MWE and their statistical regularities

Language speakers accumulate linguistic constructions of varying granularity that pair form with meaning and function, such as words, MWEs, and sentences (Goldberg, Reference Goldberg1995). MWEs are recurrent combinations of words that co-occur more often than would be expected by chance (Siyanova-Chanturia & Martinez, Reference Siyanova-Chanturia and Martinez2015; Yi & Zhong, Reference Yi and Zhong2024).Footnote ¹ They account for nearly half of the occurrences in L1 use (Siyanova-Chanturia, Reference Siyanova-Chanturia2015) and show a processing advantage compared to novel word combinations (Siyanova-Chanturia et al., Reference Siyanova-Chanturia, Conklin and Van Heuven2011).

MWE processing is closely tied to chunking processes driven by statistical learning mechanisms (Christiansen, Reference Christiansen2019). MWEs are defined by statistical properties rather than specific syntactic or semantic features, making them a broad category that includes collocations (Wolter & Yamashita, Reference Wolter and Yamashita2018), idioms (Carrol & Conklin, Reference Carrol and Conklin2014), binomials (Morgan & Levy, Reference Morgan and Levy2016; Siyanova-Chanturia et al., Reference Siyanova-Chanturia, Conklin and Van Heuven2011), and lexical bundles (Tremblay et al., Reference Tremblay, Derwing, Libben and Westbury2011). Among these, binomials have received less attention. Binomials are defined as recurrent combinations of words that occur more often than chance, joined by “and” or “or,” and exhibit a preferred word order (Siyanova-Chanturia et al., Reference Siyanova-Chanturia, Conklin and Van Heuven2011). Their uniform structure and semantic simplicity (with opaque binomials excluded from this study) make them comparable across items, serving in this study as both the focus and a window into statistical metacognition across the broad class of MWEs.

MWEs, including binomials, exhibit statistical regularities that reflect the distributional patterns of linguistic units across usage contexts, such as frequency, association strength, and dispersion. Frequency reflects the likelihood of encountering linguistic units. It drives automatized processing (Gries & Ellis, Reference Gries and Ellis2015) and is central to language acquisition (Goldberg, Reference Goldberg1995). Frequency effects are among the most robust findings in psycholinguistics (e.g., Öksüz et al., Reference Öksüz, Brezina and Rebuschat2021; Siyanova-Chanturia et al., Reference Siyanova-Chanturia, Conklin and Van Heuven2011). Nevertheless, frequency alone cannot capture the complexity of MWE statistical distribution. Dispersion instead captures how widely a linguistic unit is distributed across macro-level usage contexts (e.g., genres, registers, textual sections) in a language (Gries, Reference Gries2024; Gries & Ellis, Reference Gries and Ellis2015). Contextual learning theory (Martin, Reference Martin2014) suggests that language acquisition is shaped not only by repeated exposure to linguistic units but also involves acquiring varied macro-level communicative contexts. MWEs with identical frequency may differ in dispersion, with some context-specific and others broadly distributed. Key dispersion metrics include Juilland’s D, Carroll’s D2, and Kullback–Leibler Divergence (KLD, Gries, Reference Gries2024). Beyond frequency and dispersion, association strength quantifies the statistical relationship between MWE components (Yi et al., Reference Yi, Man and Maie2023). Language speakers are able to track such patterns, as described by associative learning theory (Gries & Ellis, Reference Gries and Ellis2015). Pointwise mutual information (PMI), log Dice, and t-score capture bidirectional associations but lack directionality (Öksüz et al., Reference Öksüz, Brezina and Rebuschat2021; Yi, 2018). Unidirectional measures—such as forward/backward transition probabilities, delta Ps, and KLD—capture directional dependencies (Gries & Ellis, Reference Gries and Ellis2015).

