A meta-analysis of 97 studies reveals that statistical learning and language ability are

only weakly correlated

Sam Boeve¹ª, Haoyu Zhou¹, Louisa Bogaerts¹

¹Department of Experimental Psychology, Ghent University, Ghent, Belgium

Henri Dunantlaan 2

9000 Ghent, Belgium

E-mail: [Sam.Boeve@UGent.be](mailto:Sam.Boeve@UGent.be)

<footnote><sup>a</sup>Corresponding author</footnote>
Abstract

Despite the widely held belief that individual differences in statistical learning (SL) abilities
are associated with linguistic skills, research has produced mixed results. To provide a
comprehensive assessment of the literature, we conducted a meta-analysis of 97 studies
examining the correlation between SL and linguistic abilities. Results revealed a small but
significant overall correlation (r = .16). Our analysis considered sample characteristics, SL
task features, and the type of language test as predictors of the strength of observed
correlations. Notably, variation across studies was only accounted for by SL task features
(i.e., paradigm, stimulus modality and stimulus domain). No indications of publication bias
were identified. These findings lend support to a positive yet limited association between SL
and language outcomes and underscore the need for thoughtful task selection.

***Keywords:*** statistical learning, language, individual differences, meta-analysis
## Introduction

Statistical learning (SL), the ability to detect and extract regularities from the sensory environment, has been recognized for its role in a wide range of cognitive functions (Bogaerts et al., 2020; Sherman et al., 2020). Amongst those functions, language learning and processing are perhaps the most illustrative examples of the theoretical reach of SL.

Inspired by the question how young language learners can segment speech, pioneering research conducted by Saffran et al. (1996) revealed that infants are able to extract statistical regularities from the linguistic input they receive. They were able to extract novel word forms embedded in a continuous speech stream based on the co-occurrences of syllables (i.e., the transitional probabilities between syllables being higher within words than at word boundaries), allowing them to acquire the basic structures and patterns of language (Saffran et al., 1996). This seminal finding sparked a surge of interest in SL as a powerful learning mechanism involved in human language acquisition and processing (Erickson & Thiessen, 2015; Romberg & Saffran, 2010; Siegelman, 2020). An initial wave of studies focused on the performance of the tested sample, ranging from newborns to adults (see Forest et al, 2023 for a review), at the group level. These studies demonstrate learners' sensitivity to various types of linguistic regularities (e.g., nonadjacent syllable co-occurrences: Newport & Aslin, 2004; phonetic distributions: Maye et al., 2002; Syntactic categories: Mintz, 2002; word-referent mappings: Yu & Smith, 2007).

Another approach has emerged in the past decade, one that focuses on individual differences as a window into the relation between SL and language abilities (see Siegelman, 2020 for a recent review).

## Individual Differences as a Window into the Relation Between Statistical Learning and Language
Recent empirical work has demonstrated that variance in SL abilities reflects stable
individual differences that are largely independent of intelligence and working memory
capacity (see Kalra et al., 2019; Kaufman et al., 2010; Siegelman & Frost, 2015). If enhanced
SL abilities contribute to language skills, variability in SL is expected to predict individual
differences in language learning and processing, and vice versa. Putting this hypothesis to the
test has been the primary rationale for examining the correlation between statistical learning
and language performance (Siegelman, 2020). Arciuli & Simpson (2012), for example,
investigated the relationship between SL and reading ability. SL ability was evaluated through
performance on a visual embedded pattern task, involving repeating triplets of alien figures.
Reading abilities, on the other hand, were assessed using a read-aloud task that included
words and letter strings. They found a significant correlation between SL and reading abilities
in both adults and children: individuals with higher visual SL abilities also exhibited better
performance on standardized reading tests.

To date, many studies have assessed the correlation between individuals’ linguistic abilities, covering different aspects of spoken and written language, and their SL performances. Various tasks have been used to operationalize SL, with paradigms ranging from the classic embedded pattern learning task (EPL; e.g., Arciuli & Simpson, 2012; Mcdonough & Trofimovich, 2016) to artificial grammar learning (AGL; e.g., Conway et al., 2010), sequence learning (e.g., serial reaction time task; e.g., Kidd, 2012), and word-object mapping (e.g., Vlach & DeBrock, 2017) (see Table I for a list of paradigms and their descriptions). These tasks incorporate auditory or visual stimuli (Evans et al., 2009; Spencer et al., 2015), which are either linguistic (e.g., spoken syllables, Misyak & Christiansen, 2012; visual letter images, Hu et al., 2023) or non-linguistic (e.g., synthesized tones, Ahufinger et al., 2022; abstract shapes, Frost et al., 2013).
<table><caption>**Table I**</caption><caption>Descriptions of Paradigms Used to Operationalize SL</caption><tbody><tr><td>Embedded pattern learning (EPL)</td><td>Participants are exposed to a continuous stream of stimuli containing embedded patterns (such as triplets or duplets). Stimuli within a pattern have a higher transitional probability than stimuli at pattern boundaries. The exposure phase is typically followed by a test in which the preference for the embedded patterns over foil patterns is assessed.</td></tr><tr><td>Artificial grammar learning (AGL)</td><td>Participants are exposed to a set of sequences generated by an underlying (artificial) grammar. They are subsequently tested on their ability to differentiate between novel grammatical and ungrammatical items.</td></tr><tr><td>Sequence learning</td><td>Participants are exposed to repeating sequence(s) of items and (a) are asked to recall the items in the correct order or (b) press buttons corresponding to the position of the item. Learning is assessed by looking at the difference between recall performance or response times for sequences that follow the learned structure and sequences that do not.</td></tr><tr><td>Mapping task</td><td>For this category, we considered different tasks that require participants to learn novel mappings, such as associating new word forms with a certain object or meaning. Cross-situational word learning, in which the ambiguous mapping in a single trial can be resolved across multiple exposures, falls under this category. Following the exposure phase, learning is assessed via a discrimination task.</td></tr></tbody></table>

