Knowledge of Statistics or Statistical Learning? Readers Prioritize the Statistics of their Native Language Over the Learning of Local Regularities

Jarosław R. Lelonkiewicz; Michael T. Ullman; Davide Crepaldi

doi:10.5334/joc.209

One of the most striking features of the human mind is its ability to rapidly learn about regularities that are present in the environment. In a matter of minutes, people can implicitly detect and acquire a range of information patterns, including distributional variability, frequency, and probability with which events co-occur in the perceptual stream. Impressively, this type of learning, often referred to as statistical learning, has been observed across different tasks, contexts, and cognitive domains (for reviews, see Aslin, 2017; Aslin & Newport, 2012; Christiansen, 2019; Frost, Armstrong, & Christiansen, 2020; Newport, 2016; Perruchet & Pacton, 2006; Saffran & Kirkham, 2018; Thiessen, Kronstein, & Hufnagle, 2013).

One domain where statistical learning has been particularly well-evidenced is visual processing. In a landmark study by Fiser and Aslin (2001), adult participants were exposed to a stream of visual scenes composed of multiple abstract shapes. They were given no instructions beyond being asked to attend to the stimuli. Unknown to the participants, some shapes were repeatedly presented next to one another, thus constituting frequent pairs. Next, in a two-alternative forced choice test, participants were asked to judge the familiarity of shape pairs, on each trial choosing between a frequent pair and a pair that had never occurred in the scenes. The results revealed that frequent pairs were more often judged as familiar, suggesting that participants had implicitly learnt the frequency with which pairs occurred across the scenes (see also Fiser & Aslin, 2002; 2005; Turk-Browne, Jungé, & Scholl, 2005). Further research extended these findings by showing that statistical learning is a feature of visual processing already in infancy (Bulf, Johnson, & Valenza, 2011; Slone & Johnson, 2018), and that it occurs for different types of visual stimuli, including complex object arrays (Orbán, Fiser, Aslin, & Lengyel, 2008), real-world scenes (Brady & Oliva, 2008), and faces (Turk-Browne, Scholl, Johnson, & Chun, 2010).

Given its prevalence in the visual domain, several theoretical accounts have claimed that statistical learning is implicated in the processing of written language. For instance, Frost (2012) observed that languages provide readers with a rich array of probabilistic regularities and argued that efficient reading relies on the fact that cognitive system is tuned to pick up this information (e.g., in Semitic languages word roots are formed using only a small number of letters, and so focusing on these letters could aid in word identification). Similarly, Grainger and Ziegler (2011) suggested that reading involves the extraction of letter co-occurrence statistics: When processing words along a fine-grained route (one of the two modes of orthographic processing proposed by Grainger and Ziegler 2011), readers identify the frequently co-occurring letters and chunk them into higher–level orthographic representations (e.g., morphemes). Numerous other accounts have converged on the idea that the ability to extract regularities from the written input is important for reading, as it supports the acquisition of orthographic codes (Dehaene, Cohen, Sigman, & Vinckier, 2005; Grainger, Dufau, & Ziegler, 2016), lexical representations (Frost, Kugler, Deutsch, & Forster, 2005), and reading skills at large (Arciuli, 2018; Arciuli & Simpson, 2012; Seidenberg & MacDonald, 2018).

But do people actually pick up on visual statistical cues as they read? Interestingly, there is some evidence that this might be the case. The ability to extract visual regularities appears to be present in several animal species, including primates. In Grainger et al. (2012), baboons saw foil strings designed to imitate English words intermixed with actual words, and received a reward every time they correctly identified a word. Since they could not rely on linguistic knowledge (e.g., semantics or phonology), the animals were given a visual cue: foil strings had lower average bigram frequency (ABF) than words, meaning that – on average – they were composed of letter bigrams that occurred less frequently within the stimuli set. The study found that baboons were able to correctly distinguish between foils and words even for items they had not seen before (and thus could not have remembered), implying that they had picked up on the purely visual information about bigram frequency (similar findings have been reported for chicks and pigeons; see Santolin & Saffran, 2018). However, though suggestive, evidence from animal studies cannot ultimately tell whether human readers extract statistics from written words.