Statistical learning mechanism and statistical metacognition

Language speakers possess robust, largely implicit statistical learning mechanisms without the involvement of explicit awareness for encoding distributional patterns (Christiansen, Reference Christiansen2019). Language speakers have shown implicit sensitivity to word frequency (Öksüz et al., Reference Öksüz, Brezina and Rebuschat2021), whereas evidence for dispersion effects is mixed: Gries (Reference Gries2024) found dispersion more predictive of reaction times than frequency, whereas Baayen et al. (Reference Baayen, Milin and Ramscar2016) reported the opposite. Frequency effects also extend to MWEs, as evidenced in the processing of binomials (Conklin & Carrol, Reference Conklin and Carrol2021; Siyanova-Chanturia et al., Reference Siyanova-Chanturia, Conklin and Van Heuven2011; Sonbul et al., Reference Sonbul, El-Dakhs, Conklin and Carrol2023), collocations (Öksüz et al., Reference Öksüz, Brezina and Rebuschat2021), and lexical bundles (Tremblay et al., Reference Tremblay, Derwing, Libben and Westbury2011). For instance, Siyanova-Chanturia et al. (Reference Siyanova-Chanturia, Conklin and Van Heuven2011) and Morgan and Levy (Reference Morgan and Levy2016) showed that both L1 and L2 speakers read frequent conventional binomials more fluently than reversed ones. Conklin and Carroll (Reference Conklin and Carrol2021) found novel binomials gain processing advantages after limited exposure in L1 speakers, and Suhad et al. (2023) showed similar effects for L2 learners. Recent studies also indicated that association strength, using metrics like PMI (Yi et al., Reference Yi, Lu and Ma2017) and log Dice (Öksüz et al., Reference Öksüz, Brezina and Rebuschat2021), moderated MWE processing.

Although statistical learning is primarily implicit, language speakers also develop a form of statistical metacognition—the explicit, conscious, and reflective evaluation of statistical regularities likely acquired intuitively (Siyanova-Chanturia & Spina, Reference Siyanova-Chanturia and Spina2015; Tryk, Reference Tryk1968; Yi et al., Reference Yi, Man and Maie2023). As suggested by implicit and explicit learning theory (Ellis, Reference Ellis2009), language learning involves both implicit automatized processes that operate without conscious awareness and explicit effortful processes that support metalinguistic reflection (Ellis, Reference Ellis2009). In this study, participants were engaged in explicit rating tasks that required them to consciously evaluate the statistical properties of binomials, in contrast to real-time language processing that typically draws on implicit routines (see Yi et al., Reference Yi, Man and Maie2023, for a review). Such offline, reflective rating tasks are cognitively demanding and may elicit conscious reasoning over intuitively acquired impressions (Ellis, Reference Ellis2009). This contrasts with the real-time, automatic processing of statistical regularities without the involvement of metalinguistic knowledge (Siyanova-Chanturia & Schmitt, Reference Siyanova-Chanturia and Schmitt2008; Siyanova-Chanturia & Spina, Reference Siyanova-Chanturia and Spina2015).

Three aspects of statistical metacognition

Statistical metacognition can be evaluated in terms of speaker-to-corpus consistency, sensitivity, and other contributing factors. Speaker-to-corpus consistency is measured by the absolute standardized difference between language speakers’ judgments and the statistical properties of language. Smaller differences indicate greater speaker-to-corpus consistency and a more precise metalinguistic representation of statistical knowledge aligned with language. Sensitivity captures how strongly language speakers’ statistical judgments systematically respond to variations in the distributional patterns of linguistic units, reflecting the strength of the statistical learning mechanism. Other contributing factors include phrasal-level statistical regularities beyond the target type being rated (e.g., association strength when rating frequency), as well as word-level statistics (e.g., word frequency and dispersion) and word-form features (e.g., word length, orthographic and phonological neighborhood).

