The Use of a Computer Display Exaggerates the
Connection Between Education and Approximate
Number Ability in Remote Populations

Edward Gibson

1

2
, Julian Jara-Ettinger

1
, Roger Levy

, and Steven T. Piantadosi

3

1

Department of Brain and Cognitive Sciences, MIT

2Department of Psychology, Yale University

3Department of Brain and Cognitive Sciences, University of Rochester

a n o p e n a c c e s s

j o u r n a l

Keywords: number comprehension, cross-culture differences, individual differences

ABSTRACT

Piazza et al. reported a strong correlation between education and approximate number
sense (ANS) acuity in a remote Amazonian population, suggesting that symbolic
and nonsymbolic numerical thinking mutually enhance one another over in mathematics
instruction. But Piazza et al. ran their task using a computer display, which may have
exaggerated the connection between the two tasks, because participants with greater
formazione scolastica (and hence better exact numerical abilities) may have been more comfortable with
the task. To explore this possibility, we ran an ANS task in a remote population using two
presentation methods: (UN) a computer interface and (B) physical cards, within participants. If
we only analyze the effect of education on ANS as measured by the computer version of the
task, we replicate Piazza et al.’s finding. But importantly, the effect of education on the card
version of the task is not significant, suggesting that the use of a computer display exaggerates
effects. These results highlight the importance of task considerations when working with
nonindustrialized cultures, especially those with low education. Inoltre, these results
raise doubts about the proposal advanced by Piazza et al. that education enhances the acuity
of the approximate number sense.

Citation: Gibson, E., Jara-Ettinger, J.,
Levy, R., & Piantadosi, S. T. (2017).
The Use of a Computer Display
Exaggerates the Connection Between
Education and Approximate Number
Ability in Remote Populations. Open
Mind: Discoveries in Cognitive
Scienza, 2(1) 37–46. https://doi.org/
10.1162/opmi_a_00016

DOI:
https://doi.org/10.1162/opmi_a_00016

INTRODUCTION

Supplemental Materials:
http://osf.io/ctaj4

Received: 4 Gennaio 2017
Accepted: 5 ottobre 2017

Competing Interests: The authors have
no competing interests to declare.

Corresponding Author:
Edward Gibson
egibson@mit.edu

Copyright: © 2017
Istituto di Tecnologia del Massachussetts
Pubblicato sotto Creative Commons
Attribuzione 4.0 Internazionale
(CC BY 4.0) licenza

The MIT Press

In order to understand the universal properties of human thought, there has been a burgeon-
ing interest in cross-cultural research focused on remote, nonindustrialized cultures (Henrich,
Heine, & Norenzayan, 2010; Norenzayan & Heine, 2005). Tuttavia, differences in behavior
must always be interpreted with care, as culture often unexpectedly influences performance
in ways that complicate interpretation (per esempio., Berry, 2002; Cole & Scribner, 1974; Medin,
Bennis, & Chandler, 2010). Recentemente, computer interfaces have gained popularity for collecting
behavioral data from remote cultures. A danger in interpreting such data is that the partici-
pants may be unfamiliar with the testing devices, leading them to perform less well than they
might otherwise. A recent example of a potential overinterpretation of results obtained from
an indigenous culture using a computer interface comes in the domain of number cognition.

Piazza, Pica, Izard, Spelke, and Dehaene (2013) used a computerized display to eval-
uate the ability to estimate approximate quantities (per esempio., Dehaene, 2011) in the Munduruku,
an indigenous population in the Brazilian Amazon. Piazza et al.
reported a strong corre-
lation between education and approximate number sense (ANS) acuity over a small sample

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Computer Displays and ANS in Remote Populations Gibson et al.

of adults (N = 38). This result is potentially important because it could mean—as Piazza
et al. speculate—that “symbolic and nonsymbolic numerical thinking mutually enhance one
another over the course of mathematics instruction” (P. 1037). Per esempio, practice with
arithmetic might afford a learner the opportunity to calibrate and sharpen their approximate
number judgments.