Two recent artificial orthography studies brought us closer to answering this question: In Chetail (2017), adult readers were exposed to a large (e.g., 320 items in Experiment 1a) lexicon of strings composed of unfamiliar psuedofonts. Importantly, the stimuli involved some highly frequent bigrams. As in the classic visual statistical learning experiments (e.g., Fiser & Aslin, 2001), participants were asked to observe the stimuli with no mention of any implicit regularities. And yet, they acquired the bigram statistics – in a subsequent wordlikeness task, previously unseen strings were judged as more word-like if they involved frequent bigrams. Using a similar paradigm, Lelonkiewicz, Ktori, and Crepaldi (2020) exposed readers to 200 pseudofont strings that contained chunks of frequently co-occurring characters. Subsequently, string processing came to resemble that of real morphologically complex words (i.e., readers became sensitive to the presence and position of chunks within strings, a finding previously observed for morphological affixes within words; see Crepaldi, Rastle, & Davis, 2010; Crepaldi, Rastle, Davis & Lupker, 2013), implying that participants had learnt the character co-occurrence statistics and used this information to decompose the pseudofont strings into chunks. While allowing good experimental control (e.g., ruling out the confounds related to semantic representations), these experiments have the obvious caveat of involving stimuli made of unfamiliar, non-linguistic symbols, which makes it difficult to understand to what extent they apply to real language processing.

To partially circumvent this issue, several studies investigated visual statistical learning in nonwords composed of familiar letters and generated using artificial grammars. For example, Ise et al. (2012) asked children to memorize and pronounce 15 such nonwords; next, children saw further nonwords and decided if these new items belonged to the same fictitious language as the memorized ones. The results were consistent with statistical learning – nonwords that contained bigrams or trigrams that frequently occurred within the memorized set were more often ascribed to the fictitious language. In a similar vein, Samara and Caravolas (2017) showed that adult readers were more likely to judge novel letter strings as grammatical if they were composed of chunks that were frequent within a set of 24 previously memorized nonwords (see also Nigro, Jiménez-Fernández, Simpson, & Defior, 2015; 2016; Maurer et al., 2010; Taylor, Davis, & Rastle, 2017).

These artificial grammar experiments go in line with the claim that people discover local statistical regularities as they read. However, their conclusions are based on a very particular case of language processing: Readers were first exposed to small and highly artificial sets of learning items and then engaged in a visual word processing task in which they received no information about the accuracy of their performance; in contrast, language learning likely benefits from some form of feedback (Dale & Christiansen 2004; Pashler, Cepeda, Wixted, & Rohrer, 2005; Rastle, Lally, Davis, & Taylor, 2021).

In the present study, we set out to extend the current evidence. To this end, we devised a paradigm capitalising on the strengths of the previous designs and addressing some of their weaknesses. In two experiments, we examined if human readers extract statistical regularities while processing a large lexicon of strings (400 distinct items). To ensure a more naturalistic context (as compared to baboons learning English words or humans reading an unfamiliar alphabet), we modelled the stimuli on real language (participants’ native Italian) and used familiar letters. (See Discussion for how this relates to real-world reading contexts, such as learning to read new words in one’s native language or learning to read in a new language.) However, to minimise the chance that the processing would be guided by the information associated with the lexical level (e.g., word meaning, word frequency), we used strings that were all nonwords. We hypothesised that, if the ability to extract regularities plays a role during visual word processing, readers should pick up on the statistical characteristics of the new lexicon.

To test this hypothesis, in Experiment 1 we presented Italian speakers with a set of letter strings and asked them to guess which strings were words in a fictitious language and which were not (henceforth, words and foils). Importantly, and unbeknownst to participants, fictitious words had higher average bigram frequency (ABF) than foil strings. Much like in Grainger et al. (2012), participants made their guesses after every string they saw and we expected them to implicitly learn the ABF pattern as they progressed with the experiment. To foster learning, each string was shown three times and feedback was given after each guess. We hypothesised that if participants are indeed sensitive to statistical characteristics of learning materials, they should pick up on the ABF pattern underlying the words vs. foils distinction and use it in their guesses. In Experiment 2, we further increased the ABF difference between words and foils and once again tested if participants would use this cue.