L1 speakers’ statistical metacognition of individual words has been examined, partially reflecting the three aspects of metacognition outlined above. Tryk (Reference Tryk1968) reported high correlations (>0.7) between L1 word frequency ratings and corpus counts. Schmitt and Dunham (Reference Schmitt and Dunham1999) used a relative estimation task where L1 speakers rated word frequency against a reference anchor, reporting generally good absolute frequency judgments of participants and moderate correlations with corpus data (~0.5). In contrast, MWE-level research remains limited. Siyanova-Chanturia and Schmitt (Reference Siyanova-Chanturia and Schmitt2008) found that L1 speakers could distinguish between high- and medium-frequency English collocations on a six-point scale. Later, Siyanova-Chanturia and Spina (Reference Siyanova-Chanturia and Spina2015) found similar results with Italian collocations rated on a four-point scale, with the clearest separation between highest- and very-low-frequency items. Beyond frequency, Yi et al. (Reference Yi, Man and Maie2023) found that L1 speakers correctly distinguished collocations across frequency and association strength bins about 40% of the time on a three-point scale, with better differentiation for higher-statistics items. Additionally, low-to-moderate correlations have been reported between L1 speakers’ frequency estimates and corpus data for Swedish three-word combinations (Backman, Reference Backman1978), Italian (Siyanova-Chanturia & Spina, Reference Siyanova-Chanturia and Spina2015), and English (Siyanova-Chanturia & Schmitt, Reference Siyanova-Chanturia and Schmitt2008; Yi et al., Reference Yi, Man and Maie2023) collocations.

Furthermore, metacognitive judgments about one type of statistical regularities (e.g., frequency) were found to be shaped by others (e.g., association strength), and vice versa (Yi et al., Reference Yi, Man and Maie2023). In addition, word-level statistics (e.g., word frequency) and word-form features (e.g., word length) may also shape phrasal statistical metacognition (Siyanova-Chanturia & Spina, Reference Siyanova-Chanturia and Spina2015), as proposed in the dual-route model (Carrol & Conklin, Reference Carrol and Conklin2014). For instance, word frequency and dispersion shape expectations about the distributional patterns (Gries & Ellis, Reference Gries and Ellis2015) and may serve as cues to phrasal probability. Word length and orthographical/phonological neighborhood—the number of orthographically/phonologically similar words differing by one letter/phoneme (Marian et al., Reference Marian, Bartolotti, Chabal and Shook2012)—reflect surface-level complexity and lexical competition. Larger neighborhoods potentially increase cognitive load in visual and auditory word recognition (Yates et al., Reference Yates2005). These word-level factors, while often overlooked in MWE studies, may influence statistical metacognition.

Differences in statistical metacognition among L1, advanced, and intermediate L2 speakers

L1 speakers and L2 learners—including advanced learners immersed in target-language environments and intermediate learners in foreign-language contexts—may differ in their statistical learning mechanisms, as reflected in empirical findings. Some studies reported stronger MWE frequency effects for L1 speakers (Siyanova-Chanturia et al., Reference Siyanova-Chanturia, Conklin and Van Heuven2011), others for L2 speakers (Yi et al., Reference Yi2018), and some reported no difference (Öksüz et al., Reference Öksüz, Brezina and Rebuschat2021) in online processing of MWEs. For metacognition, Schmitt and Dunham (Reference Schmitt and Dunham1999) found L2 speakers’ frequency ratings correlated more strongly with corpus data than L1 speakers, while others reported stronger rating-corpus correlations for medium-, high-, and very low-frequency collocations (Siyanova-Chanturia & Schmitt, Reference Siyanova-Chanturia and Schmitt2008; Siyanova-Chanturia & Spina, Reference Siyanova-Chanturia and Spina2015) and association strength (Yi et al., Reference Yi, Man and Maie2023) in L1 speakers.

