain the less clear-cut pattern of responses in participants who executed a counterclockwise rotation, as they still selected the congruent response in 27% of cases.

To conclude, the choice of the box in this task does not seem to depend much on the direction of
counting (which corresponds to the reading and writing direction; see Shaki et al., 2012) but rather on
the way the rotation is performed by participants in physical space. This echoes the findings of Patro
et al. (2016), who showed that visuo-motor activities can influence spatial biases. We could thus ques-
tion the impact of such potential factors. For example, rotations of phones or digital tablets are rarely
executed in a clockwise fashion. Such motor processes could thus account for the reversed responses
observed in this experiment.

Experiment 4

The aim of Experiment 4 was to test the impact of visuo-motor activities on children's responses. Indeed, we found that the congruency of responses in Experiment 3 was linked to the direction in which children rotated the layout after the test phase. Specifically, a clockwise rotation was preferen- tially associated with congruent responses, while a counterclockwise rotation was rather associated with reversed responses. Based on these results, we could posit that the way participants rotated the array on the physical space might reflect the way they mentally pictured the rotation when being presented with a novel and unexpected horizontal layout. By mentally imagining a counterclockwise rotation during the test phase, participants would have taken the right side of the layout as a starting point and preferentially picked the reversed box, thus undermining our estimate of the putative left- ward bias. Therefore, we hypothesized that using a design that hampers this mental rotation during the test phase would facilitate the observation of a leftward bias.

To test this hypothesis, we compared two conditions in Experiment 4: a first condition that induced a mental rotation from a vertical<fnref n="12" /> to a horizontal layout, and a second condition that hindered the mental rotation. Both conditions displayed a mummy pig searching for her baby pig. The material used in this fourth experiment was adapted from West and McCrink (2021) who presented participants with an animated rotation task. As in West and McCrink's experiment, we used an animated task in which an occluder (i.e., a wooden plank) hid the array while it was transposed from a vertical to a horizontal axis. This constituted our mental rotation condition (referred to as our occluder condition in the following

<footnote n="12">¹² We now use the vertical vs. horizontal terminology rather than the radial vs. horizontal terminology to match the new spatial configuration of this experiment.</footnote>
sections). We considered this procedure to be similar to the one we had used in our previous experi-
ments (in which participants were asked to close their eyes). In both cases, participants could not rely
on visual information to understand how the transposition was made during the test phase, and were
thus free to mentally imagine how the layout could have been rotated. In our second condition (referred
to as our translation condition), the transposition was achieved by a visual animation consisting in the
simultaneous presentation of the vertical and horizontal layouts as the mummy pig moved upward from
the vertical axis to the horizontal one. This procedure was thought to hinder the mental rotation because
the simultaneous presence of two separate layouts made it less probable that a single layout could have
been rotated from a vertical to a horizontal position.

We expected the results in the occluder condition to be similar to our previous experiments. This
means that both congruent and reversed boxes should be equally selected above chance level. Con-
versely, we predicted that in the translation condition, children would choose the congruent box
above chance level and also more frequently than the reversed box. As in Experiment 1, it was hypoth-
esized that the spatial bias would be stronger as children gain expertise in reading and writing. There-
fore, it was expected that the bias would appear at the earliest in grade 1. Additionally, it was expected
that adults would still exhibit a clear spatial bias oriented from left to right using our translation con-
dition, but also using our occluder condition. Indeed, the latter did not restrict mental rotation, as in
Experiment 1 in which a leftward preference was already observed in adults.

Method

Participants

This study was approved by Université Côte d'Azur's ethic committee (CERNI #2023-009). A sample of 585 participants took part in this experiment, divided into eight age groups and randomly assigned to one of our two conditions (i.e., occluder condition or translation condition). Thirty-nine children were excluded due to various developmental disorders, resulting in a total of 543 participants being included in the analysis. The sample consisted of 311 females and 232 males, with 479 being right-handed, 53 being left-handed, and 9 being ambidextrous<fnref n="13" />. Table 7 reports the sample size and mean age for each group and condition. A power analysis was conducted using G*Power 3.1 (Faul et al., 2009), indicating that a sample of 20 participants per age group and per condition was required to achieve a power of .80 for our critical binomial test (comparing the congruent vs. reversed responses), assuming an effect size of 0.3. Again, we used slightly larger samples because of over-recruitment.

Material

Two videos were created based on the study of West and McCrink (2021). The scenario described a mother pig searching for her offspring. The baby pig was hiding, and the mother was seeking the participant's help in locating her baby. The mother and the baby pig respectively measured 3.2×2.2 cm and 1.5×1.5 cm. The hiding places consisted of six equidistant blue circles with a radius of 1 cm, positioned on a white rectangle measuring 14.3×2.9 cm, on a black background.

Procedure

*General Design.* The experiment took place in a quiet room and children were seated approximately 30 cm away from the computer displaying the video. The video lasted for 3 min and 16 s and started with preliminary instructions. During the instructions, a cartoon character invited the participants to maintain focus throughout the video. At the end of the task, the same character thanked the children for their help in finding the baby pig. The experimenter ensured that the participants remained focused during the task.

*Introductory trial.* Both conditions began with an introductory trial that familiarized children with the transition from a vertical to a horizontal axis. The trial depicted only one hiding place (i.e., a hole), located in the center of the vertical layout. Participants were introduced with the mother pig,

<footnote n="13"><sup>13</sup> The dominant hand information is missing for two participants.</footnote>
<table><caption>**Table 7**
Sample size and mean age per group and condition in Experiment 4.</caption><thead><tr><th rowspan="2">Group</th><th colspan="2">Occluder condition</th><th colspan="2">Translation condition</th></tr><tr><th>Sample size</th><th>Age (SD)</th><th>Sample size</th><th>Age (SD)</th></tr></thead><tbody><tr><td>Preschool</td><td>30</td><td>4.4 (0.3)</td><td>27</td><td>4.3 (0.4)</td></tr><tr><td>Kindergarten</td><td>41</td><td>5.3 (0.3)</td><td>37</td><td>5.4 (0.3)</td></tr><tr><td>Grade 1</td><td>32</td><td>6.4 (0.4)</td><td>30</td><td>6.5 (0.3)</td></tr><tr><td>Grade 2</td><td>35</td><td>7.4 (0.3)</td><td>31</td><td>7.4 (0.3)</td></tr><tr><td>Grade 3</td><td>23</td><td>8.4 (0.3)</td><td>23</td><td>8.2 (0.2)</td></tr><tr><td>Grade 4</td><td>32</td><td>9.4 (0.6)</td><td>30</td><td>9.4 (0.4)</td></tr><tr><td>Grade 5</td><td>42</td><td>10.2 (0.4)</td><td>33</td><td>10.4 (0.3)</td></tr><tr><td>Adults</td><td>53</td><td>33 (16)</td><td>44</td><td>31 (14)</td></tr></tbody></table>