Further, to help understand which cognitive faculties may impact the learning of local regularities in reading, we collected additional measures of statistical learning in a non-verbal visual task (Experiment 1); of learning in declarative and procedural memory (Experiment 2); and of vocabulary span (Experiments 1–2). Statistical learning has been hypothesized to tie to a range of individual abilities (e.g., Siegelman & Frost, 2015; Arciuli, 2017; Schmalz, Altoè, & Mulatti, 2017). We reasoned that a positive correlation between the use of ABF and visual statistical learning would provide further evidence that participants acquired this cue during the task. Conversely, a positive correlation with participants’ vocabulary span would link the ability to use the cue to pre-existing linguistic knowledge.

The declarative and procedural memory measures aimed to identify possible neurocognitive substrates of regularity learning in reading. Specifically, to understand whether any such learning was linked to declarative memory (defined as the learning and memory that is rooted in the hippocampus and associated circuitry) and/or procedural memory (the learning and memory rooted in the basal ganglia and associated circuitry) (Ullman, Earle, Walenski, & Janacsek, 2020), we tested for positive correlations between the use of ABF and either memory measure. Notably, a correlation with procedural memory would strengthen the hypothesis that participants acquire regularities through implicit learning, since procedural memory seems to underlie only the acquisition of implicit knowledge (Ullman et al., 2020). In contrast, a correlation with declarative memory would be consistent with participants having learned the statistic explicitly, since this system is critical for explicit knowledge.

Experiment 1

Methods

The stimuli and experimental scripts used in the main task, as well as raw data and commented analysis scripts can be found at the project’s Open Science Framework page: https://osf.io/vc6rw/.

Participants

We recruited 45 monolingual native Italian speakers who did not use any other languages on a daily basis, had normal or corrected-to-normal vision, no learning or language disorders, and were 18–35 years old. All participants gave informed consent prior to the experiment and received 18€. All experimental procedures were approved by the Ethics Committee at Scuola Internazionale di Studi Superiori Avanzati (SISSA), where participants were tested.

Apparatus, stimuli and procedure

Participants carried the experiment out individually, in a sound-proof booth. Prior to the main task (lexical judgment), participants completed a measure of vocabulary span (MHVS) and a visual statistical learning task (VSL). All instructions were given in Italian.

Mill-Hill Vocabulary Scale (MHVS)

First, participants completed a paper-based scale where they saw 28 Italian words and for each word selected the correct synonym from a list of six alternatives (we used an Italian translation of the MHVS originally introduced as a companion to Raven’s Progressive Matrices; Raven, 1958). Vocabulary span was operationalized as the number of correct responses out of the total of 28, meaning that high numbers were indicative of a broad vocabulary. The scale took 5–10 minutes to complete.

Visual Statistical Learning (VSL)

Next, participants sat in front of a computer and performed a variant of a commonly used VSL task (e.g., Frost, Siegelman, Narkiss, & Afek, 2013; Turke-Brown et al., 2005). The task started with a familiarization phase, where participants saw 16 abstract shapes appearing one-by-one in a continuous stream (800 ms ON, 200 ms OFF). Unbeknownst to participants, shapes were arranged in 8 triplets, each appearing 24 times (triplets appeared in a pseudo-random order with the constraint that the same triplet cannot be immediately repeated). Thus, shapes within a triplet had much higher transitional probabilities (TPs = 1) than shapes between triplets (TPs = 1/7) or shapes that never appeared one after another (TPs = 0). In the testing phase, we investigated if participants successfully learnt these probabilities: Participants were presented with 34 trials where they chose between sequences composed of shapes with high TPs and “foil” sequences composed of shapes with low TPs (16 trials were 2AFC triplets, 6 trials were 2AFC pairs, 4 trials were 4AFC pairs, and 8 trials were 4AFC triplets; trials were presented in random order), and further 8 trials where they saw an incomplete sequence and they selected the shape that they thought was missing (4 trials involved a pair, and 4 trials a triplet). We operationalized visual statistical learning ability as the number of correct responses out of the total of 42, so that the higher the number, the better the individual’s ability to learn visual regularities. Participants sat in front of a 27’’ BenQ XL2720 monitor and responded using an English QWERTY keyboard. The experiment was delivered with Presentation (v19.0, Neurobehavioral Systems, Inc., Berkeley, CA, www.neurobs.com). Participants completed the VSL task in about 15 minutes.