One possible confound, Tuttavia, is that participants with less education were simply
less comfortable with the computer displays, potentially leading to worse performance based
solely on their comfort with the testing situation. Piazza et al. attempt to control for this
confound by showing that participants were matched on their ability to perform a separate
task on a computer display—choosing the larger of two discs—but participants were near
ceiling on this task (mean accuracy = 95%), suggesting that this task was too simple to reliably
differentiate among individuals. Così, it is still possible that education may simply predict
comfort with a computer display in this indigenous population, rather than participants’ ability
in an approximate number task.

To investigate the role of computer displays in number cognition in a population that
has little familiarity with computers, we worked with the Tsimane’, a native Amazonian group
living in the lowlands of Bolivia (Huanca, 2008). The Tsimane’ live in small groups, hunt, E
farm (to a limited extent) for subsistence. Unlike people from industrialized cultures, many
Tsimane’ adults have never attended school, and those that have attended often begin school
at a later age than individuals in industrialized countries, and they often leave school earlier.
Hence their education level is highly variable across the population.

We constructed the present experiment to test whether possible discomfort with the com-
puter presentation would manifest itself in the measurement of ANS acuity, much like effects
of task comfort on success that have been observed in U.S. children (Odic, Hock, & Halberda,
2014). For our purposes, such a baseline shift in performance would prevent “fair” com-
parison of acuity levels across cultures; more generally, a variable influence of task might
preclude comparison across any two populations, including adults and children. Even more
problematically, interactions between the task effect and education would lead to spurious
(or exaggerated) education effects in correlations (as in Piazza et al., 2013): When only
computerized displays were used,
it would appear as though education improved ANS
acuity, when in fact increased education might just allow participants to be comfortable in the
testing paradigm.1

EXPERIMENT

One hundred and forty-five adults (mean age: 36.8 years; SD: 16.3 years; range: 17–77 years)
were recruited from six Tsimane’ communities near the town of San Borja in the Bolivian
Amazon, in collaboration with the Centro Boliviano de Investigación y de Desarrollo Socio

1 Although there is a large literature on computer vs. paper tasks in the education literature, this literature
predominantly involves reading, such as the TOEFL (Test of English as a Foreign Language) or SAT tasks (for a
revisione, see Noyes & Garland, 2008). The results from this literature suggest that there is either a slight benefit for
doing tasks on paper rather than computer, across all levels of participants, or no benefit either way (which seems
to be the tendency in the more recent literature, possibly due to [UN] better computer screens for task presentation
E [B] people being more used to working on computer screens in recent years). Whereas this literature is
potentially related to our research question, our ANS task involves no reading whatsoever. Inoltre, we
were most interested in whether there are differences according to education level. But we are not aware of any
literature on computer versus paper tasks reporting interactions with education.

OPEN MIND: Discoveries in Cognitive Science

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Computer Displays and ANS in Remote Populations Gibson et al.

(CBIDSI), which provided interpreters,

Integral
Tsimane’ culture.

logistical coordination, and expertise in

Methods

Participants first completed a short demographic survey, including reporting the highest num-
ber of years of education they had achieved (a whole number between 0 E 16), their age,
genere, Spanish proficiency, and household size. Tsimane’ education consists of classroom
work in the village, with the local teacher (usually the most educated person in the village).
Children learn the basics of arithmetic, reading, writing, Spanish language, and training in
needed skills for village living, such as how to build houses.

Our main task consisted of two parts, performed in a random order for each participant.
Area-controlled, intermixed dot stimuli were presented in two different ways to each partici-
pant: (UN) via a touchscreen laptop computer and (B) via laminated cards that were presented
by the experimenters. The stimuli consisted of black and red dots of varying sizes, intermixed
inside a disc (Guarda la figura 1). For each version of the task, participants were asked to report
whether there were more black or red dots in the display. The sets of black and red dots were
matched for the size of the biggest and smallest dots in each set. The sets varied in ratios among
the following ratios, going from least to most complex to discriminate: 1:3, 1:2, 2:3, 3:4, 4:5,
5:6, 6:7, 7:8, 8:9, 9:10, 10:11, E 11:12. In order to minimize spurious differences among
the perceivable ratios, we kept the total number of dots as close to a total of 20 as possible,
given these ratios (cioè., 5:15, 7:14, 8:12, 9:12, 8:10, 10:12, 12:14, 7:8, 8:9, 9:10, 10:11, E
11:12). There were eight versions of each of the ratios, each with four trials where “red” was
the correct answer, and four where “black” was correct.