positioned at the bottom center of the screen. It was explained that she was searching for her baby ("Meet mummy pig. Mummy pig is a bit sad because her baby is hiding and she doesn't know where he is."). This presentation lasted for 7 s, and after a delay of another 2 s, the baby pig appeared in the central hiding place (see Fig. 4a and 4b - Introduction). The mother's expression switched from a neutral face to a happy face upon finding her baby, which was announced as: "*Baby pig is here!*".

The transition from a vertical to a horizontal axis was presented 4 s after the baby appeared on screen, and varied depending on the condition. In the occluder condition, a wooden plank was used to cover the hiding places while transitioning from a vertical to a horizontal axis. The plank was moved down from the top of the screen, as indicated by the phrase: "Oh look, we're covering up the hiding places and turning them around". During this transposition phase, the mother pig looked surprised. The plank was then removed, revealing the horizontal axis (see Fig. 4a - Introduction). This procedure lasted 7 s.

In the translation condition, the baby pig ran away from his hiding place and moved to a different layout by escaping through the top of the screen. The mother pig followed the baby and it was stated: "Oh no, baby pig escapes and hides further away. Quick, quick, mummy pig runs to fetch him.". This procedure lasted 11 s. This design enabled us to present both the vertical and horizontal layouts on screen simultaneously, as shown in Fig. 4b - Introduction. This simultaneous presentation of the vertical and horizontal layouts was thought to prevent children from imagining a rotation.

In both conditions, the baby pig was still in the central hiding place when the change of axis was revealed, as indicated by the phrase: "*Baby pig is still here!*". This step aimed at familiarizing the children with the change of axis and showing that the transposition did not affect the baby's hiding place. The baby pig remained on screen for 3 s after the transition.

**Training phase.** During the training phase, participants underwent four trials in which the layout was oriented vertically. The baby pig always hid in the same location, either in the second or the fifth box from the bottom of the layout, counterbalanced between children.

During the first trial, the location of the baby pig was marked with a pink star (see Fig. 4a and 4b - Trial 1). Mommy pig was portrayed as sad and it was stated that "*Baby pig hid in one of these hiding places again.*" (lasting for 5 s). Each hiding place was then inspected one by one, starting from the bottom of the layout, to determine whether baby pig was inside or not. For the boxes in which the baby was not hidden, it was stated: "*He's not in this hiding place!*", lasting for 2.5 s. When inspecting the box where the baby pig was hidden, the baby was revealed and it was stated: "*Look, he's in this hiding place! You see, there's even a star to tell you where he's hiding!*", lasting for 6 s. The mother's expression changed to happy after finding her baby. This first trial lasted for 24 s overall.

In the second and third trials, the location of the baby pig was not cued (see Fig. 4a and 4b - Trials 2 and 3). Again, the mommy pig was portrayed as sad and it was stated: "*Baby pig is still playing hide and seek, his mum is looking for him!*" (Trial 2) or "*Do you think that baby pig is hiding again? Yes! Let's help mummy pig find him!*" (Trial 3). This introduction phase lasted for 5 s. Then, each hiding place was inspected one by one for 2.5 s, starting with the bottom of the layout and stating whether the baby
<figure><img src="image_8.png" /><figcaption>(a) Scenes used in the occluder condition in Experiment 4, for participants who were probed with Box #2. Note. The same procedure was used for the participants probed with Box #5, except that the baby pig was hidden in the fifth box starting from the bottom/the left of the array. Time elapses from left to right and top to bottom</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>(b) Scenes used in the translation condition in Experiment 4, for participants who were probed with Box #2. Note. The same procedure was used for the participants probed with Box #5, except that the baby pig was hidden in the fifth box starting from the bottom/the left of the array. Time elapses from left to right and top to bottom.</figcaption></figure>

**Fig. 4.** Scenes used in Experiment 4.
pig was hiding inside ("Look, he's in this hiding place!") or not ("He's not in this hiding place."). These two trials lasted for 20 s each.

The final vertical trial differed slightly. For this trial, it was stated that: "*Baby pig is definitely a great prankster. Let's look for him to help mummy pig.*". However, instead of inspecting each box one after the other to find the baby, children were asked to retrieve the target location by themselves. In the occluder condition, the hiding places were covered using the same wooden plank as in the introduction, but they were still oriented vertically when the wooden plank was removed (see Fig. 4a - Trial 4). This was indicated by the phrase: "*Oh look, we're covering up the hiding places... Oh, we see them again.*". Children were then asked to point to the box in which they thought the baby pig was hiding ("*Where do you think baby pig is hiding? Show us with your finger!*"). Following this 15-s instruction phase, children were given 8 s to indicate their response. The selected box and response hand were recorded. After this 8-s response delay, the baby pig appeared in the same hiding box as in the first three trials and remained on screen for 4 s. The procedure differed in the translation condition as children were directly asked to point to the box in which they believed the baby pig was hiding (see Fig. 4b - Trial 4). Consequently, the instruction phase was reduced to 10 s.

*Testing phase.* The final trial of the task involved the transposition from a vertical to a horizontal axis (see Fig. 4a and 4b - Test Trial). This procedure lasted for 12 s for both conditions and was accompanied by the sentence: "*Poor mummy pig, baby is still playing hide and seek. And look, we're covering up the hiding places and turning them over again!*" (for the occluder condition) or "*Oh no, baby escapes again to hide further away. Quick, quick, mummy pig runs to fetch him!*" (for the translation condition). Following the transposition, children were invited to indicate the location of the baby pig among the six hiding places. The instructions lasted for 6 s, during which children were told: "*Mummy pig doesn't know where her baby is, do you know where he is? Show us with your finger!*". Participants were given an 11-s delay to respond, after which the baby pig appeared on screen for 4.5 s. The selected box and response hand were recorded. This final trial lasted 33.5 s.