Lexical Judgment

Participants then moved onto the primary task of the study: They were told they would see words in a fictitious “Turistino” language, as well as combinations of letters that were similar, but were “something else”. The task was to distinguish between strings that were fictitious words (e.g., etesse) and foil strings (e.g., spizio). Participants were given no further information on how to tell these two types apart.

The stimuli were all nonwords, but to increase the chance that they would be processed similarly to real words, we ensured that they were pronounceable and consisted of bigrams and letters naturally occurring in participants’ native Italian. Word strings and foils were similar to one another: They were comparable in length (either were 4–6 letters long; Mdn_words = 6, Mdn_foils = 6; U = 20113, p = .907; non-parametric Man-Whitney U test, two-sided) and constructed using identical sets of 150 unique bigrams and 21 unique letters. They were also orthographically equidistant to Italian (as captured by Coltheart’s N; Mdn_words = 0, Mdn_foils = 0; U = 20770; p = .119).

Critically, however, word strings differed from foils insofar that they tended to have higher average bigram frequency (ABF; see Figure 1). ABF was defined as the average frequency of all closed bigrams present in a string. Frequencies of individual closed bigrams were based on the Italian lexicon (SUBTLEX-IT; Crepaldi et al., 2015). They were calculated as occurrence probabilities (i.e., count of the occurrences of a given bigram in the Italian lexicon divided by the count of all occurrences of all bigrams in this lexicon), in a position-independent manner (i.e., all occurrences of a given bigram were counted towards a single score, regardless of the bigram position within words). See Figure 2 for an illustration of how ABF was calculated.

Figure 1

Experiments 1–2: Density plots illustrating average bigram frequency (ABF), minimal bigram frequency (minBF), and maximal bigram frequency (maxBF) for fictitious words, foils, and real words in the Italian lexicon.

Figure 2

Experiments 1–2: An illustration of how average bigram frequency (ABF), minimal bigram frequency (minBF), and maximal bigram frequency (maxBF) were calculated. For each of the novel strings (e.g., etesse), we identified all bigrams present in this string and matched them with the frequencies with which these bigrams occur in the Italian lexicon (SUBTLEX-IT; Crepaldi et al., 2015; Italian bigram frequencies were calculated as position-independent occurrence probabilities). ABF was defined as the average value of the frequencies of all the bigrams present in that string, minBF was equivalent to the frequency of the bigram with the lowest frequency from all the bigrams present in this string (e.g., f[ss] = 0.0055), and maxBF was equivalent to the frequency of the bigram with the highest frequency (e.g., f[e ] = 0.0212).

Participants were given no explicit information about the ABF pattern, and were expected to learn it on their own as they were doing the task. To support such learning, each lexical judgment was followed by a feedback message telling the accuracy of the judgment and revealing whether the string was a fictitious word or a foil. However, we did not know a priori if participants would pick up on the ABF pattern underlying the word vs. foil distinction. Specifically, given the high degree of similarity between the experimental strings and real Italian words, it was plausible that participants, all native speakers of Italian, could instead rely on some other regularities derived from the Italian lexicon. For example, lexical judgments could be guided by the presence of bigrams that are particularly rare or particularly common in Italian. To capture this possibility, for each string we calculated minimal bigram frequency (minBF), defined as the frequency of the bigram with the lowest Italian-based frequency from all the bigrams present in this string, as well as maximal bigram frequency (maxBF), defined as the frequency of the bigram with the highest Italian-based frequency (for an illustration, see Figure 2). This allowed us to control for a possible effect of these metrics at the stage of statistical analysis.