Participants were instructed to touch a red square below the presentation disc if there
were more red dots or a black square if there were more black dots. These squares were on the
screen of the touchscreen computer version, or on a laminated card in the card version. Stimuli
remained in front of the participant until they touched one of the squares. In the cards version of
the task, the correct answer was printed on the card in a coded form. The experimenter would

Figura 1. An example stimulus consisting of black and red dots of varying sizes, intermixed inside
a disc.

OPEN MIND: Discoveries in Cognitive Science

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Computer Displays and ANS in Remote Populations Gibson et al.

put his thumb over this code when placing the card in front of the participant, so that neither
he nor the participant could see it until the trial was complete. This way, the experimenter
could not provide cues to the participants about correct answers.

Participants were trained on eight practice trials consisting of dots in a 1:3 ratio. If they
made any mistakes, the experimenter would explain the task again, and then they would repeat
the set of eight practice trials, in a different random order. Participants were given at most three
attempts to complete the practice trials correctly. Four participants failed this criterion and
no further data were collected for them. Once a participant finished one version of the task
(computer or cards), they would start the other version (cards or computer). We report data
from the 141 participants who succeeded in the practice trials (78 who did the cards version
first; 63 who did the computer version first).

In the test part of each task, participants performed 30 total trials, starting at the 1:2 ratio,
and using a two-up, one-down staircase design, such that if they got two answers in a row
If, Tuttavia, they got an answer
correct at one level, they moved up a level of difficulty.
wrong, then they were moved down a level. Participants who got trials incorrect at the
1:2 ratio continued at the 1:2 ratio. The eight trials per level were randomized/shuffled before
each participant.

Analysis

All subjects’ behavior on each task was characterized by fitting a Weber fraction (W) to their
entire set of responses. The Weber fraction W indexes the amount of variance in participants’
ANS number representations, such that a smaller Weber fraction indicates better performance
and sharper Gaussian curves. We use Piantadosi’s (2016) method for fitting W, which is closely
related to the maximum likelihood fitting used widely in the field (per esempio., Halberda, Mazzocco,
& Feigenson, 2008), but introduces a weak prior bias (for small W) in order to combat the
problem that high W are difficult to distinguish statistically. The small bias decreases the vari-
ance of each subjects’ estimated W, while introducing a negligible influence on the mean of
the estimate, leading to quantifiably better estimates.2 We treat all subjects’ fit Ws as point
estimates of their acuity in each ANS task. We predict Log W from our dependent features.

Results

Data and analyses are available at http://osf.io/ctaj4 (Gibson, 2017). A statistical
evaluation of the relationship between Education and Log W for the sum-coded card and
computer versions of the task is provided in Tables 1 E 2. Figura 2 shows the relationship
between years of education and Log W for the two versions of the task. As is visually apparent
in the figure, there is a reliable interaction between Tsimane’ education and task, such that
there is a strong correlation between education and Log W for the computer version of the task
on the right, but much less so in the card version on the left. These correlations are presented
in Table 2.

Figura 3 shows another visualization of these data, giving the difference score (Cards
minus Computer) as a function of education. A smoothed nonparametric fit (loess) is shown
for each of males and females, con 95% confidence bands. This figure demonstrates that for
low education, Log Card W is less than Log Computer W, meaning that participants perform

2 The statistical patterns are very similar when we used standard maximum likelihood fits: Any effect that we

report as significant using Piantadosi’s methods is also significant using maximum likelihood fits.

OPEN MIND: Discoveries in Cognitive Science

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Computer Displays and ANS in Remote Populations Gibson et al.

Tavolo 1. A linear mixed effects regression (including a by-subject random intercept to account for
repeated within-subjects measurements) predicting Log W from Tsimane’ education level and task
(computer vs. card version).