## Results

Responses were coded as congruent when they corresponded to the expected left-to-right mapping bias (i.e., choosing either Box #2 or Box #5 depending on the habituation participants received). Responses were considered reversed if they corresponded to a right-to-left mapping bias (i.e., choosing Box #2 from the left in the horizontal trial when participants were habituated to see the baby appear in Box #5 from the bottom in the vertical trials, and vice versa). All other responses were considered incongruous.

## Comparison between conditions

We first compared the results obtained for each of the two conditions. A $\chi^2$ test conducted across all age groups showed a significant difference in the distribution of congruent, reversed, and incongruous responses between our conditions ($\chi^2(2) = 25.33, p < .001$, Cramer's $V = 0.22$). We then conducted a log-linear analysis to evaluate whether the distribution of congruent, reversed, and incongruous responses varied not only as a function of condition, but also as a function of age group. The distribution of responses for each age group and condition is reported in Table 8. We found a difference in the distribution of responses between conditions ($L(2) = 25.83, p < .001$), and between age groups ($L(14) = 41.19, p < .001$), but no interaction was found between age and condition (see Table B in Appendix). Overall, participants in the translation condition produced more congruent responses, and fewer reversed responses, as shown in Fig. 5. The proportion of incongruous responses was also higher in the translation condition than in the occluder condition. Still, when examining "left-to-right compatible" errors (i.e., choosing either Box #1 or Box #3 when being probed with Box #2, and conversely, choosing Box #4 or Box #6 when being probed with Box #5), results showed that these errors tended to occur more often in the translation condition than in the occluder condition (63% vs. 36% of "left-to-right compatible" errors, respectively). However, when applying a binomial test based on $\pi = \frac{1}{2}$ to determine whether the proportion of "left-to-right compatible" errors in the
<table><caption>**Table 8**
Distribution of responses per age group and for each condition in Experiment 4.</caption><thead><tr><th>Group</th><th>N</th><th>Congruent</th><th>Incongruous</th><th>Reversed</th><th>Congruent or Reversed</th><th>p value Congruent vs. Reversed</th></tr></thead><tbody><tr><td colspan="7" style="text-align: center; font-weight: bold;">Occluder condition</td></tr><tr><td>Preschool</td><td>30</td><td>14 (47%)*</td><td>7 (23%)</td><td>9 (30%)</td><td>23 (77%)*</td><td>p = .20, h = 0.15</td></tr><tr><td>Kindergarten</td><td>41</td><td>19 (46%)*</td><td>10 (24%)</td><td>12 (29%)</td><td>31 (76%)*</td><td>p = .14, h = 0.16</td></tr><tr><td>Grade 1</td><td>32</td><td>13 (41%)*</td><td>1 (3%)</td><td>18 (56%)</td><td>31 (97%)*</td><td>p = .24, h = 0.11</td></tr><tr><td>Grade 2</td><td>35</td><td>20 (57%)*</td><td>3 (9%)</td><td>12 (34%)</td><td>32 (91%)*</td><td>p = .11, h = 0.18</td></tr><tr><td>Grade 3</td><td>23</td><td>11 (48%)*</td><td>1 (4%)</td><td>11 (48%)</td><td>22 (96%)*</td><td>p = .59, h = 0.00</td></tr><tr><td>Grade 4</td><td>32</td><td>21 (66%)*</td><td>1 (3%)</td><td>10 (31%)</td><td>31 (97%)*</td><td>p = .035, h = 0.26</td></tr><tr><td>Grade 5</td><td>42</td><td>23 (55%)*</td><td>1 (2%)</td><td>18 (43%)</td><td>41 (98%)*</td><td>p = .27, h = 0.09</td></tr><tr><td>Adults</td><td>53</td><td>31 (58%)*</td><td>1 (2%)</td><td>21 (40%)</td><td>52 (98%)*</td><td>p = .11, h = 0.14</td></tr><tr><td colspan="7" style="text-align: center; font-weight: bold;">Translation condition</td></tr><tr><td>Preschool</td><td>27</td><td>15 (56%)*</td><td>8 (30%)</td><td>4 (15%)</td><td>19 (70%)*</td><td>p = .01, h = 0.44</td></tr><tr><td>Kindergarten</td><td>37</td><td>18 (49%)*</td><td>11 (30%)</td><td>8 (22%)</td><td>26 (70%)*</td><td>p = .038, h = 0.28</td></tr><tr><td>Grade 1</td><td>30</td><td>17 (57%)*</td><td>4 (13%)</td><td>9 (30%)</td><td>26 (87%)*</td><td>p = .084, h = 0.22</td></tr><tr><td>Grade 2</td><td>31</td><td>23 (74%)*</td><td>3 (10%)</td><td>5 (16%)</td><td>28 (90%)*</td><td>p &lt; .001, h = 0.49</td></tr><tr><td>Grade 3</td><td>23</td><td>16 (70%)*</td><td>3 (13%)</td><td>4 (17%)</td><td>20 (87%)*</td><td>p = .0059, h = 0.46</td></tr><tr><td>Grade 4</td><td>30</td><td>20 (67%)*</td><td>6 (20%)</td><td>4 (13%)</td><td>24 (80%)*</td><td>p &lt; .001, h = 0.52</td></tr><tr><td>Grade 5</td><td>33</td><td>19 (58%)*</td><td>5 (15%)</td><td>9 (27%)</td><td>28 (85%)*</td><td>p = .043, h = 0.26</td></tr><tr><td>Adults</td><td>44</td><td>33 (75%)*</td><td>3 (7%)</td><td>8 (18%)</td><td>41 (93%)*</td><td>p &lt; .001, h = 0.46</td></tr></tbody></table>

Note. Significance for choosing a congruent response more than all other boxes was based on $\pi = \frac{1}{6}$. Significance for choosing an undirectional correct response more than all other boxes was based on $\pi = \frac{2}{6}$. For both of these tests, values followed by a * represent significant values above chance level. Significance for choosing a congruent response more than a reversed response (or conversely) was based on $\pi = \frac{1}{2}$. Using a Bonferroni correction, the p-value threshold was set at $\frac{0.05}{8} = .006$. The h value corresponds to the effect size assessed by Cohen's h.