A noteworthy aspect of our method is that the bigram frequencies used in the calculation of ABF, minBF, maxBF were based on the Italian lexicon. However, another approach could be to calculate bigram frequencies based on how often the bigrams occurred within the experimental stimuli. After all, participants could use such local frequencies to distinguish between word strings and foils, of course providing there would be a systematic difference between the two types (e.g., a certain bigram could be very frequent in words, but not in foils). Similarly, participants could rely on local letter frequencies.

Table 1 offers a comparison between the frequency statistics as calculated based on Italian lexicon vs. on the experimental stimuli. As illustrated in Table 1, whereas word strings were similar to foils with regards to letter frequency statistics, they differed in terms of bigram frequencies. This was most likely due to the nature of our manipulation (i.e., word strings were designed to have higher average bigram frequency than foils, which might have led to some bigrams being used more often in words than foils). We return to this point in the Results section (see the passages reporting the interaction between Type and Seen).

Table 1

Experiments 1–2: A correlation matrix (Spearman’s ρ; all ps < .01) illustrating the similarity in letter and bigram probabilities as calculated based on fictitious word strings, foils, and the Italian lexicon.


EXPERIMENT 1
		ITALIAN	WORDS	FOILS

letter probabilities	Italian	–	0.97	0.91

	words	0.97	–	0.92

	foils	0.91	0.92	–

bigram probabilities	Italian	–	0.78	0.43

	words	0.78	–	0.37

	foils	0.43	0.37	–

EXPERIMENT 2

		ITALIAN	WORDS	FOILS

letter probabilities	Italian	–	0.96	0.86

	words	0.96	–	0.86

	foils	0.86	0.86	–

bigram probabilities	Italian	–	0.84	0.35

	words	0.84	–	0.28

	foils	0.35	0.28	–

Returning to the description of the lexical judgment task, in each trial participants saw a fixation cross (500 ms), followed by either a word string or a foil, appearing centrally on the screen. After participants’ response (or after 2000 ms has lapsed, whichever occurred first), the string would be replaced by a feedback message (“Corretto/Scorretto! Questa era una parola/nonparola”; English translation:“Correct/Incorrect! This was a word/nonword”). Participants completed 1200 trials organised into 10 blocks: There were 200 words and 200 foils, each stimulus shown three times, presented in random order, with the constraint that all repetitions of a stimulus had to occur within the same block.

Stimuli were displayed in black, against a light gray background (#f0f0f0). Participants operated the same set-up as in the VSL task, except here they responded by pressing F/J (response type to key assignment was counter-balanced between participants). The experiment was programmed in OpenSesame (v3.1.9; Mathôt, Schreij, & Theeuwes, 2012). The lexical judgment task took about 60 minutes to complete.

Statistical Analysis

Prior to analysis, we removed 2 participants whose data was not usable (1 due to data corruption, 1 due to a technical failure; leaving n = 43 in the analysis).

Based on the hypothesis that readers can discover the implicit statistical structure of learning materials, we predicted that lexical judgments in our task would be guided by ABF. Specifically, we expected that the likelihood of judging a string to be a fictitious word should be positively related to this string’s ABF.

To test this prediction, we conducted a binomial generalized linear mixed model (GLMM) estimating the odds of making a “word” response. We included ABF, Type (foil vs. word), and Seen (unseen vs. seen; i.e., whether at the time of making the response participant had already seen the string) as predictors, as well as random by-participant intercepts and slopes for the three-way interaction between ABF, Type, and Seen, and by-item intercepts and slopes for Seen. We applied effect contrast-coding to the factorial predictors (Type, Seen), and scaled and centred the continuous predictor (ABF). The model had the following structure: “word” response ~ (ABF * Type * Seen) + (ABF * Type * Seen | Participant) + (Seen | Item). All GLMM’s reported in this paper were computed using lme4 R package (lme4 version 1.1–14; Bates, Maechler, Bolker, & Walker, 2015; R version 3.4.2; R Core Team, 2017).