AIC

401.8

Scaled residuals:

Min
−2.1824

Random effects:

BIC

423.7

1Q
−0.6418

Groups

Nome

Subject
Residual
Number of obs: 282, groups: subject, 141

(Intercept)

Fixed effects:

(Intercept)
Education
task1
Education:task1

Estimate
−1.252289
−0.042551
−0.165655
0.031667

logLik
−194.9

Median
−0.0226

Variance

0.02481
0.20978

SE

0.041399
0.008400
0.037229
0.007554

deviance

389.8

3Q

0.4943

SD

0.1575
0.4580

t value
−30.249
−5.066
−4.450
4.192

Correlation of fixed effects:

Education
task1

(Intr)
−0.681
0.000

Eductn

task1

0.000

−0.681

Note: summary(lmer(W_value_lg ~ Education * task + (1 | subject), REML=F, data=gathered_d))
Linear mixed model fit by maximum likelihood [’lmerMod’]
Formula: W_value_lg ~ Education * task + (1 | subject)

better on the card task. Tuttavia, the positive trend of the average line indicates that the effect
disappears with high education. Inoltre, this figure reveals no obvious trends with respect
to age and the difference score, but one can see that high education participants tend to be
younger and male, reflecting current Tsimane’ demographics.

To assess statistical significance, we computed a linear regression predicting the differ-
ence in Log W (Cards) minus Log W (Computers) from demographic and task factors (Vedere
Tavolo 3). The resulting fit suggests that adults with no education perform significantly worse
when the task is administered on a computer interface, as the intercept is significantly less than
zero. The regression reveals a significant effect of education such that the difference between
the tasks vanishes with increasing education. The magnitude of the coefficients accords with
Figura 3: The tasks do not differ after approximately 5 O 6 years of education (.287 / .051 =
5.6 years). The regression also included a (sum-coded) predictor for which task was run first
within participants: when the computer version was run first, the difference between the com-
puter and cards version was larger. Inoltre, the regression reveals no effect of (standard-
ized) age, but a marginal effect of gender (sum-coded), such that the difference between the

OPEN MIND: Discoveries in Cognitive Science

41

df.resid

276

Max

4.9975

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Computer Displays and ANS in Remote Populations Gibson et al.

Tavolo 2. Linear regressions predicting Log W from Tsimane’ education level for the computer task
(highly significant) followed by the card task (nonsignificant).

Residuals:

Min
−1.1209

Coefficients:

(Intercept)
Education

Residuals:

Min
−0.75909

Coefficients:

