Introduction

Given the sheer amount of constantly changing information, our brains cannot represent everything. To deal with this limitation, we build condensed representations – mental models – that capture regularities and contingencies evident in the world (Filipowicz et al., 2016; Griffiths & Tenenbaum, 2006). Mental models are updated when contingencies change to maintain efficacy in predicting the sensory outcomes of action choices (Danckert et al., 2012; Filipowicz et al., 2016; Griffiths & Tenenbaum, 2006; Stöttinger et al., 2014). One mechanism whereby we update our mental models is statistical learning (Turk-Browne, 2012).

Statistical learning is our ability to learn regularities across sequential stimuli (Turk-Browne, 2012). Research shows that humans are proficient in guessing means and learning conditional probabilities (Saffran et al., 1996; Shaqiri et al., 2018). Even 8-month-old infants can extract transitional probabilities from strings of nonsense syllables (Saffran et al., 1996). One element crucial for successful statistical learning is the time scale over which information changes. Contingencies may change gradually (i.e., a global contingency) or from one instance to the next (i.e., a local contingency). A classic paradigm that exploits this distinction in visual perception is the Navon figures task in which alphanumeric stimuli are composed of both global and local components, with global features more readily perceived than local features (Navon, 1977). Jun and Chong (2016) adapted Navon figures to have participants learn global and local hierarchical levels that changed over time. They found that visual statistical learning was similar for both global and local properties. In a visuo-auditory cueing task, Arjona and colleagues (2018) had participants respond to auditory targets, preceded by either a valid or an invalid visual cue. They manipulated cue validity at both global and local levels. The probability of valid and invalid cues across three blocks of trials was conceptualized as a global manipulation. Local contingencies were determined by trial sequences (i.e., were trials valid or invalid, or some combination of the two). Results replicated well-known cueing effects and demonstrated that local probability significantly influenced reaction times and participant responses. Moreover, while both global and local properties influenced neural activity, local contingencies showed greater effects in modulating event-related potentials (ERPs) associated with attention, integrating new stimuli with the current mental model, and the detection of stimulus novelty.

This global-local distinction may also manifest in mental model updating. For example, when predicting tomorrow’s weather, we may consider the time of year or season (i.e., global information), as well as information from the recent past (i.e., local information), such as whether it rained yesterday. Successful updating likely requires incorporating both sources of information.

We explored whether mental model updating unfolds differently according to global and local statistical features. For perception, global properties are more readily perceived than local properties. Therefore, we expected participants would rely more heavily on global features when updating mental models (Hughes et al., 1984; Navon, 1977; Paquet & Merikle, 1988). Alternatively, it is plausible that local contingencies, which guide the allocation of attention (Arjona et al., 2018), may also influence mental model updating. We tested this in two experiments in which global changes were indicated by either background (Experiment 1) or triangle color (Experiment 2), and local changes were manipulated by trial-to-trial contingencies.

Methods

Participants

University of Waterloo undergraduate students participated in exchange for course credit. In Experiment 1, data were collected from 74 participants (56 female; mean age = 19.82 years, SD = 1.65). In Experiment 2, data were collected from 67 participants (44 female; mean age = 20.64 years, SD = 2.51). In both instances, we had decided a priori to collect as many participants as possible during a single school term. Therefore, the sample sizes for the two studies were slightly different. Study recruitment and data collection were concluded before any statistical analyses were conducted. Both sample sizes were deemed adequately powered given the directional hypotheses, the large number of trials (500) per participant, and that previous studies with smaller sample sizes were able to detect significant differences in global and local properties (Arjona et al., 2018; Jun & Chong, 2016; Jones & Kaschak, 2012).

The experiment took 30 min to complete and was administered online. Participants gave informed consent prior to completing the study, which had received clearance from the University of Waterloo’s Office of Research Ethics.

Procedure

Each trial began with an isosceles triangle centered on the screen such that the apex pointed up or down (Fig. 1). The triangle had a base of 200 pixels and a height of 212 pixels. As this was an online study, we did not have direct control over the size of the participants’ monitors, their resolutions, or the distances participants sat from the display. Participants guessed the orientation of the next triangle in the sequence by pressing the up and down arrows on the keyboard. Undisclosed to participants, the next triangle’s orientation reflected global and local properties of the task. Triangles remained on the screen until participants responded. Participants could take as long as needed to make a prediction. After making their choice, the next triangle was shown on screen. There was no explicit feedback. The experiment began with three practice trials to ensure participants understood the task, followed by 500 trials, with a break halfway through.