<figure><img src="image_10.png" /><figcaption>**Fig. 5.** Comparison of the distribution of responses by age group for each condition in Experiment 4.</figcaption></figure>
translation condition was greater than that of "right-to-left compatible" errors, the results showed no significant difference ($p = .063$, Cohen's $h = 0.18$). We did not detect that the occluder condition yielded significantly more "right-to-left compatible" errors than "left-to-right compatible" errors either ($p = .115$, Cohen's $h = 0.2$).

## Occluder condition

We assessed the presence of a left-to-right spatial bias for each condition separately. In the occluder condition, $\chi^2$ tests showed that the distribution between congruent, incongruous, and reversed choices differed significantly from a random distribution from grade 1 to adults (all $\chi^2 \ge 8.7$, all $p \le .013$, all Cohen's $W \ge 0.6$). Note however that after Bonferroni correction (i.e., using a $p$-value threshold of $0.05/8 = .006$), the result found for children in grade 3 was no longer significant ($p = .013$ in grade 3, all other $p \le .002$). Results did not reach significance in preschool and kindergarten ($\chi^2(2) = 2.6$, $p = .273$, Cohen's $W = 0.29$ and $\chi^2(2) = 3.27$, $p = .195$, Cohen's $W = 0.28$ respectively).

Binomial tests were subsequently performed to evaluate whether the undirectional correct responses (i.e., congruent and reversed responses) were selected above chance level, revealing a good comprehension of the task in each age group (all $p < .001$, all Cohen's $h \ge 0.63$). Moreover, the congruent box was also selected more than chance level in each group (using $\pi = 1/6$, all $p < .001$, all Cohen's $h \ge 0.38$). We then conducted binomial tests for each age group to assess whether the congruent box was selected more than the reversed box. We did not observe any preference for the congruent box over the reversed box that remained significant after Bonferroni correction in any group (see Table 8). We thus did not observe a left-to-right bias in this condition<fnref n="14" />.

A developmental analysis was then conducted using $\chi^2$ tests to explore the evolution of responses with age. This test indicated a significant difference in the distribution of responses (between congruent, reversed, and incongruous) across all age groups ($\chi^2(14) = 35$, $p = .001$, Cramer's $V = 0.25$). The same test was still significant when excluding adults ($\chi^2(12) = 27.8$, $p = .006$, Cramer's $V = 0.24$). This analysis shows that as age increased, participants tended to produce fewer incongruous responses, while the overall distribution between the congruent and reversed responses remained relatively constant across all age groups.

## Translation condition

The same analyses were then applied to the translation condition. First, we observed that the distribution between congruent, incongruous, and reversed responses differed significantly from a random distribution in all groups except for children in kindergarten (all $\chi^2 \ge 6.89$, all $p \le .032$, all Cohen's $W \ge 0.51$ against $\chi^2(2) = 4.27$, $p = .118$, Cohen's $W = 0.34$ for children in kindergarten). However, after applying Bonferroni correction (i.e., using a $p$-value threshold of $0.05/8 = .006$), the results found for children in preschool, grade 1, and grade 5 were no longer significant. Following this, binomial tests revealed that undirectional correct responses were selected above chance level across all age groups (all $p < .001$, all Cohen's $h \ge 0.53$). Additionally, the congruent box was also consistently chosen more than chance level in each group (all $p < .001$, all Cohen's $h \ge 0.5$).

As in the occluder condition, extra binomial tests were conducted to assess a preference for choosing the congruent box more than the reversed one. The results showed that only children in grade 1 did not choose the congruent box significantly more than the reversed box. However, after applying Bonferroni correction to our $p$-value, we found that neither children in preschool, kindergarten, nor grade 5 could be considered as choosing the congruent box more than the reversed one, in addition to children in grade 1. The results of all binomial tests are reported in Table 8. Overall, a left-to-right spatial bias was thus observed in children in grades 2, 3, 4, and in adults<fnref n="15" />.

<footnote n="14">¹⁴ The same analysis conducted on children who were considered good seekers only (i.e., children who selected the congruent box in the last vertical trial) did not change this pattern of result (see Table C in Appendix).</footnote>

<footnote n="15">¹⁵ The same analysis was also conducted by including only children who were considered good seekers (i.e., children who selected the congruent box in the last vertical trial), which modified the results for the children in grade 3 only (see Table C in Appendix). For this group, our binomial test was not significant anymore after Bonferroni correction ($p = .009$).</footnote>
<figure><img src="image_11.png" /><figcaption>**Fig. 6.** Comparison of the distribution of responses by age group between Experiment 1 and each condition in Experiment 4.</figcaption></figure>

Then, a developmental analysis was conducted using $\chi^2$ tests. The results did not indicate any significant differences in the distribution of congruent, reversed, and incongruous responses across the seven groups of children ($\chi^2(12) = 12.7, p = .39$, Cramer's V = 0.17). This lack of significance persisted even when including the adult group ($\chi^2(14) = 17.94, p = .21$, Cramer's V = 0.19). The results thus suggest that the distribution of responses in this condition was constant across all age groups.

### Comparison with previous experiments

A final analysis was conducted to compare the results of the current experiment with those of the previous ones. To do so, we conducted four separate log-linear analyses to compare the distribution of responses across age groups for each condition in Experiment 4 with the distribution of responses across age groups in each of the first two experiments<fnref n="16" />. For Experiment 3, we only used chi-squared tests to compare the distribution of responses as this experiment included solely fifth graders.

We first conducted two log-linear analyses to assess the difference in results between Experiment 1 and each of our two conditions in Experiment 4 (see Fig. 6). We found that the distribution of responses differed significantly between Experiment 1 and Experiment 4 for both the occluder condition ($L(2) = 18.3, p < .001$) and the translation condition ($L(2) = 20.41, p < .001$). Compared to Experiment 1, the translation task of the current experiment yielded more congruent responses (42% in Experiment 1 against 63% in the translation condition) and fewer reversed responses (35% in Experiment 1 against 20% in the translation condition). The proportion of incongruous responses was also higher in Experiment 1 than in the translation condition (23% in Experiment 1 against 17% in the translation condition). Similarly, results indicated a higher proportion of congruent responses in the occluder condition compared to in Experiment 1 (42% in Experiment 1 against 53% in the occluder condition). The proportion of incongruous responses was also higher in Experiment 1 than in the

<footnote n="16">¹⁶ Note that for the comparison between Experiment 1 and 4, the children in grades 4 and 5 from Experiment 4 were grouped together, as they were in Experiment 1.</footnote>
occluder condition (23% in Experiment 1 against 9% in the occluder condition). However, the pattern slightly differed regarding the reversed responses as we found similar proportions across Experiment 1 and the occluder condition (35% and 38% respectively).