(Intercept)
Education

1Q
−0.4343

Median
−0.1016

3Q

0.3188

Max

2.5396

Estimate
−1.08663
−0.07422

1Q
−0.20395

SE

0.07125
0.01446

Median

0.02276

t value
−15.251
−5.134

Pr(>| T |)
<2e–16 *** 9.39e–07 * 3Q 0.23466 Max 0.63624 Estimate −1.417943 −0.010884 SE 0.034819 0.007065 t value −40.723 −1.541 Pr(>| T |)
<2e–16 *** 0.126 Note: lm(formula = W_value_lg ~ Education, data = just_comp) † p < .1. ∗∗∗ p < .001. ∗∗ p < .01. ∗ p < .05. computer and cards version was slightly larger for women than men.3 When we omit partic- ipants with more than 10 years of education, we find very similar statistical trends as in the analyses reported in the table: All reliable effects are also reliable here. Thus it is not the 13 Tsimane’ participants with 12+ years of education that are driving the observed effects. Fi- nally, the regression in Table 4 shows that Tsimane’ education is largely predicted by age and gender: More educated Tsimane’ participants tend to be young and male. DISCUSSION Our results demonstrate that participants with lower education levels performed worse on the task with the computer display than with the card display, whereas participants with higher education levels did just as well on the card or computer versions of the task. These results emphasize the importance of task comfort and understanding, particularly when working with populations that are unfamiliar with experimental psychology and behavioral paradigms. The fact that task performance is influenced by education level suggests that, if we had not noticed the potential confound with task, we might have found a spurious education effect. Indeed, as seen in Table 2, if we only analyze the effect of education on W, as measured by the computer version of the task, the effect is statistically significant, even though the effect of education on the card version of the task is not. The variable effect of education within 3 In another analysis, we investigated a potential interaction between education and task order, but this ef- fect was nonsignificant (p = .12), so we left this interaction term out of the presented analysis. Although not significant, the direction of this interaction was such that lower education participants had a larger difference score. OPEN MIND: Discoveries in Cognitive Science 42 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u o p m i / l a r t i c e - p d f / / / / / 2 1 3 7 1 8 6 8 2 9 7 o p m _ a _ 0 0 0 1 6 p d . i f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Computer Displays and ANS in Remote Populations Gibson et al. Figure 2. Plot of the relationship between years of Tsimane’ education and Log(W) for the two versions of the task: Cards vs. Computer. As shown in Table 1, there is a reliable interaction between Tsimane’ education and task, such that there is a strong correlation between education and Log W for the computer version of the task on the right, but nothing reliable in the card version on the left (see Table 2).4 the Tsimane’ population on these task factors might therefore have led us to conclude that education strongly influenced ANS if we had run only the computer version. Of course, the influence of task does not show that there is no education effect, only that if task is not con- trolled, we cannot be sure. This is a plausible alternative explanation for the findings of Piazza et al. (2013), discussed above. Though it is plausible that education influences ANS in these populations (we find a small nonsignificant tendency in this direction), detailed controls for task are required to rule out alternative explanations. A comparison of the slope of the effect in our computer task—about .034 W / year (note that the regression in Table 2 is computed over Log W, not W)—to the slope of the effect in Piazza et al. (2013)—about .25 W / year—suggests that the Piazza et al. effect is much larger, even on the matched computer task. But this comparison assumes that the education years are matched. Alternatively, it is possible that the education in the Munduruku is more organized than in the Tsimane’, leading to a larger effect each year. Note that the effect is miniscule for the Tsimane’ cards task—.003 W / year—and this is not significant in the regression. There are several plausible explanations for the strong education effect on task that we observed, due to factors that correlate with educational level. First, it is not the case that ex- perience with computers could explain the observed differences, because almost none of the participants had ever seen a computer or computer tablet before, independent of their educa- tional level, according to their own self-reports. One possible source for the education effect on task is more experience with technology more generally, such as radios, TV screens, and phones. People with more education are more likely to travel to the local Bolivian (Spanish) 4 The regressions in Table 2 are similar if we predict W instead of Log W. In particular, for the computer task the relationship is significant (beta = −.034, t = −3.13, p = .002), but for the card task the relationship is not (beta = −.0029, t = −1.67, p = .098). OPEN MIND: Discoveries in Cognitive Science 43 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u o p m i / l a r t i c e - p d f / / / / / 2 1 3 7 1 8 6 8 2 9 7 o p m _ a _ 0 0 0 1 6 p d . i f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Computer Displays and ANS in Remote Populations Gibson et al. Figure 3. Difference score (Log Cards W minus Log Computer W) as a function of education for males and females separately (which don’t differ significantly). A smoothed nonparametric fit (loess) is shown for each, with 95% confidence bands. This figure demonstrates that for low education, Log Card W is less than Log Computer W (negative values on this plot), meaning that participants perform less well on computer tasks. However, the positive trend of the red average line indicates that the effect disappears and potentially reverses for high education. In addition, this figure reveals no obvious trends with respect to age and the difference score, but one can see that high-education participants tend to be younger and male, reflecting current Tsimane’ demographics. towns, where there is access to technology, such as a television in the town square. Another possibility is that people with greater education might have better developed cognitive control (Brod, Bunge, & Shing, 2017; Burrage et al., 2008; Morrison, Smith, & Dow-Ehrensberger, 1995; Roebers, Röthlisberger, Cimeli, Michel, & Neuenschwander, 2011) so that they can Table 3. A linear regression predicting the difference in Log W (Cards minus Computers) from demographic and task factors. Residuals: Min −2.4145 Coefficients: (Intercept) Education Comp.First.sum scale(Age) Gender1 1Q −0.3365 Median 0.1191 3Q 0.4094 Max 1.3290 Estimate −0.28733 0.05106 −0.38043 0.01967 −0.09847 SE 0.08092 0.01663 0.10809 0.05797 0.05915 t value −3.551 3.071 −3.519 0.339 −1.665 Pr(>|T|)

