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By 4 months, infants have domain-specific knowledge regarding physical reasoning, making inferences in accord with solidity, cohesion, and continuity (Spelke et al., 1992). Six-month-olds have access to a domain-general statistical inference mechanism, based on their intuitions about probabilistic relationships between samples and populations (e.g., Denison et al., 2013). Here we show that 11-month-old infants can use probability to infer a physical constraint, namely, an object size constraint.
In Experiment 1, infants (Mage=10;29) were assigned to one of two conditions, an improbable and a probable condition (N=32). Infants completed 6 test trials (see Figure 1). In the improbable condition, infants saw a box with mostly large yellow balls and fewer smaller pink balls, while the probable condition contained the reverse proportions. The experimenter shook the box upside down to produce 5 pink balls. She then revealed the top of the box to the infant, alternating between an opening that was large enough for both balls to get through or only large enough for the smaller pink balls.
Infants in the improbable condition looked longer at the large opening (Munexpected=10.778s, SE=.969, Mexpected= 8.151s, SE=.802, F(1, 15)=11.282, p=.004). Infants in the probable condition looked approximately equally, (Mlarge=8.085s, SE=1.228, Msmall=7.878s, SE = 1.010, F(1, 15)=.029, p=.866). This suggests that infants in the improbable condition inferred that the box opening would be small, because the samples they observed violated random sampling. Infants in the probable condition did not make these inferences, because the samples they observed were in line with random sampling.
Preliminary findings with adults suggest that they share similar intuitions. Adults (currently N=25) rate the large opening in the improbable condition as more surprising than the small opening, and find both openings in the probable condition unsurprising.
Experiment 2 provides a conceptual replication. Infants (Mage=10;25) were assigned to an improbable or probable condition (N=32). All infants saw a large box with 40% large yellow balls, 40% medium pink balls, and 10% small blue balls, and three demonstration trials, with samples that varied by condition. In the improbable condition, the experimenter shook the box upside down to produce 5 medium-sized pink balls on all three trials. In the probable condition just one medium pink ball was produced on all three trials. Infants in both conditions then saw 4 alternating test trials, where the experimenter shook the box upside down to produce one large yellow ball, or one small blue ball.
Infants in the improbable condition looked longer at the large yellow ball (Munexpected=7.118, SE=.754, Mexpected=5.273s, SE=.775, F(1, 15)=10.687, p=.005). Infants in the probable condition looked approximately equally (Munexpected=6.898s, SE=.925, Mexpected=7.880s, SE=1.045, F(1, 15)=.530, p=.478). This suggests that infants in the improbable condition generated the expectation that larger balls are prevented from exiting the box, as the demonstration samples suggested that the box was not producing random samples, as it is extremely unlikely that no yellow balls would exit with 3 five-ball samples. Infants in the probable condition did not generate such expectations because the samples produced in the demonstrations aligned with random sampling.