The log-linear analyses also showed a significant difference in the distribution of responses between age groups both in the occluder condition ($L(12) = 51.21, p < .001$) and in the translation condition ($L(12) = 36.66, p < .001$). In both conditions, children tended to produce less incongruous responses and more congruent responses as age increased. However, there was no interaction between experiment and age ($L(12) = 19.85, p = .07$ for the occluder condition, and $L(12) = 14.95, p = .244$ for the translation condition, see Table D in Appendix for the details of the log-linear analysis).

When comparing the results of the current experiment with those of Experiment 2 (see Fig. 7) using log-linear analyses, we did not observe a significant difference in the distribution of responses between experiments both for the occluder condition ($L(2) = 0.325, p = .85$) and the translation condition ($L(2) = 1.02, p = .60$). We did find a significant difference between age groups, but solely in the analysis regrouping children from Experiment 2 and the occluder condition ($L(2) = 13.18, p = .001$). As they grew older, children across Experiment 2 and the occluder condition tended to exhibit more congruent responses (43% in kindergarten against 58% in grade 5), more reversed responses (31% in kindergarten against 41% in grade 5), and less incongruous responses (26% in kindergarten against 1% in grade 5). However, the interaction between experiment and age did not reach significance in either condition. The detailed results of this log-linear analysis are reported in Table E in Appendix.

Finally, we did not observe any significant difference in the distribution of responses between Experiment 3 and either of our two conditions in Experiment 4 ($\chi^2(2) = 5.08, p = .079$, Cramer's $V = 0.28$ for the translation condition and $\chi^2(2) = 0.46, p = .795$, Cramer's $V = 0.08$ for the occluder condition, see Fig. 8).

## Discussion

The objective of Experiment 4 was to determine whether a potential confound was induced by a mental rotation in our previous designs. To achieve this objective, we compared a task that could induce a mental rotation (occluder condition), as in previous experiments, with a task that hampered mental rotation (translation condition). We expected to find a leftward spatial bias in children from grade 1 onward in the task limiting the rotation, while –based on our first three experiments– we did not expect any specific leftward spatial bias in the task inducing a mental rotation.

As we did find a left spatial bias in the translation condition while it was not the case in the alternative condition, this experiment suggests that the absence of a clear left-to-right bias in our previous experiments was due to participants performing a mental rotation during the task. The translation condition however induced a greater number of incongruous responses than the occluder condition. Still, these incongruous responses tended to correspond more to a “left-to-right compatible” mapping in the translation condition (i.e., 63% of “left-to-right compatible” errors) than in the occluder condition (i.e., 36% of “left-to-right compatible” errors). Although not significant, this result tends to indicate that participants’ errors corresponded to a leftward preference in the translation condition.

Therefore, the translation condition has a tendency to globally increase the number of left-to-right responses, regardless of whether these are the expected congruent response (which corresponds to the majority of responses) or not. We hypothesized that our new translational protocol would make the use of a mental rotation less probable, thus reducing the chance to rely on a right-to-left framework when considering the horizontal axis. The increase in the expected congruent responses is in favor of this hypothesis. However, we did not predict the increase in incongruous responses. We believe that this is due to our new protocol making clearer that the two axes corresponded to different objects, as the mummy pig went from one axis to the other by moving on the screen. The new horizontal axis could have prompted children to think that the baby pig might hide in a new location compared to the previous vertical axis, while still being influenced by a leftward preference.

In the translation condition, our results regarding the youngest children are not entirely consistent with the findings of West and McCrink (2021). The authors found a bias in preschool children (4 years
Kindergarten

Grade 5

<figure><img src="image_12.png" /><figcaption>**Fig. 7.** Comparison of the distribution of responses by age group between Experiment 2 and each condition in Experiment 4.</figcaption></figure>

Grade 5

<figure><img src="image_13.png" /><figcaption>**Fig. 8.** Comparison of the distribution of responses between Experiment 3 and each condition in Experiment 4.</figcaption></figure>

old) but not in kindergarten children (5 years old). In the current experiment, we found an effect in both of these groups (although the *p*-value was not below the Bonferroni correction threshold set at *p* < .006). These results contradict our hypothesis as we expected the bias to appear from grade
1 onward and to consolidate in older children. In our older groups, we indeed found a bias in grades 2, 3, and 4, but the effect did not reach significance both in grade 1 ($p = .08$) and in grade 5 after Bonferroni correction ($p = .04$). However there is a possibility that the use of many age groups (which lowered the threshold of significance using Bonferroni correction) could explain the statistical fluctuations. The overall statistics are still in favor of a general left bias for the translation condition, as children were overall three times more likely to pick the congruent box than the reversed box (128 congruent responses vs. 43 reversed responses across all age groups).

Assuming that this general left bias is valid, finding a strong effect size in the youngest children (Cohen's $h = 0.44$) is not compatible with the idea that a spatial bias strictly develops with expertise in reading and writing. The strength of the effect in preschool could be due to other forms of cultural experiences, such as children having a story read to them using finger-pointing. Indeed, studies have shown that these gestures in adults tend to follow individuals' reading and writing direction (Göbel et al., 2018; Troadec & Zarhbouch, 2011). As the effect was weaker in kindergarten (Cohen's $h = 0.28$) and absent in grade 1 ($p = .08$, Cohen's $h = 0.22$), one interpretation could be that the effect tends to vanish before being boosted again by formal teaching of reading and writing (given that the effect size from grade 2 to 3 was similar to that of preschool children)<fnref n="17" />. But again, a simpler explanation is that we might have observed random fluctuations across age groups in the translation condition.