In most published studies, SL performance as measured with these various tasks was shown to exhibit significant (albeit typically small) correlations with subjects' language proficiency in phonology, orthography, and syntax, encompassing both vocabulary and sentence comprehension (e.g., Gabay et al., 2015; Misyak & Christiansen, 2012). Findings like these were taken as evidence of a close relationship between SL and language abilities. However, null findings have also been reported in behavioral studies (e.g., Pavlidou & Bogaerts, 2019; Qi et al., 2019; Schmalz et al., 2019; van Witteloostuijn et al., 2021), computational modeling simulations (e.g., Schmalz, 2023), and meta-analyses on SL deficits in individuals with language impairments (e.g., Schmalz et al., 2017; van Witteloostuijn et al.,
2017; West et al., 2021). These mixed findings raise questions regarding the replicability and
the strength of the current evidence in support of the relation between SL and language
abilities.

One factor that may have contributed to these equivocal findings is the historical view
of SL as a unified capacity. However, evidence of modality-specificity (e.g., Conway &
Christiansen, 2005; Raviv & Arnon, 2018) and stimulus-specificity (e.g., Lukics & Lukács,
2022; Shufaniya & Arnon, 2018) suggests that SL cannot be treated as a unified construct
(Arciuli, 2017; Siegelman, Bogaerts, Christiansen, et al., 2017). Viewing SL as a
componential construct implies that “different SL tasks may tap into separate sub-components
of SL that are not necessarily interchangeable” (Siegelman, Bogaerts, Christiansen, et al.,
2017, p. 1). Paradigms such as EPL, AGL, sequence learning, and mapping tasks vary across
several dimensions, encompassing differences not only in the modality and nature of the
presented sensory input, but also in the type of statistical regularities targeted for learning. As
a result, these differences most probably implicate distinct computational processes (Bogaerts
et al., 2020). Additionally, it has been proposed that SL measures can be either processing-
based or reflection-based. According to Christiansen (2019), processing-based measures
assess the processing benefits for statistical regularities that tap the primary effects of
participants’ learning, such as changes in reaction time to stimuli that are predictable given
their occurrence in a recurring pattern (e.g., Godfroid & Kim, 2021). In comparison,
reflection-based measures such as discrimination tasks require participants to deliberate on
what they have learned and to make explicit decisions about the stimuli (e.g., Christiansen,
2019; Conway et al., 2010; Kidd & Arciuli, 2016). Indeed, this is problematic for
developmental samples, for whom reflection-based SL measures show poor reliability
(Arnon, 2020). As such, we argue that these different measurement approaches may also
contribute to variations in findings across studies.
In the same vein, the capacity for language is not a singular ability (Bogaerts et al., 2021). Different linguistic tasks, such as acquiring new word forms vs. comprehending sentences with complex syntax, involve different task demands and distinct types of statistical regularities at different ranges (Siegelman, Kearns, et al., 2020; Snell & Theeuwes, 2020). In assessing the relationship between SL and language, we also aimed to investigate the potential interactions between the characteristics of SL tasks and language tasks.

## The Current Meta-analysis

Through the current meta-analysis, we aimed to address the question of what the current state of evidence is in support of a relationship between individuals' SL performance and different measures of language ability. Whereas the meta-analyses that have been conducted before focused on the SL impairments of individuals with developmental (language) disorders compared to a control group (Lammertink et al., 2017; Lee et al., 2022; Obeid et al., 2016; Schmalz et al., 2017; van Witteloostuijn et al., 2017), here we focused on correlational findings, considering both SL and language skills as a continuum (e.g., Fletcher, 2009).

To quantify the overall effect, we calculated the weighted mean effect size of published studies that have investigated this correlation. In addition, we were interested in what explains the differences between the findings of individual studies. We hypothesized that these differences can be better understood considering the recently proposed view of SL as a componential construct. According to this view, not all SL tasks and learning measures tap overlapping computations, and what they do tap is likely not equally relevant to the range of language abilities we have. Therefore, the specific tasks and learning measures used to operationalize SL are expected to affect the size of correlations detected between SL and linguistic performance (Frost et al., 2019; Siegelman, 2020). We provide an overview and
quantification of the empirical evidence thus far, encompassing a wide range of SL tasks,
language abilities, and types of participants. By unpacking the features of SL tasks that
potentially influence individual performance, we aim to shed light on the construct of SL and
gain insights regarding what drives its connection to language learning and processing. As
illustrated in Figure 1, we considered three classes of study aspects to account for variations
in correlation strengths across studies: characteristics of the tested sample, the features of the
employed SL task, and the type of language test that was administered.

<caption>**Figure 1**</caption>

Overview of Predictors of Interest

<figure><img src="image_1.png" /></figure>

## Predictions

All predictions were preregistered using the Open Science Framework (https://doi.org/10.17605/OSF.IO/GE5YB) and are listed with more detailed motivations below.

1. Based on our review of the literature, we expected a positive, although small correlation between SL and language abilities when measured by independent tasks.

**Predictions regarding sample characteristics.**
2. The theoretical stand that SL plays a role in both language acquisition and processing, combined with the documentation of successful SL across the lifespan led us to predict that the relation between SL and language would be present across all development stages. The effect of sample age likely depends on how SL is measured (processing-based vs. reflection-based), see also prediction 9.