Moreover, we wanted to test for the possibility that lexical judgments would be driven by a different measure of bigram frequency, one that was not reinforced during the lexical judgment task, but could nevertheless influence participants’ performance. Thus, we ran two further models based on the GLMM described above: One including minBF as an additional predictor, and another including maxBF. As before, we contrasted the factorial predictors and scaled and centred the continuous ones. The models had the following structure: “word” response ~ (ABF * Type * Seen) + (minBF/maxBF * Type * Seen) + (ABF * Type * Seen | Participant) + (minBF/maxBF * Type * Seen | Participant) + (Seen | Item).

To determine which model provided the best fit to our data, we compared the three models in terms of explained variance. We found that the ABF + minBF model was superior to the other two (i.e., the ABF model, and the ABF + maxBF model; ps < .001; comparisons were done using the anova function; base R). For this reason, throughout this paper, we consider this model to provide the primary representation of our data (results from the other two models can nevertheless be found in the Supplement; see Tables S15 and S16).

Apart from investigating our main hypothesis, we wanted to explore whether the effects of statistical cues on lexical judgment would increase over time, thus indicating that participants were learning to rely on such cues as they progressed through the task (prior to this analysis we excluded 1 further participant who did not produce responses in the last two blocks of the experiment; leaving n = 42). To this end, we re-fit the ABF + minBF model including also experimental block as a predictor (scaled): “word” response ~ (ABF * Type * Seen * Block) + (minBF * Type * Seen * Block) + (ABF * Type * Seen * Block | Participant) + (minBF * Type * Seen * Block | Participant) + (Seen | Item).

Finally, to investigate if the use of statistical cues was related to participants’ vocabulary span or their ability to learn visual regularities, we re-fit the ABF + minBF model including participants’ MHVS score, and (as a second, separate model) re-fit it including participants’ VSL score (MHVS/VSL scores were scaled and centred). The models followed the structure: “word” response ~ (ABF * Type * Seen * MHVS/VSL) + (minBF * Type * Seen * MHVS/VSL) + (ABF * Type * Seen * Block | Participant) + (minBF * Type * Seen * Block | Participant) + (Seen | Item).

Results

The main findings are visualised in Figure 3 and model summaries are reported in Table 2. First, we observed a main effect of Seen (p < .001), which was further qualified by a significant interaction with Type (p < .001), indicating that although the odds of making a “word” response were overall higher for word strings than foils, this effect was greater in strings that participants had already seen compared to previously unseen strings. Moreover, a follow-up analysis revealed that the effect of Type was significant for previously seen items (p < .001), but not for unseen items (p = .651; full results in Table S1), meaning that participants were able to successfully distinguish between fictitious words and foils only when judging items for which they had already received feedback (recall that after responding to a string participants received feedback that revealed the identity of a string). Conversely, when judging items on which they had not received feedback, they could not tell the two types apart (Figure 3; see also Figure S1 in the Supplement showing the proportion of “word” responses by the first, second, and third presentation). An important implication of this finding is that it suggests that participants did not base their judgments on the differences in the statistical characteristics of word strings vs. foils (if there would be any systematic difference between words and foils that the participants could use, we would expect them to successfully distinguish between words and foils also for previously unseen strings).

Figure 3

Experiments 1–2: Mean percentages of “word” responses for each item, shown by Type (foil vs. word strings) and Seen (previously unseen vs. seen). The fitted lines represent the effect of minimal bigram frequency (minBF).

Table 2

Experiments 1–2: Results from the fixed effects structure of the GLMM’s including ABF, minBF, Type (foil vs. word) and Seen (unseen vs. seen).


EXPERIMENT 1

	$β^$ M1 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat \beta \] \end{document}	SE	z	p

Intercept	.06	.09	.67	.504

ABF	.06	.07	.92	.356

Type	–.04	.08	–.50	.620

Seen	–.32	.07	–4.85	<.001

minBF	.22	.06	3.62	<.001

ABF * Type	.00	.08	.02	.981

ABF * Seen	.07	.06	1.10	.273

Type * Seen	.87	.11	7.98	<.001

minBF * Type	–.16	.07	–2.35	.018

minBF * Seen	–.11	.05	–2.00	.045

ABF * Type * Seen	–.11	.08	–1.47	.142

minBF * Type * Seen	.09	.06	1.49	.137

EXPERIMENT 2

	$β^$ M2 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat \beta \] \end{document}	SE	z	p