Differences in statistical metacognition across L1 speakers, advanced L2 learners, and intermediate L2 learners can be explained by differences in acquisition modes (implicit vs. explicit), learning contexts, cognitive resources, developmental trajectories, and processing strategies. First, usage-based (Ellis & Wulff, Reference Ellis and Wulff2014) and explicit-implicit learning theories (Ellis, Reference Ellis2005, Reference Ellis2009) suggest L1 speakers acquire language implicitly through rich exposure, while intermediate L2 learners rely largely on explicit, rule-based classroom learning. Advanced L2 learners may benefit from a more effective combination of richer statistical knowledge acquired through natural exposure and enhanced metalinguistic reflection fostered by explicit instruction, probably leading to stronger statistical metacognition in rating tasks. Second, contextual learning theory (Martin, Reference Martin2014) emphasizes the importance of communicative contexts in language development. L1 speakers gain context-rich MWE input through early, varied natural exposure (Adolphs & Durow, Reference Adolphs and Durow2004). Advanced L2 learners in English-speaking environments, though less immersed than L1 speakers, receive more authentic input than intermediate learners, whose exposure is largely limited to constrained discourse (Batstone, Reference Batstone2002). Third, cognitive cost shapes processing strategies. Under the shallow-structure hypothesis (Clahsen & Felser, Reference Clahsen and Felser2006), intermediate L2 learners rely on surface-level cues (e.g., word length) due to higher demands, whereas advanced L2 learners and L1 speakers engage in deeper, usage-based processing with less effort. Fourth, developmental timing matters. According to the power law of practice (DeKeyser, Reference DeKeyser2020), early-stage learning yields greater marginal gains, as each input instance makes up a larger share of total language experience. As a result, L1 speakers—whose extensive language experience overshadows statistical variation—may show weaker metacognitive sensitivity to statistical regularities than advanced and intermediate L2 learners. Finally, the dual-route model (Carrol & Conklin, Reference Carrol and Conklin2014) suggests that L1 speakers can process MWEs more holistically, enhancing fluency and reducing cognitive load. Advanced L2 learners may also rely less on word-level processing, especially with extensive natural exposure to MWEs. In contrast, intermediate learners tend to use analytical strategies and focus on constituent words.

Together, these theoretical frameworks suggest that statistical metacognition differs across L1 speakers, advanced L2 learners, and intermediate L2 learners.

Participants

We recruited 94 participants via Prolific: 34 L1 English speakers (19 males), 30 advanced L2 learners (14 males), and 30 intermediate L2 learners (19 males), all aged 18–35 with a bachelor’s degree. Participants were paid $16/hour.

L1 speakers acquired English from birth. L2 speakers had a non-English L1, began learning English after age three, and received formal instruction. All L1 speakers and advanced L2 learners were residing in the U.S. during participation. To distinguish L2 proficiency levels, extended immersion in an English-speaking environment served as the primary criterion. Advanced L2 learners met the following criteria: (1) length of residence in English-speaking countries ≥8 years (required), plus at least two of: (2) ≥50 hours/week English use, (3) age of acquisition ≤10, and (4) self-rated proficiency ≥8 on a 9-point Likert scale across all language skills. Intermediate L2 learners had ≤ 2 years of residence (required) and met no more than two of the other criteria.

Mean ages were 28.5 (SD = 6.0) for L1 speakers, 28.9 (SD = 4.6) for advanced L2 learners, and 27.0 (SD = 4.1) for intermediate L2 learners. Advanced L2 learners began acquiring English at 7.3 years old (SD = 3.2), lived in the U.S. for 219.5 months (SD = 78.0), and used English 82.8 hours/week (SD = 35.5) over 212.9 months (SD = 212.6), through both formal instruction and daily use. Intermediate L2 learners began acquiring English at 8.2 years old (SD = 3.3), had little to no residence in English-speaking environments (M = 2.7 months, SD = 6.1), and used English 24.5 hours/week (SD = 23.0) over 75.7 months (SD = 79.0), primarily in classroom settings. On a 9-point self-assessment scale, advanced L2 learners rated higher in overall proficiency (8.5 vs. 7.2), reading (8.4 vs. 7.9), listening (8.6 vs. 7.7), speaking (8.5 vs. 6.6), and writing (8.1 vs. 6.9; see Table 1).