Fig. 1
figure 1

A schematic representation of the global-local updating task. Participants were presented with a triangle on the screen that pointed up or down and made a guess as to the orientation of the next trial in the sequence. In Experiment 1 (left), the global context was signalled by the background color. In Experiment 2 (right), the color cue for global bias was assigned to the triangle itself

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The task was coded in JavaScript using the jsPsych library (de Leeuw, 2015). Due to COVID-19 restrictions, the task was administered online.

Global and local statistical properties

The simplicity of our task design allowed for manipulating the probability independent of perceptual properties. The task comprised a single condition in which global and local statistical properties occurred simultaneously (Fig. 2). The global property was indicated by the color of the background (Experiment 1) or the target triangle (Experiment 2; Fig. 1). Color was classified according to the percentage value of rgb (red, green, and blue) parameters ranging from 0% to 100%. Color gradually alternated between red (100%, 0%, 0%) and blue (0%, 0%, 100%), with intermediate colors in the purple spectrum (Fig. 2). The motivation for having colors gradually change was to ensure the epochs alternated seamlessly. Although intermediate colors were present, the global property itself was classified as binary according to the rgb values. That is, “red” epochs had parameters ranging from rgb (52–100%, 0%, 0–48%) and “blue” epochs had colors with rgb (0–48%, 0%, 52–100%). Epochs were 25 trials in length. The global property was such that for “red” (or “blue”) epochs, there was a probability of 0.8 that the next triangle would point down (or up).

Fig. 2
figure 2

A schematic representation of how color transitioned between red and blue in a sequence of 100 trials. White triangles represent expected results according to the global property (i.e., trial followed the color) and grey triangles represent unexpected results according to the global property (i.e., trial was opposite to that indicated by the color). In reality, participants only saw grey triangles in Experiment 1

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The local statistical property for both experiments was manipulated by making the next triangle’s direction (i.e., trial n+1) depend on the current target triangle (i.e., trial n). By direction, we mean the up/down direction of the apex of the triangle (Fig. 1). The local probability was set to 0.8 (i.e., trial n+1 was 80% likely to point in the same direction as trial n).

To determine the pointing direction on each trial, we mixed these two distributions. Practically speaking, we generated the next trial based solely on the global and local contingencies, and then displayed one of the two options randomly, with equal likelihood. We then coded each triangle as consistent with global (i.e., pointing in the probable global direction) and/or local history.

Feedback questions

To assess whether participants were aware of task structure, we asked a number of questions upon completion (Table 1). Participants first answered open-ended, free-response questions to determine whether they spontaneously understood the nature of the task. They then answered six questions on a sliding scale with agree and disagree anchors (Table 1).

Table 1 Feedback questions presented at the end of Experiment 1 and Experiment 2
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Statistical analyses

Global and local changes occurred simultaneously, whereas our statistical analyses considered both properties separately. For the current trial’s triangle, there were four combinations: (1) Global Down, Local Down (i.e., red color, current triangle pointing down); (2) Global Down, Local Up (i.e., red color, current triangle pointing up); (3) Global Up, Local Down (i.e., blue color, current triangle pointing down); (4) Global Up, Local Up (i.e., blue color, current triangle pointing up). A multiple logistic regression analysis (R version 4.0.3; package stats) was conducted to determine the association between participants’ choices and the global and local structures. Participant data were fitted to a model containing the global property, local property, and their interaction as predictors for participants’ choices.

Free-response feedback data were coded for how often participants reported that their choices followed either the global or local properties, or both. Slider-response data were analyzed using a dependent-samples t-test that compared participant responses to the statement “the background/triangle color impacted the direction of the next triangle” (i.e., endorsement of the global property) versus responses to “direction of the current triangle impacted the direction of the next triangle” (i.e., endorsement of the local property).