Intercept	.06	.09	.71	.473

ABF	.08	.07	1.07	.285

Type	–.10	.09	–1.15	.252

Seen	–.26	.08	–3.05	.002

minBF	.14	.04	3.46	<.001

ABF * Type	.02	.10	.25	.800

ABF * Seen	–.01	.07	–.15	.877

Type * Seen	.71	.13	5.55	<.001

minBF * Type	–.04	.05	–.93	.355

minBF * Seen	–.05	.04	–1.15	.250

ABF * Type * Seen	.12	.09	1.31	.190

minBF * Type * Seen	–.02	.05	–.52	.603

In line with this finding, the analysis also revealed no effects of ABF (ps > .141), implying that participants did not use this cue for lexical judgments. Instead, they relied on minBF: We observed a significant main effect of minBF, such that the higher the string’s minBF, the greater the odds of judging this string to be a fictitious word (p < .001). Further, this effect was qualified by a significant interaction with Seen (p = .045) and by a separate interaction with Type (p = .018), suggesting that minBF had a particularly strong impact when participants were responding to previously seen strings or to foils (see Figure 3; these findings were confirmed in a model controlling for string length, and another model controlling for orthographic similarity; see Tables S11–14).

The unexpected finding that lexical judgments were guided by minBF prompted us to ask if participants were somehow able to learn to use this cue during the task. However, the model controlling for the effect of experimental block found no evidence for such learning: Whereas the effect of minBF was once again present (p = .0498), there was no main effect of Block and no significant interactions including this predictor (ps > .082), suggesting that the tendency to rely on minBF was unlikely acquired during the experiment. Further, there were no interactions involving ABF and Block (ps > .679), implying that, despite receiving feedback, participants did not learn to use ABF over the course of the experiment (full results in Table 3).

Table 3

Experiments 1–2: Results from the fixed effects structure of the GLMM’s including ABF, minBF, Type (foil vs. word), Seen (unseen vs. seen), and controlling for Block.


EXPERIMENT 1

	$β^$ M3 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat \beta \] \end{document}	SE	z	p

Intercept	.06	.12	.47	.636

Block	–.01	.11	–.12	.906

ABF	.07	.10	.76	.448

Type	–.24	.13	–1.86	.062

Seen	–.33	.13	–2.44	.015

minBF	.18	.09	1.96	.0498

ABF * Block	–.02	.10	–.20	.838

Type * Block	.22	.13	1.73	.083

ABF * Type	.07	.15	.51	.607

Seen * Block	.00	.13	.00	.997

ABF * Seen	.07	.13	.52	.603

Type * Seen	1.05	.18	5.63	<.001

minBF * Block	.03	.10	.28	.778

minBF * Type	–.15	.11	–1.34	.181

minBF * Seen	.02	.12	.14	.891

ABF * Type * Block	–.06	.14	–.41	.680

ABF * Seen * Block	.00	.12	.02	.986

Type * Seen * Block	–.19	.17	–1.07	.285

ABF * Type * Seen	–.15	.18	–.79	.428

minBF * Type * Block	.00	.11	–.04	.967

minBF * Seen * Block	–.12	.12	–1.02	.306

minBF * Type * Seen	–.01	.14	–.09	.925

ABF * Type * Seen * Block	.03	.18	.19	.850

minBF * Type * Seen * Block	.10	.13	.77	.443

EXPERIMENT 2

	$β^$ M4 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat \beta \] \end{document}	SE	z	p