3. Many studies have tested unselected samples in terms of their language abilities, except studies on language impairments. Low correlations might be partly attributable to range restriction in terms of linguistic abilities (Thorndike, 1950). Hence, we predicted that studies with samples that include both typically developing controls and participants with language disorders would show higher correlations by assessing language abilities across the entire spectrum.

**Predictions regarding SL task features.**

4. Viewing SL as a componential ability, we predicted that SL paradigms that more closely match the challenges posed by natural language such as mapping sounds to images (mapping task), transitional probability learning (i.e., EPL) and AGL would show a stronger relation to language ability as opposed to sequence learning which commonly has a significant motor component to it.

5. The sensory modality of the stimuli (i.e., auditory, visual or crossmodal) was also expected to moderate the observed relation between SL and language but contrasting predictions can be made. Previous literature suggests that auditory SL predicts certain aspects of language better than visual SL (Qi et al., 2019), yet this could be due to auditory SL studies using syllables as stimuli compared to unfamiliar shapes in visual SL.

6. We expected the domain of the stimuli (i.e., linguistic, non-linguistic) to have an impact on the observed correlations. Specifically, we predicted larger correlations
for tasks using linguistic stimuli as in these cases the SL task and the language test
might rely to a larger degree on the same mechanisms.

7. When comparing the two types of SL measures, we expected a stronger correlation between language abilities and the processing-based SL measures than the reflection-based measures as the latter might introduce additional variance due to the need to consciously reflect on the learned regularities (Christiansen, 2019).

**Predictions regarding language test category interacting with SL task properties.**

8. Although we had no specific predictions about differences in the size of correlations given specific language test categories, we did predict an interaction with SL paradigm. Larger positive correlations between the SL test and the measure of language ability were expected when their proposed underlying computations are more closely matched (Siegelman, Bogaerts, Christiansen, et al., 2017). More specifically, assuming similar computations underlying the learning of adjacent patterns and vocabulary acquisition we expected them to correlate more strongly than transitional probability learning and syntax. In contrast, non-adjacent regularity learning would theoretically be more closely related to syntax processing, so we predicted a stronger correlation between those.

**Predictions regarding sample properties interacting with SL task properties.**

9. Given that meta-cognitive reasoning poses a greater challenge for younger cohorts compared to adults and previous findings suggesting that reflection-based measures lead to smaller effect sizes in children (Isbilen & Christiansen, 2022), we anticipated an interaction between age and the type of SL measure: reflection-based measures were expected to have low predictive power for younger samples and higher predictive power for older samples.
Method

Literature Search

We conducted a comprehensive literature search using the PubMed and Scopus
database. Both databases were searched using the query ‘language’AND ‘statistical’OR
‘distributional’AND ‘learning’ (see Isbilen & Christiansen, 2022). On Scopus, publication
dates were restricted to ranging from January 1996 to March 2023. To narrow down the
results, we limited the scope to papers belonging to the subject areas of social sciences, arts
and humanities, psychology, neuroscience, computer science or multidisciplinary studies. In
addition to the structured literature search, we screened the references of recent theoretical
reviews (Bogaerts et al., 2021; Siegelman, 2020) for relevant studies. This resulted in a total
of 6940 papers of which 5202 remained after duplicate removal.

Study Selection

Figure 2 shows a diagram of the study selection procedure according to the Preferred
Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines (Moher et
al., 2009). Two independent researchers screened the titles of the 5202 studies to exclude
papers containing the search terms but that were not related to the current topic. Additionally,
we excluded reviews, meta-analyses, computational modelling papers, computer science
papers and other studies lacking human behavioural data. Next, the remaining 592 papers'
abstracts were screened<fnref n="1" />. We only included papers that correlated individual differences in SL
ability to an independent measure of language skills. Studies exclusively reporting a neural
measure of SL (e.g., Liu et al., 2021) or using participants with acquired brain dysfunction
(i.e., post-stroke aphasia; Schevenels et al., 2022) or hearing loss (Hamza et al., 2020;

<footnote n="1">¹ Two researchers screened the study list separately. In case of disagreement on the inclusion decision, the outcome was decided during a meeting.</footnote>
Monroy et al., 2022) were omitted from further analysis. We also chose to omit studies that did not use an independent test of SL and language abilities (e.g., Brice et al., 2021; Siegelman, Rueckl, et al., 2020). While the initial submission of this meta-analysis was under review, two related meta-analyses were published (Oliveira et al., 2023; Ren et al., 2023). We chose to merge the studies included in those meta-analyses that were missing in our search results to ensure maximal coverage of the literature. Using the data of Ren et al. (2023) meant including another 14 articles. The study by Oliveira et al. (2023) had 25 non-overlapping studies. Combined, this approach resulted in 97 papers that were included in the meta-analysis.

<caption>**Figure 2**
PRISMA Flowchart</caption>

<figure><img src="image_2.png" /></figure>

## Data Extraction

The effect size of interest was the correlation coefficient between SL ability and the performance on a language test. These were extracted manually from the selected studies and missing data were obtained by contacting the corresponding authors. In total, the 97 papers
reported 710 effect sizes relevant to the current meta-analysis.<fnref n="2" /> In studies where a lower score on either the SL task or language test reflected better performance, the correlation sign was flipped. In case a study reported a partial correlation, we included the partial correlation on the prerequisite that it controlled for a variable not directly related to SL or language ability (e.g., non-verbal IQ). Some studies reported only partial correlations controlling for age (Arciuli & Simpson, 2012; Hu et al., 2023), which we included as well.