Results

Experiment 1

From the 74 participants who completed the study, data were excluded from two participants who misunderstood task instructions. After data trimming for reaction time (faster than 200 ms or longer than 5 s) and run-length (same response exceeded 35 sequential trials), the final dataset excluded a median of 1.7% trials from each participant (interquartile range: 0.4–6.9).

Figure 3 shows participants’ choices according to four combinations of properties. Numerically, the data show that when global and local properties were congruent (i.e., Global Down, Local Down or Global Up, Local Up), participants were more likely to act in accordance with this information when guessing the next triangle’s orientation. However, when global and local properties were incongruent (i.e., Global Down, Local Up or Global Up, Local Down), participants followed the local property more closely.

Fig. 3
figure 3

A box and whisker plot of the participants’ probability of choosing up according to the global and local properties of the current screen in Experiment 1. When participants saw the current triangle on the screen, there are four combinations of properties that could occur: (1) Global Down, Local Down (i.e., red background, current triangle pointing down); (2) Global Down, Local Up (i.e., red background, current triangle pointing up); (3) Global Up, Local Down (i.e., blue background, current triangle pointing down); (4) Global Up, Local Up (i.e., blue background, current triangle pointing up)

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To test these differences, a multiple logistic regression analysis investigated which properties of the current trial predicted choices of the next triangle’s orientation. A chi-square analysis showed that compared to a null model (i.e., no predictors), the multiple logistic regression model was significantly better at predicting choices (χ2 = 32.78, p <.001; McFadden’s pseudo R2 = 0.32). The model provided a significant fit to the data with the local property positively predicting choices (ß =2.50, z =3.91, p <.001), while the global property, and the interaction term, were non-significant predictors (Table 2). A chi-square analysis also compared the multiple logistic regression model with a model that used only the local property as the predictor. Results showed that the difference between the two models was not significant (χ2 = 0.94, p = .63), suggesting that the local property predicted participants’ choices sufficiently well.

Table 2 Experiment 1 logistic regression results for participants’ choice for the next triangle’s orientation
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For the free-response question, “Did you notice any regularities or patterns in the study?” (Table 1), 21% of participants noticed changes in the background color, yet only four of those participants also noted that the background colors were associated with triangle direction. While all four participants explicitly detected the association with red backgrounds, only one indicated the association with blue backgrounds. A further 25% of participants reported that the direction of triangles appeared in runs of either up or down.

When asked “Did you use any strategies in guessing?” (Table 1), four participants (6%) mentioned that they followed both color and repeating sequences. A further 10% said they tried to follow the background color. In contrast, 42% of participants (n = 33) mentioned following runs of triangles in the same direction, with nine of these participants indicating that they repeated the direction of the current triangle on the screen (i.e., local property). Of the remaining participants, 19% wrote a vague response or a strategy that was irrelevant (e.g., “intuition”), and 23% stated they did not use a strategy.

For the remaining questions, results indicated that participants were more likely to agree with the statement endorsing the impact of the current triangle’s direction on the next triangle’s orientation (i.e., local property; mean = 47.36, SD = 31.66) than the statement endorsing the impact of background color (i.e., global property; mean = 58.95, SD = 28.49; note the anchors for these responses had “agree” to the left such that smaller numbers represent stronger endorsement). Responses were significantly different, indicating a bias in detecting the local property (t = 2.34, p = 0.028).

The evidence from feedback questions demonstrates that the global property was reported to a lesser extent than the local property when updating mental models, in accordance with participants’ actual choices.

In this version of the task, participants explicitly focused on the triangle, while the global property was indicated by background color changes. It may have been the case that this biased participants away from the global property. To test this, we repeated the task with the global probability signalled by changing the color of the target triangle such that both the global and local probabilities were evident in the object of the task itself.

Experiment 2

From the original dataset of 67 participants, data from one participant was removed due to alternating responses between up and down for 99% of the task. For the remaining 66 participants, the same data cleaning for reaction time and run-length was performed, with the final dataset removing a median of 3.4% trials from each participant (interquartile range: 1.25–7.85).

Experiment 2 successfully replicated the findings from Experiment 1 (Figs. 3 and 4).