Table 1.

Demographic characteristics of L2 learners

Table 1. Long description

The table is organized into five columns. The first column lists the demographic or proficiency category. The next two columns provide the Mean and S D for Advanced L2 speakers. The final two columns provide the Mean and S D for Intermediate L2 speakers.

* Age: Advanced Mean 28.9, S D 4.6; Intermediate Mean 27.0, S D 4.1.

* Age of acquisition: Advanced Mean 7.3, S D 3.2; Intermediate Mean 8.2, S D 3.3.

* Length of residence: Advanced Mean 219.5, S D 78.0; Intermediate Mean 2.7, S D 6.1.

* Hours of usage per week: Advanced Mean 82.8, S D 35.5; Intermediate Mean 24.5, S D 23.0.

* Length of such rate (hours per week) using English: Advanced Mean 212.9, S D 212.6; Intermediate Mean 75.7, S D 79.0.

* Overall proficiency: Advanced Mean 8.5, S D 0.8; Intermediate Mean 7.2, S D 1.3.

* Speaking proficiency: Advanced Mean 8.5, S D 0.8; Intermediate Mean 6.6, S D 1.7.

* Listening proficiency: Advanced Mean 8.6, S D 0.7; Intermediate Mean 7.7, S D 1.2.

* Reading proficiency: Advanced Mean 8.4, S D 1.0; Intermediate Mean 7.9, S D 1.0.

* Writing proficiency: Advanced Mean 8.1, S D 1.1; Intermediate Mean 6.9, S D 1.4.

Note: We did not report English test scores, as only 14 L2 learners had taken an English test, with varied types (e.g., IELTS, TOEFL, SAT).

Stimuli

As previously noted, binomials are defined as “and”- or “or”-linked recurrent combinations of words that co-occur more often than chance and show a preferred order. We focused on transparent, noun-noun binomials joined by “and” for their structural regularity and semantic simplicity, which allow better control and measurement of statistical properties compared to structurally variable (e.g., lexical bundles) or opaque (e.g., idioms) MWEs. Using regular expressions, we extracted 28,967 “Noun + and + Noun” pairs from COCA (1990–2019; ~950M words, https://www.corpusdata.org), a widely used, thematically diverse corpus balanced across eight registers (e.g., spoken, fiction). COCA is considered a reliable proxy for large-scale, broad, balanced English usage patterns, and its pre-labeled text units enable precise dispersion computation. We retained binomials with above-chance co-occurrence (t-score > 2)Footnote ² and more than 10 occurrences, yielding 4,813 items. We then removed abbreviations (e.g., CEO), redundancies (e.g., hour and hour), proper nouns (e.g., Israeli and Arab), and semantically opaque items (e.g., spick and span). For binomials with both higher-frequency conventional (e.g., sun and moon) and lower-frequency reversed (e.g., moon and sun) forms, only conventional forms were kept. To ensure consistency, we retained only those with dominant singular forms, resulting in 2,054 binomials.

To enhance representativeness, we grouped all pre-labeled text units in COCA into 2,700 balanced sections. We then applied bootstrap resampling to extract 2,700 sections 1,000 times, generating 1,000 corpora matching the original COCA’s size. For each corpus, we calculated binomial frequency (per million words, log-transformed), forward and backward association strength, and dispersion, then averaged these values across all 1,000 corpora. KLD was used for association strength as it captures directionality and is less correlated with frequency than some of traditional association metrics (e.g., p_Fisher-Yates, z; Gries, Reference Gries2024). Table 2 shows the contingency table (Gries, Reference Gries2013). Equations (1) and (2) compute forward and backward association. Higher values indicate stronger associations. For the bigram “word1 word2,” forward association quantifies how word2’s distribution following word1 diverges from its overall distribution. Backward association does the same for word1 given word2.