The standard error (SE) of each reported correlation coefficient was calculated using the following formula: $SE(r) = \sqrt{(1 - r^2)/(N - 2)}$. Since a correlation is bounded between [-1,1] the sampling distribution might be skewed for highly correlated variables. By applying Fisher's Z transformation (Fisher, 1915), the variances of the correlation coefficients are more stable, and the distribution becomes more symmetric. Fisher's Z transformation entails taking the inverse hyperbolic tangent of the correlation coefficients: $z = \operatorname{arctanh}(r)$ which is equivalent to $z = \frac{1}{2} \ln(\frac{1+r}{1-r})$. The standard errors of the Fisher's Z scores were calculated as $SE(z) = \frac{1}{\sqrt{N-3}}$, which is independent of the correlation coefficient. We performed all analyses using Fisher's Z scores.

For each study, we coded a range of moderator values belonging to one of three categories: characteristics of the sample, information on the SL task, and specifications of the language assessment. The sample characteristics included the average age of the participants (in case the SL test and the language test were administered at different ages we recorded the age at the final test occasion), and the type of sample (i.e., typically developing, clinical or mixed). For the SL task that was used during the experiments, we recorded the SL paradigm (i.e., EPL, AGL, sequence learning, or mapping task), stimuli modality (i.e., auditory, visual,

<footnote n="2">² Note that two studies used the same sample (i.e., Lammertink, Boersma, Rispens, et al., 2020; Lammertink, Boersma, Wijnen, et al., 2020), these studies were therefore coded as a single study in the analyses.</footnote>
or crossmodal), stimuli domain (i.e., linguistic, non-linguistic), pattern range (i.e., adjacent, non-adjacent), and the SL measure (i.e., reflection-based, processing-based, or combination of both). Lastly, we recorded the specific language test that was administered (e.g., Peabody picture vocabulary test, Clinical Evaluation of Language Fundamentals) as well as what language aspect it measured (i.e., vocabulary, phonology, literacy, or comprehension). An overview of all the included studies and their characteristics can be found in the supplementary materials (see Table S1).

## Statistical analyses

The meta-analysis was conducted using R statistical software (v4.2.2; R Core Team, 2021) following the guidelines by Harrer et al. (2021) and using the ‘metafor’ package (Viechtbauer, 2010). We fitted a multilevel random effects meta-analysis model using the restricted maximum likelihood method to estimate the residual heterogeneity variance (τ²). Our data followed a nested structure (i.e., multiple effect sizes nested within one study) with two grouping variables (effect size and study), resulting in a three-level model. Since the individual effect sizes are nested within studies the random effects are specified as ‘~ 1 | study/individual effect size’. The fit of the three-level model was compared to that of simpler models using a likelihood ratio test. To account for the dependencies in the data (i.e., correlated sampling errors of effect sizes based on the same sample), we used robust variance estimation (RVE; ‘ClubSandwich’ package; Pustejovsky, 2023). We assumed a constant sampling correlation of .80 and conducted several sensitivity analyses at varying correlation coefficients (ρ = .0; .50; .80; 1). Additionally, for the calculation of confidence intervals and hypothesis tests, we used the bias-reduced linearization variance estimator (i.e., CR2; Bell & McCaffrey, 2002; Pustejovsky & Tipton, 2018).
Using separate mixed-effects meta-regression models, we estimated the effect of each
moderator on the correlation between SL and language. All contrasts were specified using
treatment coding with the reference level chosen based on our predictions (see Table II).
Continuous predictors were scaled and centered. Effects of moderators were tested using
small sample adjusted z-tests. Following the analyses, Fisher's Z estimates were converted
back to Pearson's r for the reporting of estimates, standard errors, and confidence intervals.

To get an indication of potential publication bias (i.e., a preference for publishing
studies with positive and significant results), we used a combination of methods. First, we
tested for funnel plot asymmetry using Egger's regression test (Egger et al., 1997). Second,
potentially missing effects were estimated using the trim and fill method (Duval & Tweedie,
2000). Lastly, we used the rank test examining the correlation of observed effect sizes and
corresponding sampling variances (Begg & Mazumdar, 1994). All data and analysis scripts
are available on OSF
(https://osf.io/w4dcy/?view_only=d5960ef9dd4747a7a7afef02d4fec735).

## Results

### Overall Correlation Between Statistical Learning and Language

First, we examined the overall mean effect size across studies (97 papers, 710 effect
sizes) weighted for the precision of the effect size measurement (i.e., the standard error). We
found that the average effect size based on the three-level meta-analytic model was small yet
significant (N = 710, estimated average effect size = .16, t = 8.16, p < .001, 95% CI [.12;
.20]). Note that this concerns Fisher's Z scores, when backtransformed to a Pearson's
correlation coefficient the estimate remains the same (r = .16). The estimated variance
components for the different levels were τ<sup>2</sup><sub>level2</sub> = 0.04 and τ<sup>2</sup><sub>level3</sub> = 0.005, meaning that
63.41% (I<sup>2</sup><sub>level2</sub>) of the total variation can be attributed to within-study heterogeneity and
8.00% ($I^2_{level3}$) of the total variation to between-study heterogeneity. We found that the three-level model did not provide a significantly better model fit compared to the model with two levels ($\chi^2_1 = 2.64; p = .10$). Yet as the three-level model does represent the data-generating process better, we opted to use this model for the moderator analyses (Harrer et al., 2021). Furthermore, the sensitivity analysis showed near-identical results when varying the assumed correlation of the effect sizes ($\rho = .0; .50; .80; 1$), $r = .17; .17; .16; .16$; respectively.