## General discussion

The experiments conducted in this study aimed at unraveling the development of a left-to-right bias when processing unlabeled serial information (i.e., when information does not present any intrinsic order, contrary to numbers or letters). Experiment 1 did not show any clear-cut developmental effect that could have reflected a progressive emergence of a leftward bias in primary school children, in spite of our use of a paradigm that did highlight such a bias in adults. In a second experiment, we tried to manipulate the reference frame used by the participants (i.e., shifting from an allocentric to an egocentric reference frame) to increase the likelihood of measuring a leftward bias in children. This manipulation did not allow us to observe significant results either. We further controlled the position of the experimenter in a third experiment, and reinforced the use of an egocentric reference frame during the task. In spite of these modifications, no bias towards the left was observed, as 50% of participants still produced reversed responses. We interpreted these reversed responses as probably being associated with a counterclockwise mental rotation, which potentially hindered the measure of a spontaneous left-to-right spatial coding.

In a final experiment, we attempted to hamper the putative mental rotation using a translation that consisted in the simultaneous presentation of a vertical and horizontal axis (positing that the simultaneous view of two objects would limit the use of this mental rotation to transition from a vertical representation to a horizontal one). As expected, significant results were found in the condition that hampered mental rotation. This translation condition allowed us to observe a quite general leftward preference across our different samples in spite of fluctuations which could be due to the use of several age groups. Our results thus indicate that unlabeled ordinal information can be preferentially coded from left to right from preschool, and that this leftward bias consolidates until adulthood.

While we observed inconsistencies in our results regarding children, our translation task showed a significant leftward bias in adults. These results contradicts those of (West & McCrink, 2021), as they did not find any effect in adults. We could argue that hampering mental rotation in our new protocol allowed us to better detect the effect in comparison with their study. However, note that a strong bias was also found in adults in our first experiment, even though the procedure did not particularly hamper mental rotation. As such, the detection of a bias in adults in Experiment 4 cannot be solely attributed to a change in the experimental design. Furthermore, another key difference between the experiment of West and McCrink (2021) and the current study lies in the dependent variable used to assess the presence of a spatial bias. While we asked participants to point to the chosen location

<footnote n="17">¹⁷ Note that we also found a weaker effect in grade 5 (Cohen's $h = 0.26$), which could suggest that the effect is still inconsistent in children, before it further consolidates in adulthood with greater enculturation.</footnote>
in Experiment 1 to 4, West and McCrink used eye-tracking to determine whether participants looked at a specific location during the test. As participants in their study were only asked to visually search for the target location, their responses could have been overall noisier than when explicitly asked to pick a location. Indeed, as the authors stated, participants could have visually explored several possibilities, even if they knew where the critical location was. Also, because participants were habituated with a vertical array before the test phase, they could have persisted with glancing at the center of the screen. As such, the difference between our results and those of West and McCrink could be attributed to the method used to assess the presence of a spatial bias<fnref n="18" />.

Overall, we believe that the current study further extends the results provided by West and McCrink (2021). The authors found a bias in preschool (i.e., 4-year-old children), an age group in which we found a strong effect size in Experiment 4 (although the effect was not significant anymore after applying Bonferroni correction, which is nonetheless also the case in West and McCrink's study if we apply such correction to their results). The authors also showed that the bias tends to vanish when children grow up (i.e., they did not observe any bias in 5-year-old children). The fact that we observed a weaker bias in kindergarten and an absence of bias in grade 1 in our final experiment could align with their results. However, West and McCrink (2021) also failed to observe an effect in adults, while the effect was detected in this population using our translation task. We thus suggest that the absence of bias in both adults and older children in West and McCrink (2021) could be due to the protocol they used, as suggested by the authors themselves. Future studies should thus investigate how exactly the bias we observed in the current study consolidates with age when formal teaching of reading and writing is introduced in school as we could not observe the bias in grade 1. This result recalls the findings of Guida et al. (2020) who investigated a leftward bias in children from kindergarten to grade 5 and in adults using a paradigm in which participants were asked to guess in which cave an animal was hidden among two caves that were displayed on the left and on the right side of a computer screen. The authors found a leftward preference from grade 3 onward (and a marginally significant bias in grade 2). Additionally, the effect was the weakest in grade 1, which echoes our findings as we could not detect a leftward bias in grade 1 in the current study. As using several age groups in both our study and in Guida et al. (2020) could have caused fluctuations in the results, we believe that future studies should investigate whether this absence of effect in grade 1 was random or rather caused by education.

Also, note that the translation condition of our fourth experiment allowed us to detect a leftward bias in preschool (i.e., 4 year-olds) using a liberal *p*-value threshold, whereas McCrink et al. (2017) did not find a spatial bias in younger children (i.e., 2 to 3 year-olds) using the same type of unlabeled information. The question thus remains as to whether our translation condition (hampering mental rotation by the more continuous change of locations) could contradict their result. We thus believe future studies should also measure the presence of a leftward bias in younger children to distinguish the methodological vs. developmental factors that yielded to an absence of significant results at this exact age in the study of McCrink et al. (2017).

In addition, one limitation in our last experiment is a potential confound between the translation condition and our previous experiments. The confound lies in the spatial arrangement of the material. While the axis was presented *radially* in Experiment 1 to 3, our animated task (which was displayed on

<footnote n="18">¹⁸ However, we believe that it is unlikely that the diverging patterns found between West and McCrink's results and ours are actually due to a difference between an implicit response measured using eyetracking and an explicit response measured using pointing. Indeed, our occluder condition did not show a significant leftward bias in adults, even if they were asked to point to the boxes. It thus seems that the use of an eye-tracking procedure in West and McCrink (2021) might not have been the key factor in the inability to detect a spatial bias in adults. Knowing that a spatial bias is detectable in this population using a live-action paradigm (which can induce a mental rotation as in Experiment 1 of the current study), but not when using an animated task (still allowing a mental rotation, like in our occluder condition of Experiment 4), it appears that the mental rotation that we identified as a methodological confound could be enhanced when using an animated task. Indeed, our main hypothesis was that a putative leftward bias could be hindered by a mental rotation performed in a counterclockwise manner during the test phase. We also thought that this particular behavior could be driven by the habit of physically rotating tablets or phones. As these kind of gestures would be highly consolidated in adulthood (due to the extensive use of electronic devices), using a digital task could increase the probability of making such a counterclockwise rotation. This could overall explain why adults did not exhibit a leftward bias both in West and McCrink's study and in our occluder condition.</footnote>
a computer screen) presented participants with a *vertical* axis. It thus could be argued that the detection of the bias was facilitated using this new vertical mapping. However, this account does not appear much plausible since we failed to detect a consistent leftward bias in the occluder condition. Still, future studies could refine this last protocol to determine whether this particular factor can effectively play a role in the detection of the spatial bias.