Table 2.

Contingency table

Table 2. Long description

The table consists of four columns and four rows.

Header Row: The first column is blank. The second column is Co-occurring element X. The third column is Other elements (not X). The fourth column is Row totals.

Row 1: The first cell is Element E. The intersection with Element X is ‘a’. The intersection with Other elements is ‘b’. The row total is ‘a plus b’.

Row 2: The first cell is Other elements (not E). The intersection with Element X is ‘c’. The intersection with Other elements is ‘d’. The row total is ‘c plus d’.

Row 3: The first cell is Column totals. The total for Element X is ‘a plus c’. The total for Other elements is ‘b plus d’. The grand total in the final cell is ‘a plus b plus c plus d equals n’.

A note below the table defines the variables: cell ‘a’ represents E occurring with X; ‘b’ represents E occurring without X; ‘c’ represents X occurring without E; and ‘d’ represents neither E nor X occurring.

Note: Cell a = E occurs with X; b = E occurs without X; c = X occurs without E; d = neither E nor X occurs.

(1) $$ {D}_{KL}(p\left(X|E\right)\Big\Vert p(X)=\frac{a}{a+b}\times {\log}_2\frac{a\times n}{\left(a+b\right)\times \left(a+c\right)}+\frac{b}{a+b}{\times \log}_2\frac{b\times n}{\left(a+b\right)\times \left(b+d\right)} $$

(2) $$ {D}_{KL}(p\left(E|X\right)\Big\Vert p(E)=\frac{a}{a+c}\times {\log}_2\frac{a\times n}{\left(a+c\right)\times \left(a+b\right)}+\frac{c}{a+c}{\times \log}_2\frac{c\times n}{\left(a+c\right)\times \left(c+d\right)} $$

Dispersion was calculated using KLD across COCA’s 2,700 predefined sections, each representing a document varying in genre, topic, or register. This segmentation helps explore contextual learning theory (Martin, Reference Martin2014), which emphasizes the role of micro-level contextual exposure in language acquisition. KLD was chosen to ensure comparability with the KLD-based association strength. Equation (3) shows the dispersion of unit a, where i is the number of corpus parts, v is its frequency in each part, f is the total frequency, and s is the percentage of each part size.

(3) $$ KLD={\sum}_{i=1}^n\frac{v_i}{f}\times {\log}_2\left(\frac{v_i}{f}\times \frac{1}{s_i}\right) $$

To balance binomials across low and high bands of frequency, association strength, and dispersion, we split them into two bins per dimension, forming 16 groups (see Appendix 1 for the detailed binomial profiles within each statistical group). From each, 15–20 binomials were selected. Familiarity of each binomial was rated through an online questionnaire by two L1 speakers and five intermediate L2 learners (not in the main study) on a 5-point Likert scale (1 = completely unfamiliar, 5 = very familiar). Binomials were retained only if they received an average rating above 4 from L1 speakers and above 3 from L2 speakers. We also ensured no repeated words across binomials. In total, 300 binomials were selected as stimuli.

Procedure

We created questionnaires (see Appendix 2) on Qualtrics and distributed them via Prolific to collect ratings of statistical regularities. Each included demographic questions and four statistical rating blocks, with block order balanced via a Latin square design and binomial order randomized within each block. Detailed instructions and examples were provided for each block. For frequency, participants rated how often a binomial occurred in their language use (1 = a few times, 9 = many times). For dispersion, they rated the number of different usage contexts in which they encountered a binomial (1 = few contexts, 9 = many contexts). For forward association, they assessed how easy it was to predict the second word from the first (1 = very difficult, 9 = very easy). For backward association, they rated how easy it was to predict the first word from the second (1 = very difficult, 9 = very easy). Participants rated all 300 binomials on a 9-point slider (1-decimal precision) across four blocks of statistical regularities. The questionnaire had no time limit and took approximately 100 minutes to complete. We also collected word-level information of binomials. Word frequency (log-transformed per million) and dispersion were extracted from COCA. Word-form features (word length, orthographic and phonological neighborhood) came from CLEARPOND (Marian et al., Reference Marian, Bartolotti, Chabal and Shook2012, see Appendix 1 for rating data, binomial list, and all word-level information).