## Moderators of the Correlation Between Statistical Learning and Language

Next, we fitted a multilevel random effects meta-regression model with each moderator separately and using RVE. Table II provides an overview of the results. The full forest plot with all 710 effect sizes can be found in the supplemental materials.

### Results Regarding Sample Characteristics

Age was not a significant moderator of the correlation between SL performance and language ability ($F_{1,708} = 0.05; p = 0.82; \beta = .004, SE = .02, z = 0.23, p = .82, 95% CI [-.03; .04]$). When defining age as a categorical variable (i.e., infants (< 6y), children (6y-17y) and adults (≥ 18y)) the effect was also not significant ($F_{2,93} = 1.16; p = .32$). Figure 3 illustrates the correlations observed for different age categories. In all three age categories the observed correlation was significantly different from 0 (infants: $r = .12, SE = .24, t(83) = 4.65, p < 0.001$; children: $r = .08, SE = .27, t(442) = 6.27, p < 0.001$; adults: $r = .15, SE = .23, t(182) = 8.79, p < 0.001$).

Sample type did not significantly impact the observed correlation either ($F_{2,707} = 20.24; p = 0.13$). With typically developing samples as reference, the following regression coefficients were obtained: Clinical: $\beta = -.04, SE = .04, z = -1.01, p = .31, 95% CI [-.12; .04]$; Mixed: $\beta = .05, SE = .09, z = 0.58, p = .57, 95% CI [-.12; .21]$).
<caption>**Figure 3**</caption>

*Effect of Age*

<figure><img src="image_3.png" /></figure>

*Note:* This figure illustrates the correlation distribution across various age categories. Boxplots display the median, first quartile, and third quartile of correlations. The mean correlation for each group is as follows: Infants (.12), Children (.08), and Adults (.15). Infants are defined as those younger than 6 years old, Children are aged 6-17, and Adults include participants 18 years old or older.

**Results Regarding SL Task Features**

Paradigm had a significant effect on the observed correlation (F<sub>3,706</sub> = 5.44; *p* = .001).

Performance on an AGL and mapping task showed a significantly stronger correlation with language abilities than sequence learning (AGL: β: .15, *SE* = .05, *z* = 2.84, *p* = .005, 95% CI [.05, .24]; Mapping task: β: .22, *SE* = .08, *z* = 2.83, *p* = .005, 95% CI [.07; .36]). EPL showed no difference to sequence learning (β: .03, *SE* = .03, *z* = 1.11, *p* = .27, 95% CI [-.02, .08]).

The effect of modality was also significant (F<sub>2,707</sub> = 6.12; *p* = .002). We found that crossmodal stimuli yielded significantly higher correlations with language abilities than strictly auditory stimuli (Crossmodal: *β* = .12, *SE* = .06, *z* = 2.13, *p* = .03, 95% CI [.01, .22])
and that the use of visual stimuli is associated with lower correlations compared to auditory stimuli (Visual: $\beta$ = -.06, *SE* = .03, *z* = -2.16, *p* = .03, 95% CI [-.11, -.01]).

The domain of the stimuli (i.e., linguistic/non-linguistic) was a significant moderator of the observed correlation with language as well, with non-linguistic stimuli yielding smaller correlations ($F_{1,708}$ = 6.39, *p* = .01) (Non-linguistic: $\beta$ = -.08, *SE* = .03, *z* = -2.86, *p* = .004, 95% CI [-.13, -.02]).

Finally, the effect of the type of SL test was not significant ($F_{2,93}$ = 0.96; *p* = 0.38).

Processing-based measures: $\beta$ = -.04, *SE* = .03, *z* = -1.25, *p* = .21, 95% CI [-.11, .02]). Combination of processing and reflection: $\beta$ = -.01, *SE* = .03, *z* = -0.38, *p* = .74, 95% CI [-0.08, 0.05].

## Results Regarding Language Test Category in Interaction with SL Task Properties

The likelihood ratio test of the interaction between SL paradigm and the type of language measure was not significant (log-likelihood = 8.91, *p* = .45). However, some combinations of SL paradigm and language test occurred very infrequently in the data (see Figure 4A). As a second approach to investigating the interaction between language test category and SL task properties, we limited the dataset to studies using SL tasks with either adjacent or non-adjacent patterns and vocabulary or syntax and comprehension as a measure of language ability. This filtering left us with 419 observations, and a minimum of 19 effect sizes per combination (see Figure 4B). Next, we fitted a model entering only pattern range (adjacent and non-adjacent) and language test category (vocabulary and syntax/comprehension) as predictors together and a model also including their interaction. This interaction was not significant (log-likelihood = 0.45, *p* = .50).
<caption>**Figure 4**</caption>

*Number of Effect Sizes per Combination of SL Task and Language Test Characteristic*