Finally, we believe that it would be beneficial for future studies to investigate the development of this bias in atypical children. Indeed, a leftward bias observed in typical children in a judgment task of the length of pre-bisected lines (Hoyos et al., 2021) was not found in children with dyslexia (Sireteanu et al., 2005). This discrepancy could be due to the task involving visuospatial attention, as several studies have reported a deficit in these processes in children with dyslexia (Valdois et al., 2004). Since our task also involves visuospatial attention, we predict that children with dyslexia would not exhibit the bias we observed in typical children in the current study. Such a result would further expand the literature on visuospatial deficits in dyslexia and emphasize the need for effective remediation strategies (see Franceschini et al., 2022). Developing such remediation strategies is particularly needed as visuospatial attention influences eye movements during reading and is thus considered to be an important predictor of reading development (Bellocchi et al., 2013).

## Conclusion

We believe that the use of specific experimental conditions may lead to variations in the way participants code spatial information during spatialization tasks. Such variations can hinder the observation of consistent results for a given age across experiments. It seems that the translation condition we designed in our last experiment offers the most generalizable results, suggesting that future studies could further investigate spatial biases in humans by employing a similar protocol.

## CRediT authorship contribution statement

The authors' contributions are reported following the CRediT taxonomy (see https://credit.niso.org/contributor-roles-defined/). Conceptualization, M.V., M.F., A.G., and F.M.; Methodology, M.V., M.F., A.G., and F.M.; Investigation, M.V. and M.F.; Formal Analysis, M.V. and M.F.; Writing, M.V., M.F., A.G., and F.M. Funding Acquisition, F.M. and A.G.

## Data availability

The data and R scripts for each experiment are available at https://osf.io/5sg87/. The experiments were not preregistered.

## Declaration of Competing Interest

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.
**Acknowledgments**

This work was supported by the Agence Nationale de la Recherche [ANR-22-CE28-0002-01]. We gratefully thank the third-year students of the Experimental Course 2023 for their assistance with the data collection for Experiment 4.

**Appendix**

<figure><img src="image_14.png" /><figcaption>Figure A. Colored drawings used as stimuli in the rotation task of Experiment 1, 2, and 3.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Figure B. Material used for the live-action rotation task. Note. A different material with the same configuration was used in Experiment 1 and 2. This more resistant material was designed for Experiment 3.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>Figure C. Distribution of responses for each combined group in Experiment 1.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>Figure D. Distribution of responses for each age group in Experiment 1.</figcaption></figure>
<figure><img src="image_18.png" /></figure>

Figure E. Correlation between undirectional correct responses and age (excluding adults) in Experiment 1. *Note.* Undirectional correct responses were coded 1 when participants chose the second box regardless of direction vs. 0 for other boxes. Each dot represents one participant. Jittering was added to the ordinate values to avoid overlapping. For this reason, data are scattered around the values 0 and 1.

<figure><img src="image_19.png" /></figure>

Figure F. Distribution of responses for each age group in Experiment 2.
Grade 5

<figure><img src="image_20.png" /><figcaption>Figure G. Distribution of responses in Experiment 3.</figcaption></figure>

<table><caption>Table A. Features for each animal name used as stimulus.</caption><thead><tr><td>Name</td><td>Frequency*</td><td>Age of Acquisition</td></tr></thead><tbody><tr><td>Ant</td><td>5.14</td><td>1.92</td></tr><tr><td>Bee</td><td>3.18</td><td>1.88</td></tr><tr><td>Frog</td><td>4.59</td><td>1.92</td></tr><tr><td>Pig</td><td>12.7</td><td>1.76</td></tr><tr><td>Sheep</td><td>14.12</td><td>1.65</td></tr><tr><td>Turtle</td><td>4.66</td><td>1.92</td></tr></tbody></table>

Note. * Frequency of the word in 218 literary texts (per million occurrences). All animal names were bisyllabic in French.