0.000528 ***
0.002579 **
0.000589 ***
0.734911
0.098286

†

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lm(formula = CardsMinusComputers.lg ~ Education + Comp.First.sum + scala(Age) +

Note:
Gender, data = d)
∗ p < .05. † p < .1. ∗∗ p < .01. ∗∗∗ p < .001. OPEN MIND: Discoveries in Cognitive Science 44 Computer Displays and ANS in Remote Populations Gibson et al. Table 4. A linear regression showing that Tsimane’ education is largely predicted by age and gen- der: More educated Tsimane’ people tend to be young and male. (This accounts for the gender and age effects that are visible in Figure 3. Residuals: Min −5.6181 Coefficients: 1Q −2.0344 Median −0.3949 3Q 1.2314 Max 11.9871 (Intercept) scale(Age) Gender1 scale(Age):Gender1 Estimate 3.5706 −1.2454 −1.2057 −0.4277 SE 0.2849 0.2818 0.2849 0.2818 t value 12.532 −4.420 −4.232 −1.518 Pr(>|T|)
< 2e–16 *** 1.99e–05 *** 4.22e–05 *** 0.131 Note: lm(formula = Education ~ scale(Age) * Gender, data = d) † p < .1. ∗∗∗ p < .001. ∗∗ p < .01. ∗ p < .05. better ignore irrelevant aspects of the testing situation, such as the novel computer presenta- tion. People with lower education might have a harder time focusing on the relevant aspects of the task in the novel situation. Thus, removing computer interfaces from cross-cultural studies would not address the current concerns. These results also have important ramifications beyond cross-cultural research: anywhere where familiarity with technology may covary with another dimension, such as age, socio- economic class, or gender. In such cases, participants might be unfamiliar with computers, and researchers should therefore be careful to show that their participants don’t behave differently depending on how the task is administered. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u o p m i / l a r t i c e - p d f / / / / / 2 1 3 7 1 8 6 8 2 9 7 o p m _ a _ 0 0 0 1 6 p d . i Our results show that one should be careful when designing tasks with participants who are not used to cognitive research, and careful about interpreting results from studies on remote populations, especially if a study purports to show performance that is different from a popu- lation with industrialized education. If the remote group performs similarly to industrialized nation participants, then the remote group understood the task as well as the industrialized par- ticipants (e.g., Dehaene, Izard, Pica, & Spelke, 2006, 2008; Izard, Pica, Dehaene, Hinchey, & Spelke, 2011; Izard, Pica, Spelke, & Dehaene, 2011; McCrink, Spelke, Dehaene, & Pica, 2012; Pica, Jackson, Blake, & Troje, 2011; Pica, Lemer, Izard, & Dehaene, 2004). But when they perform relatively poorly, this may not reflect a genuine cognitive difference between groups. f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Perhaps most importantly, our results suggest that the effect of education on ANS that Piazza et al. (2013) had observed in the Munduruku may be much weaker—if it exists at all— than suggested by Piazza et al.’s study. Future work will be needed to see if there is a reliable correlation between education and ANS that is unconfounded by task. AUTHOR CONTRIBUTIONS EG, JJE, and STP designed the study. EG, JJE, and RL carried out the experiment. STP did the analyses. EG and STP drafted the manuscript. JJE and RL provided critical feedback on the manuscript, and all authors contributed to the final draft of the manuscript. OPEN MIND: Discoveries in Cognitive Science 45 Computer Displays and ANS in Remote Populations Gibson et al. ACKNOWLEDGMENTS We thank Ricardo Godoy and Tomas Huanca for logistical help. Dino Nate Añez, Robertina Nate Añez, and Salomon Hiza Nate helped with translating and running the task. We thank Evelina Fedorenko and Rachel Ryskin for comments on earlier drafts of this paper. Research reported in this publication was supported by National Science Foundation Grant 1022684 from the Research and Evaluation on Education in Science and Engineering (REESE) program to EG. The project was also supported by the Eunice Kennedy Shriver National Institute of Child Health & Human Development of the National Institutes of Health under Award Number F32HD070544 to STP. 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