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

*Note:* A. Counts of the number of times a specific SL paradigm was combined with a certain language test category. B. Counts of the number of times a specific pattern range was combined with a certain language test category.
<table><caption>Table II</caption><caption>Summary of the model's results</caption><thead><tr><th>Moderator</th><th></th><th>Est.</th><th>SE</th><th>z</th><th>p</th><th>95% CI</th><th></th></tr></thead><tbody><tr><td>Overall Effect</td><td></td><td>.16</td><td>.02</td><td>8.15</td><td>&lt;.001</td><td>[0.12; 0.20]</td><td>***</td></tr><tr><td>Age</td><td></td><td>.004</td><td>.02</td><td>.23</td><td>.82</td><td>[-0.03; 0.04]</td><td></td></tr><tr><td rowspan="3">Sample Type</td><td>TD (intercept)</td><td>.16</td><td>.02</td><td>7.87</td><td>&lt;.001</td><td>[.12; .20]</td><td></td></tr><tr><td>Clinical</td><td>-.04</td><td>.04</td><td>-1.01</td><td>.31</td><td>[-.12; .04]</td><td></td></tr><tr><td>Mixed</td><td>.05</td><td>.09</td><td>.58</td><td>.57</td><td>[-.12; .21]</td><td></td></tr><tr><td rowspan="5">Paradigm</td><td>Sequence learning (intercept)</td><td>.14</td><td>.02</td><td>5.84</td><td>&lt;.001</td><td>[.10; .19]</td><td></td></tr><tr><td>EPL</td><td>.03</td><td>.03</td><td>1.11</td><td>.27</td><td>[-.02; .08]</td><td></td></tr><tr><td>AGL</td><td>.15</td><td>.05</td><td>2.84</td><td>&lt;0.01</td><td>[.05; .24]</td><td>**</td></tr><tr><td>Mapping Task</td><td>.22</td><td>.08</td><td>2.83</td><td>&lt;0.01</td><td>[.07; .36]</td><td>**</td></tr><tr><td>Auditory (intercept)</td><td>.19</td><td>.03</td><td>6.37</td><td>&lt;.001</td><td>[.13; .24]</td><td></td></tr><tr><td rowspan="3">Modality</td><td>Visual</td><td>-.06</td><td>.03</td><td>-2.16</td><td>.03</td><td>[-.11; -.01]</td><td>*</td></tr><tr><td>Crossmodal</td><td>.12</td><td>.06</td><td>2.13</td><td>.03</td><td>[.01; .22]</td><td>*</td></tr><tr><td>Linguistic (intercept)</td><td>.21</td><td>.03</td><td>6.86</td><td>&lt;.001</td><td>[.15; .27]</td><td></td></tr><tr><td rowspan="3">Domain</td><td>Non-Linguistic</td><td>-.08</td><td>.03</td><td>-2.86</td><td>.004</td><td>[-.13; -.02]</td><td>**</td></tr><tr><td>Reflection (intercept)</td><td>.18</td><td>.03</td><td>5.75</td><td>&lt;.001</td><td>[.12; .24]</td><td></td></tr><tr><td>Processing</td><td>-.04</td><td>.03</td><td>-1.25</td><td>.21</td><td>[-.11; .02]</td><td></td></tr><tr><td rowspan="2">Test Measure</td><td>Combination</td><td>-0.1</td><td>.03</td><td>-0.38</td><td>.74</td><td>[-.08; .05]</td><td></td></tr><tr><td>Paradigm – Language Test</td><td></td><td></td><td>8.91</td><td>.45</td><td></td><td></td></tr><tr><td>Interaction</td><td>Age – Test Measure</td><td></td><td></td><td>2.24</td><td>.33</td><td></td><td></td></tr></tbody></table>

Note: Results are Pearson's correlation coefficients. All continuous predictors are scaled. All factors are treatment coded. The reference levels for the different factors are as follows: Sample Type = Typically developing; Paradigm = EPL; Modality = Auditory; Domain = Linguistic; SL Test = Reflection based; Language Test Category = Vocabulary. Abbreviations: TD = typically developing; AGL = artificial grammar learning, EPL = embedded pattern learning, LRT = likelihood ratio test. Significance: p < 0.1 ; * p < 0.05 ; ** p < 0.01 ; *** p < 0.001

## Results Regarding Sample Properties in Interaction with SL Task Properties

The interaction between the average age of the participants and the type of SL test was also not significant, as shown by the likelihood ratio test comparing the model with and without the interaction (log-likelihood = 2.24, * = .33).

## Publication Bias
Figure 5 shows a funnel plot of all the studies present in this meta-analysis. Using Egger's regression test, we found no evidence of significant asymmetry in the funnel plot (intercept = 0.07, z = 1.52, *p* = .12, 95% CI [0.02, 0.12]). A positive intercept indicates that the plot is more biased toward the right side. These results were corroborated by the trim-and-fill method as the number of missing studies on the left side was estimated at 0 (SE = 1.41, *p* = .5). Finally, the result of the rank correlation test (Kendall's τ = 0.03, *p* = .33) was also in line with the conclusion that the present set of studies shows no signs of publication bias.

<caption>Figure 5</caption>

Funnel Plot

<figure><img src="image_5.png" /></figure>

*Note:* Funnel plot showing the relationship between the observed effect sizes and the standard error. The contours denote statistical significance to aid in the plot's interpretation (Palmer et al., 2008).

Discussion
SL is highly variable across the population yet stable at the individual level (Siegelman, Bogaerts, Christiansen, et al., 2017; Siegelman, Bogaerts, Kronenfeld, et al., 2018). Considering that SL is a componential ability and that various tasks capture different facets of SL (Arciuli, 2017; Bogaerts et al., 2021; Siegelman, Bogaerts, Christiansen, et al., 2017), analyzing correlational data has the potential to clarify the intricate relationship between SL and language. Here, we used meta-regression to quantify the available evidence of the association between individual differences on independent tasks of SL performance and language abilities. We calculated the overall correlation across studies, and evaluated what factors affect the observed relation. Three categories of moderators were considered, namely the characteristics of the sample, the features of the SL task and the type of language test. Using the combined data of 97 papers, good for 710 effect sizes, we tested several preregistered predictions.