<table><caption>Table B. Results of the log-linear analysis performed on the distribution of congruent, reversed, and incongruous responses as a function of condition and age group in Experiment 4</caption><thead><tr><td></td><td>df</td><td>L</td><td>p value</td></tr></thead><tbody><tr><td>Condition</td><td>1</td><td>2.01</td><td>.157</td></tr><tr><td>Age Group</td><td>7</td><td>24.08</td><td>.001</td></tr><tr><td>Response type</td><td>2</td><td>173.79</td><td>&lt; .001</td></tr><tr><td>Condition * Age Group</td><td>7</td><td>0.65</td><td>.999</td></tr><tr><td>Condition * Response type</td><td>2</td><td>25.83</td><td>&lt; .001</td></tr><tr><td>Age Group * Response type</td><td>14</td><td>41.19</td><td>&lt; .001</td></tr><tr><td>Condition * Age Group * Response type</td><td>14</td><td>8.03</td><td>.888</td></tr></tbody></table>
<table><caption>Table C. Distribution of responses per age group and for each condition in Experiment 4, for good seekers only</caption><thead><tr><th>Group</th><th>N</th><th>Congruent</th><th>Incongruous</th><th>Reversed</th><th>p value Congruent vs. Reversed</th></tr></thead><tbody><tr><td colspan="6" style="text-align: center; font-weight: bold;">Occluder condition</td></tr><tr><td>Preschool</td><td>22</td><td>11 (50%)</td><td>4 (18%)</td><td>7 (32%)</td><td>p = .24, h = 0.16</td></tr><tr><td>Kindergarten</td><td>30</td><td>17 (57%)</td><td>3 (10%)</td><td>10 (33%)</td><td>p = .124, h = 0.19</td></tr><tr><td>Grade 1</td><td>24</td><td>9 (38%)</td><td>0 (0%)</td><td>15 (62%)</td><td>p = .154, h = 0.18</td></tr><tr><td>Grade 2</td><td>24</td><td>15 (63%)</td><td>2 (8%)</td><td>7 (29%)</td><td>p = .067, h = 0.26</td></tr><tr><td>Grade 3</td><td>17</td><td>8 (47%)</td><td>0 (0%)</td><td>9 (53%)</td><td>p = .5, h = 0.04</td></tr><tr><td>Grade 4</td><td>24</td><td>17 (71%)</td><td>1 (4%)</td><td>6 (25%)</td><td>p = .017, h = 0.35</td></tr><tr><td>Grade 5</td><td>33</td><td>19 (58%)</td><td>0 (0%)</td><td>14 (42%)</td><td>p = .243, h = 0.11</td></tr><tr><td>Adults</td><td>48</td><td>29 (60%)</td><td>1 (2%)</td><td>18 (38%)</td><td>p = .072, h = 0.17</td></tr><tr><td colspan="6" style="text-align: center; font-weight: bold;">Translation condition</td></tr><tr><td>Preschool</td><td>18</td><td>14 (78%)</td><td>1 (5%)</td><td>3 (17%)</td><td>p = .006, h = 0.5</td></tr><tr><td>Kindergarten</td><td>29</td><td>16 (55%)</td><td>6 (21%)</td><td>7 (24%)</td><td>p = .046, h = 0.28</td></tr><tr><td>Grade 1</td><td>26</td><td>17 (65%)</td><td>1 (4%)</td><td>8 (31%)</td><td>p = .054, h = 0.26</td></tr><tr><td>Grade 2</td><td>25</td><td>20 (80%)</td><td>1 (4%)</td><td>4 (16%)</td><td>p &lt; .001, h = 0.52</td></tr><tr><td>Grade 3</td><td>22</td><td>15 (68%)</td><td>3 (14%)</td><td>4 (18%)</td><td>p = .009, h = 0.44</td></tr><tr><td>Grade 4</td><td>29</td><td>19 (65%)</td><td>6 (21%)</td><td>4 (14%)</td><td>p = .001, h = 0.5</td></tr><tr><td>Grade 5</td><td>32</td><td>19 (59%)</td><td>5 (16%)</td><td>8 (25%)</td><td>p = .026, h = 0.3</td></tr><tr><td>Adults</td><td>44</td><td>33 (75%)</td><td>3 (7%)</td><td>8 (18%)</td><td>p &lt; .001, h = 0.46</td></tr></tbody></table>

Note. Significance for choosing a congruent response more than all other boxes was based on $\pi = \frac{1}{6}$. Significance for choosing a congruent response more than a reversed response (or conversely) was based on $\pi = \frac{1}{2}$. Using a Bonferroni correction, the p-value threshold was set at $0.05/\sqrt{8} = .006$.

<table><caption>Table D. Results of the log-linear analysis performed to compare the distribution of congruent, reversed, and incongruous responses as a function of experiment and age group, between Experiment 1 and each condition of Experiment 4</caption><thead><tr><th></th><th>df</th><th>L</th><th>p value</th></tr></thead><tbody><tr><td colspan="4" style="text-align: left; font-weight: bold;">Occluder condition</td></tr><tr><td>Response type</td><td>2</td><td>97.98</td><td>&lt; .001</td></tr><tr><td>Experiment</td><td>1</td><td>20.24</td><td>&lt; .001</td></tr><tr><td>Age Group</td><td>6</td><td>30.29</td><td>&lt; .001</td></tr><tr><td>Response type * Experiment</td><td>2</td><td>18.3</td><td>&lt; .001</td></tr><tr><td>Response type * Age Group</td><td>12</td><td>51.21</td><td>&lt; .001</td></tr><tr><td>Experiment * Age Group</td><td>6</td><td>15.03</td><td>.020</td></tr><tr><td>Response type * Experiment * Age Group</td><td>12</td><td>19.85</td><td>.070</td></tr><tr><td colspan="4" style="text-align: left; font-weight: bold;">Translation condition</td></tr><tr><td>Response type</td><td>2</td><td>86.18</td><td>&lt; .001</td></tr><tr><td>Experiment</td><td>1</td><td>9.53</td><td>.002</td></tr><tr><td>Age Group</td><td>6</td><td>22.41</td><td>.001</td></tr><tr><td>Response type * Experiment</td><td>2</td><td>20.41</td><td>&lt; .001</td></tr><tr><td>Response type * Age Group</td><td>12</td><td>36.66</td><td>&lt; .001</td></tr><tr><td>Experiment * Age Group</td><td>6</td><td>14.98</td><td>.02</td></tr><tr><td>Response type * Experiment * Age Group</td><td>12</td><td>14.95</td><td>.244</td></tr></tbody></table>
<table><caption>Table E. Results of the log-linear analysis performed to compare the distribution of congruent, reversed, and incongruous responses as a function of experiment and age group, between Experiment 2 and each condition of Experiment 4</caption><thead><tr><th></th><th>df</th><th>L</th><th>p value</th></tr></thead><tbody><tr><td colspan="4"><strong>Occluder condition</strong></td></tr><tr><td>Response type</td><td>2</td><td>17.56</td><td>&lt; .001</td></tr><tr><td>Experiment</td><td>1</td><td>2.39</td><td>.122</td></tr><tr><td>Age Group</td><td>1</td><td>0.1</td><td>.756</td></tr><tr><td>Response type * Experiment</td><td>2</td><td>0.325</td><td>.85</td></tr><tr><td>Response type * Age Group</td><td>2</td><td>13.18</td><td>.001</td></tr><tr><td>Experiment * Age Group</td><td>1</td><td>0.04</td><td>.841</td></tr><tr><td>Response type * Experiment * Age Group</td><td>1</td><td>0.55</td><td>.458</td></tr><tr><td colspan="4"><strong>Translation condition</strong></td></tr><tr><td>Response type</td><td>2</td><td>12.42</td><td>.002</td></tr><tr><td>Experiment</td><td>1</td><td>0.11</td><td>.744</td></tr><tr><td>Age Group</td><td>1</td><td>0.00</td><td>.976</td></tr><tr><td>Response type * Experiment</td><td>2</td><td>1.02</td><td>.601</td></tr><tr><td>Response type * Age Group</td><td>2</td><td>3.05</td><td>.218</td></tr><tr><td>Experiment * Age Group</td><td>1</td><td>0.131</td><td>.717</td></tr><tr><td>Response type * Experiment * Age Group</td><td>1</td><td>0.248</td><td>.619</td></tr></tbody></table>

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