Data analyses

We collected data from 34 L1, 30 advanced L2, and 30 intermediate L2 speakers, yielding 28,200 data points. One L1 speaker was excluded for giving identical ratings to over 80% of items. For each binomial under each statistical measure, we excluded ratings beyond 2.5 standard deviations within each language speaker group (458 outliers from L1 speakers, 414 from advanced L2 learners, and 531 from intermediate L2 learners). We then standardized ratings within each participant and corpus data across binomials for each statistical measure. Other phrase- and word-level continuous predictors were also standardized.

To address RQ₁ (speaker-to-corpus consistency), we constructed a linear mixed-effects model with type of statistical regularities (frequency, dispersion, forward and backward association) and speaker group (L1, advanced L2, intermediate L2) as fixed effects. Both variables were treated as categorical and treatment-coded, with their interaction also included as predictors. The dependent variable was the absolute difference between standardized corpus values and standardized ratings (see Appendix 3 for model RQ₁-RQ₃ formulas).

To address RQ₂ (sensitivity) and RQ₃ (other contributing factors), four linear mixed-effects models were built, each with one type of statistical rating (frequency, dispersion, forward and backward association) as the dependent variable. For RQ₂, one type of statistical regularity from COCA, corresponding to the type of statistical rating used as the dependent variable, was employed as the independent variable. The COCA-based statistical regularities were divided into tertiles (low, medium, and high statistical bins) based on ranked values, with equal item counts per bin, to capture non-linear statistical effects (e.g., thresholds, plateaus) on metacognition observed in prior studies (Yi et al., Reference Yi, Man and Maie2023; Yi & Zhong, Reference Yi and Zhong2024). For RQ₃, additional standardized continuous variables, including other types of phrase-level statistical regularities that are distinct from the dependent variable, word-level statistics (e.g., word frequency and dispersion), and word-form features (e.g., word length, orthographic/phonological neighborhood), were included as independent variables.

Correlation coefficients for all variables were calculated. Four pairs showed high correlation: word1 (i.e., left conjoint) frequency and dispersion (r = 0.87), word2 (i.e., right conjoint) frequency and dispersion (r = 0.84), word1 orthographic and phonological neighborhoods (r = 0.93), and word2 orthographic and phonological neighborhoods (r = 0.93). Variance inflation factors for the four variable sets ranged from 4 to 7. To mitigate multicollinearity and model complexity, we applied group-wise Principal Component Analysis (PCA, Tomaschek et al., Reference Tomaschek, Hendrix and Baayen2018) to each variable set. PCA combined word1/word2 orthographic and phonological neighborhood into word1/word2 neighborhood (PCA₁ = 0.94 for word1, 0.92 for word2), reflecting lexical neighborhood diversity. Word1/word2 frequency and dispersion were merged into word1/word2 statistics (PCA₁ = 0.97 for both word1 and word2), capturing the likelihood of encountering a linguistic unit while correcting for frequency- or dispersion-only bias.

To compare statistical metacognition across speaker groups, language proficiency was treatment-coded into three levels (L1, advanced L2, and intermediate L2), and its interactions with other predictors were included in the models in RQ₂ and RQ₃. Participants were included as a random effect to account for individual differences.

Model diagnostics showed no significant concerns with convergence, residuals, homoscedasticity, multicollinearity, or outliers (see Appendix 4). All models were built in R (version 4.5.0; R Core Team, 2025) with lme4 (version 1.1-34; Bates et al., Reference Bates, Maechler, Bolker, Walker, Christensen, Singmann and Bolker2015).