Small Significant Overall Correlation Between Statistical Learning and Language

In line with our expectations (prediction 1) and with the results of two other recent
meta-analysis (Olivera et al., 2023; Ren et al., 2023)<fnref n="3" />, we found that the estimated
relationship of SL abilities and language skill is small (r = .16) yet significant. This result
provides support for the hypothesis that SL and language are, to some degree, related. At first
glance, the size of this overall correlation might seem underwhelming, and it could indeed
support the conclusion that the two constructs are only weakly related. At the same time, this
correlation needs to be evaluated with the current shortcomings of SL research focusing on

<footnote n="3">³ This estimate surpasses the overall correlation observed by Oliveira et al. (2023), where procedural learning as measured by serial reaction time task performance, showed a correlation of r = 0.06 with language measures. At the same time, it is lower than the estimation reported by Ren et al. (2023), who conducted a recent meta-analysis encompassing approximately half the number of articles as our current analysis, revealing a correlation of r = 0.24 between statistical learning and language outcomes.</footnote>
individual differences in mind. We outline three issues which potentially affected the size of
the observed correlations. First, while there are exceptions (Kidd, 2012; Misyak et al., 2010a,
2010b), the bulk of studies provide few theoretical arguments for the exact type of SL task
and test they use. Perhaps this is a symptom of the lingering view of SL as a unitary concept
which led to an implicit assumption that all SL tasks are interchangeable (see Siegelman,
Bogaerts, Christiansen, et al., 2017 for a discussion). It has been argued that a more fine-
grained approach to SL tasks might help in offering precise theoretical accounts while also
providing stronger evidence for the link between SL and language abilities as well as
language difficulties by considering their shared computations (Bogaerts et al., 2020).

Second, as illustrated in Figure 4, most studies still rely on either a task with simple duplet or
triplet patterns (i.e., EPL), usually with transitional probabilities of one (meaning zero
exceptions in the pattern), or the serial reaction time task (i.e., sequence learning) to probe
one's SL skills. These tasks of SL do not scale up to the challenges presented by a real-world
linguistic environment and capture only a small chunk of SL variance that might explain
linguistic skills (Frost et al., 2019; Siegelman, 2020). Lastly, there is the issue of reliability.

While most of the language measures have acceptable psychometric qualities (i.e., test-retest
reliability of approximately .8), most SL measures are notoriously unreliable at the individual
level (Arnon, 2020; Siegelman & Frost, 2015; West et al., 2018), attenuating the correlation
that can be found (Spearman, 1904). To illustrate the impact of task reliability, let us assume
that the reliability of an SL task lies around .5 for adults (based on Arnon, 2020; Siegelman &
Frost, 2015). We can estimate the disattenuated correlation to be *r* = .25 (Spearman, 1904).

When considering the reliability across adults *and* children (approximately .3; taking the
average of Arnon, 2020; Siegelman & Frost, 2015; West et al., 2018), the disattenuated
correlation would be even higher, *r* = .33. These correlations corrected for imperfect
reliability are of course only a rough estimation, but it highlights the need for more studies
investigating task reliability across paradigms and age groups. Note that our quantification of
the overall effect also speaks to the issue of statistical power as well. With current reliability
levels, the overall effect was estimated at .16 (roughly *d* = .3), hence a study would need
more than 195 participants to show an effect with a power of 80% (Brysbaert, 2019). This
number is substantially larger than the average sample size used by the studies covered here,
which was 49 participants.

The methodological challenges of low task reliability and underpowered studies also
tie into publication bias. Together, they raise the possibility that some positive effects are due
to random chance. Yet the studies covered in this meta-analysis showed no indications of
publication bias. Some methods, such as the trim-and-fill method, are not well equipped to
deal with high between-study heterogeneity (which was the case in the current collection of
studies; Peters et al., 2007). However, two different tests (Egger's regression test and
Kendall's rank correlation) also yielded no evidence of publication bias.

Towards a better Understanding of Between-Study Differences

Next, we turn to the question of what explains between-study differences in the
observed correlations. While there appears to be an overall positive correlation between SL
and language across the lifespan, our results indicate that its strength is not significantly
affected by the age of the participants. This finding is in contrast with the results of Ren et al.
(2023), who found age to be the only significant moderator of the association between SL and
language. Note that it made no difference whether we tested age as a continuous predictor, or
as a categorical variable similar to the approach by Ren et al. (2023). More work on the
developmental trajectory of different aspects of SL in relation to language is necessary. Yet
equally important is additional work on reliable measures of SL in both adults and children.
Additionally, sample type was not a significant predictor (prediction 3). This is surprising
given that samples more heterogenous in its language and/or SL abilities were predicted to
show a larger correlation between both measures. In other words, we did not find evidence
that the limited correlation strength is attributable to range restriction in unselected samples.