Fig. 4
figure 4

A box and whisker plot of the participants’ probability of choosing up according to the global and local properties of the current screen in Experiment 2. When participants saw the current triangle on the screen, there are four combinations of properties that could occur: (1) Global Down, Local Down (i.e., red triangle, current triangle pointing down); (2) Global Down, Local Up (i.e., red triangle, current triangle pointing up); (3) Global Up, Local Down (i.e., blue triangle, current triangle pointing down); (4) Global Up, Local Up (i.e., blue triangle, current triangle pointing up)

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The multiple logistic regression model was significant when compared to a null model (χ2 =38.62, p <.001, McFadden’s pseudo R2 =0.40), but not when compared to a model with just the local property as a predictor (χ2 =0.65, p =.72). This suggests that the local property alone was a sufficient predictor for participants’ choices. The multiple logistic regression analysis showed that only the local property was a significant predictor for participants’ choices (ß = 2.76, z = 4.12, p < .001) (Table 3).

Table 3 Experiment 2 logistic regression results for participants’ choice for the next triangle’s orientation
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As with the open-ended responses in Experiment 1, when asked what they noticed in the study, 31% of participants detected the triangle changing color, but only four wrote that there was an association between this and orientation. Only one participant stated that red triangles were associated with down-facing triangles and that blue triangles were associated with up-facing triangles. A further 27% of participants noticed that triangles appeared in repeated sequences of the same orientation. In total, 7% of participants reported both the changes in color and trial-by-trial orientation contingencies. Of the remaining participants, 21% reported either a vague response or noticed a pattern that was not relevant to the task, and 28% stated they did not notice anything.

When asked about the strategies used, four participants (6%) mentioned both color and following the previous trial’s orientation, while 9% said they tried following the triangle’s color. In contrast, 18% of participants specifically mentioned following the direction of the current triangle (i.e., local property). Of the other participants, 28% followed runs of triangles in the same direction, 9% wrote a vague response or a strategy that was irrelevant, and 30% stated they did not use a strategy.

Lastly, responses to slider feedback questions (0 = agree, 100 = disagree) showed that participants were more likely to agree with the statement that the next triangle’s orientation was influenced by the current triangle’s direction (mean endorsement of local property = 39.34; SD = 23.69) than the statement on the influence of the current triangle’s color (mean endorsement of global property = 56.64; SD = 24.93). As in Experiment 1, responses were significantly different (t = 4.40, p < .001), indicative of a bias in detecting the local property.

This experiment replicated the results of Experiment 1. Even when the color changes signalling the global probabilities were incorporated into the object participants were explicitly attending to, judgements were still significantly biased toward the local property (Figs. 3 and 4).

Discussion

Effective mental model updating requires efficient representation of global and local changes in the environment. Results from these two experiments suggest that participants rely more strongly on local statistical information when learning regularities across sequential stimuli. This bias is consistent with findings from Argona and colleagues (2018), in which there was a stronger influence from local contingencies in their spatial cueing task. While Arjona and colleagues (2018) manipulated global statistical properties serially in three blocks of trials, our study had global contingencies continuously evolve, alternating between a greater likelihood of pointing up or down. Our results demonstrate that when local and global properties change simultaneously over time, as they do in the environment, people are biased towards using local contingencies to guide choices.

Our results are inconsistent with visual object recognition studies showing a prevalent influence from global properties (Hughes et al., 1984; Navon, 1977; Paquet & Merikle, 1988). One explanation may be that utilizing global information is more cognitively demanding. Monitoring long-range regularities across time requires remembering more items and sustaining attention for longer intervals (Marti et al., 2014). Another possibility is that violations of local properties are more salient and thus may distract from global influences. Future work could explore whether the current findings would hold if global regularities were easier to detect.

While we did find a local bias in mental model updating, it is not the case that global contingencies did not influence predictions at all. Self-report feedback demonstrated that some participants did in fact detect and use the global feature to guide their predictions. This is consistent with prior research showing that people are sensitive to global temporal regularities (Jones & Kaschak, 2012).

While global and local properties may both influence mental model updating, the current results suggest that healthy participants utilize local contingencies to a greater extent than global contingencies when learning statistical regularities. Future research should further investigate why local statistical properties exert a more powerful influence on learning than do global regularities.