Intercept	–.09	.14	–.68	.494

Block	.17	.13	–1.26	.207

ABF	–.04	.14	–.34	.736

Type	–.06	.17	–.38	.704

Seen	–.20	.17	–1.17	.242

minBF	.26	.07	3.49	<.001

ABF * Block	.14	.13	1.03	.303

Type * Block	–.05	.17	–.31	.754

ABF * Type	.19	.17	1.09	.274

Seen * Block	–.08	.15	–.55	.583

ABF * Seen	.11	.16	.68	.497

Type * Seen	.75	.22	3.35	<.001

minBF * Block	–.13	.08	–1.71	.087

minBF * Type	–.14	.09	–1.62	.105

minBF * Seen	–.19	.10	–1.92	.055

ABF * Type * Block	–.16	.17	–.97	.332

ABF * Seen * Block	–.13	.16	–.85	.398

Type * Seen * Block	–.02	.20	–.10	.922

ABF * Type * Seen	–.01	.22	–.06	.949

minBF * Type * Block	.12	.09	1.25	.211

minBF * Seen * Block	.15	.09	1.63	.103

minBF * Type * Seen	.11	.11	.99	.323

ABF * Type * Seen * Block	.15	.21	.72	.468

minBF * Type * Seen * Block	–.16	.11	–1.43	.152

Finally, with regards to our secondary measures, we found that the effect of minBF was positively related to participants’ vocabulary span (p = .008), such that the higher the individual’s MHVS score, the stronger the effect of minBF; there were no other reliable effects involving this measure (ps > .050; full results in Table S3). Participants’ ability to learn visual regularities as measured by the VSL task had no effect on performance in our task (ps > .208; full results in Table S5).

Discussion

Experiment 1 found no evidence that participants discovered the pattern underlying the structure of the novel lexicon: Despite receiving accuracy feedback, they did not learn to use ABF in their lexical judgments. Instead, performance was guided by minBF, insofar that strings that had higher minBF were more likely to be judged as novel words. But curiously, this tendency was unlikely to have been acquired during the task, as we found no evidence that the effect of the minBF statistics increased over time (i.e., across experimental blocks). Further, the results from our additional measures also point to the possibility that participants did not engage in much local statistical learning – the individual’s capability to detect visual regularities was uncorrelated with the use of ABF or minBF (nor it was predictive of the performance in general).

One explanation for these unexpected findings is that the ABF cue was not strong enough to be detected amongst many other statistics present in our word-like stimuli. Note that ABF was manipulated in a continuous manner, meaning that some foil strings might have had very similar, or even virtually the same ABF values as words (see Figure 1). Moreover, both fictitious words and foils closely resembled existing Italian words, which might have prompted participants to ignore local regularities, and instead focus on cues that are important for the processing of real words (a possibility suggested by the fact that the extent to which participants relied on the minBF cue was related to their vocabulary span). Indeed, there is some indication that the processing of novel, previously unseen letter strings may at times be driven by the statistics of one’s native language (e.g., Cassar & Treiman, 1997; Pacton, Perruchet, Fayol, & Cleeremans, 2001; Pollo, Kessler, & Treiman, 2009). Thus, we reasoned that increasing the informativity of ABF for the words vs. foils distinction could help participants learn this cue. To put this intuition to the test, and to assess the robustness of the minBF effect, we ran Experiment 2.

Experiment 2

In Experiment 2, we once again used our lexical judgment task to investigate if readers learn the statistical patterns characterising a novel lexicon. However, we developed new stimuli to ensure that the difference in ABF between foils and word strings was more clearly pronounced (see Figure 1), and tested if lexical judgments would now be affected by ABF. We also tested if the finding that readers rely on the minBF statistics would replicate with these new stimuli.

In addition, we asked if the use of the ABF and minBF statistics would be related to participants’ capability for procedural or declarative learning. A positive association with procedural learning would suggest that the cue was learnt based on the procedural memory system, and would indicate an implicit status of this cue (consistent with the hypothesis that the cue is picked up by a statistical learning mechanism), whereas an association with declarative learning would suggest that the cue was learnt based on declarative memory systems, and could indicate its explicit status in memory. To investigate these relationships, participants completed a procedural learning task (i.e., serial reaction time task; Nissen & Bullemer, 1987) and a measure of declarative learning (i.e., recognition memory task; Hedenius, Ullman, Alm, Jennische, & Persson, 2013), which have respectively been closely tied to the declarative and procedural memory systems (Janacsek et al., 2020; Reifegerste et al., 2020). Additionally, we once again measured participants’ vocabulary span and tested if it was related to their use of statistical cues.