Importantly, we did find that variation across studies was accounted for by different
SL task features indicating that the choices made when operationalizing SL shape the relation
observed with language abilities. First, the effect of SL paradigm was significant. We found a
significant positive effect of using a mapping task or AGL as a paradigm (compared to
sequence learning). This is in line with our prediction that paradigms that are more closely
aligned with the cognitive demands of language learning/processing would show larger
effects (prediction 4), except that EPL was not significantly different from sequence learning.
The explanation of what drives the different outcomes for these paradigms is not
straightforward as many of them, despite their distinctions, also exhibit partial overlap in the
mechanisms they require and the knowledge they install. For example, EPL mimics the
segmentation problem which language learners face, but previous experimental work showed
that extracting word forms during EPL facilitates associating them with novel objects as in
the mapping task (Hay et al., 2011). Each of these paradigms can be used with all types of
stimuli, varying the modality, domain, and the type of test probing one's knowledge of the
patterns. A priori, we predicted an effect of stimulus modality (prediction 5), yet the type of
effect was open for discussion (Shufaniya & Arnon, 2018; Qi et al., 2019). Our results
showed that use of auditory stimuli was associated with stronger correlations than visual
stimuli. Crossmodal stimuli, however, showed an even stronger correlation. It is possible that
the use of crossmodal stimuli shows a greater overlap with the mechanisms invoked during
the exercise of our language skills. Take the case of reading, where visual symbols are
rapidly converted into sounds and linked to concepts stored in our memory. This process taps
into letter-sound as well as form-to-meaning regularities (Castles et al., 2018). This might be
captured better by using crossmodal stimuli to test SL ability.

As predicted, we also found that linguistic stimuli tend to correlate more strongly with
language abilities (prediction 6). Linguistic SL tasks rely to a larger degree on the same
mechanisms as those employed in language. Another related aspect that needs to be
considered with linguistic SL tasks is the extent to which the tested regularities overlap with
the regularities as found in the language(s) known by the participant. Some people might be
very well attuned to the statistical regularities in their native language, which might help
them learn new patterns that resemble this prior knowledge but lead them to fail on a SL test
using artificial patterns that do not conform to these earlier learned language regularities
(Commissaire & Besse, 2019; Siegelman, Bogaerts, Elazar, et al., 2018; Elazar et al., 2022).
An exciting avenue is thus to probe for one's SL ability using language itself thereby
bypassing the need for artificial stimuli (Brice et al., 2021; Siegelman, Rueckl, et al., 2020).

In sum, the individual moderator analyses highlight that different dimensions of SL
tasks impact the size of the observed correlations. This aligns with the notion that it might be
overly simplistic to consider SL tasks as uniformly tapping into an individual's SL capacity
(Bogaerts et al., 2022). Variance in a skill as complex as language, with a vast array of
regularities at different levels and in different modalities can likely only be captured with
tasks ambitious enough to contend with this complexity. One possible approach raised as a
future direction in previous work is developing SL test batteries and composite scores
probing distinct dimensions of SL (Siegelman, Bogaerts & Frost, 2017).

Based on the hypothesized componentiality of both SL and language abilities, we
expected the language test category to interact with SL task properties such as the paradigm
used (prediction 8). However, this interaction was not significant. Also further exploring this
effect by limiting the language test to two ‘extreme’ cases of vocabulary (supposedly
requiring the extraction of short-range patterns) and syntax/comprehension (requiring the
assimilation of patterns at a larger scale), we did not find evidence in support of the type of
statistical pattern being an important component within a componential SL construct. Finally,
the predictions that processing-based tests would be superior in terms of finding a correlation
with language outcomes (prediction 7), potentially even more so for younger samples
(interaction between age and SL test, prediction 9), were not confirmed. Either way, it
remains important to use appropriate measures for the developmental stage of the population
of interest as this ties into the issue of task reliability. Reflection-based SL requires conscious
reasoning about what is learned (Christiansen, 2019; Isbilen et al., 2017). Especially in
children, individual differences in introspective abilities may introduce variability that is
unrelated to SL per se causing these measures to be less reliable in child populations (Arnon,
2020; West et al., 2018).

Limitations and Future Avenues

The meta-analysis revealed interesting results on the relation between SL and
language yet there are some limitations. Even though this meta-analysis is substantially larger
than many others looking at SL, the data presented here still represents a sample of the
literature and aggregates over only 710 effect sizes. In addition, while coding the individual
studies, we noticed large between-studies differences in the way theoretical constructs are
defined and operationalized. A striking example of this is that some studies take fast mapping
purely as a task probing SL ability (Ellis et al., 2021; Gerbrand et al., 2022; Haebig et al.,
2017; Lany, 2014; Venker, 2019) while others also use fast mapping to quantify an aspect of
language ability (Vlach & DeBrock, 2017; Yim et al., 2021). This might be confusing at first,
yet what could help is to look at SL and language as two endpoints on a continuum of task
contents. Considering the faded boundaries between both constructs, studies taking the
individual differences approach should pay extra attention to the components of SL and/or
language they target and motivate their task selection accordingly. An alternative approach
was taken by two recent studies on reading. Instead of using an independent artificial task to
estimate SL abilities, their approach identified individual differences in children's
(Siegelman, Rueckl, et al., 2020) and second-language learners' (Brice et al., 2021) reliance
on statistical patterns such as print-speech regularities as reflected in their actual reading
behavior. What is notable is that they observe considerably higher correlations compared to
typical individual differences studies. This is a valuable approach as it avoids the need to use
artificially constructed stimuli that need to be controlled on a variety of aspects. Furthermore,
it makes use of the multiplicity of patterns already present in a language and our unique
ability to implicitly (and explicitly) attune to those patterns and use them in our interactions
with language (Treiman & Kessler, 2022).

Finally, we only considered one potential set of predictors out of many. The data used
in this study is completely open and can be leveraged by others to explore theoretical
questions and make methodological decisions based on existing evidence. Our intention is for
the present open database to be the start of an ongoing endeavor in the sense the database can
be updated with new studies and elaborated upon (e.g., by coding new study variables) by the
research community.

Acknowledgements

We thank Gershon Ben-Shakhar and Dries Debeer for their advice on the data analysis. This
project (G0F3121N) has received funding within the framework of the Odysseus program
from the Research Foundation Flanders (FWO).
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