What Are the Odds? Preschoolers’ Ability to Distinguish Between Possible, Impossible, and Probabilistically Distinct Future Outcomes Jessica Crimston, Jonathan Redshaw, and Thomas Suddendorf Early Cognitive Development Centre, School of Psychology, The University of Queensland Previous research has suggested that infants are able to distinguish between possible and impossible events and make basic probabilistic inferences. However, much of this research has focused on children’s intuitions about past events for which the outcome is already determined but unknown. Here, we investigated children’s ability to use probabilistic information to guide their choices and actively shape future events. In two experiments, we examined whether children could successfully direct a marble through a series of tubes, selecting between routes where success was possible, impossible, or guaranteed (i.e., 50% vs. 0%, or 50% vs. 100%; Experiment 1), and routes where success was mutually possible but probabilistically distinct (e.g., 33% vs. 50%; Experiment 2). In total, we tested 136 two- to five-year-old children (76 males), recruited predominantly through a museum in Brisbane, Australia. In Experiment 1, we found that while younger children typically did not perform above chance, the vast majority of 4- and 5-year-olds consistently distinguished between possible and impossible or guaranteed outcomes. In Experiment 2, children of all ages had greater difficulty with distinguishing between two possible outcomes with different likelihoods than between possible and impossible/guaranteed outcomes, although some individual 4- and 5-year-olds demonstrated competence when making both distinctions. Public Significance Statement This study examined the development of children’s ability to reason about the possibility and probability of future outcomes. Two- to 5-year-old children were given the opportunity to choose between two actions that would be more or less likely to lead to a reward. In contrast to previous studies, the results showed that many children struggled to select the better action well into the preschool years, which may have implications for how to best introduce probability concepts in the classroom. Keywords: foresight, possibility, probability, uncertainty, preschool Supplemental materials: https://doi.org/10.1037/dev0001587.supp The capacity for foresight has been hailed as one of the hallmarks of human intelligence and a key reason for our success as a species, allowing us to anticipate future needs and forestall potential threats (Suddendorf & Corballis, 1997). Of course, given that the future is inherently uncertain, the utility of our forecasting abilities often rests on the accuracy of our predictions. In some instances, we may be able to foresee multiple possibilities but it would typically not be practical to prepare for them all. As adults, therefore, we will often first consider whether an imagined scenario is possible and, if there are multiple possibilities, we may consider the respective probability of each occurring. Following such assessment, we will then typically only prepare for or pursue those outcomes that seem most likely, or which, even if relatively unlikely, might have great consequences. For example, we may check the daily weather forecast before deciding what to wear, the odds on our favorite team before placing a bet, or the chances of losing our homes to Jessica Crimston https://orcid.org/0000-0003-2093-601X We thank Queensland Museum and its patrons for their participation in the study. We also thank caregivers, children, and staff at Early Cognitive Development Centre at the University of Queensland for their participation. This research was funded by an Australian Research Council Discovery Project Grant (DP210101572) awarded to Thomas Suddendorf and Jonathan Redshaw. The authors hereby declare no conflicts of interest. The preregistration for Experiment 2 (Experiment 1 was not preregistered), along with the raw data, analytic code, and supplementary materials for both experiments are available via the Open Science Framework at Anonymous: https://osf.io/x8as4/?view_only=642d869148a84373b13343c3eddb3a9b. Original: https://osf.io/x8as4. Jessica Crimston served as lead for data curation, investigation, methodology, project administration, resources, and writing–original draft and contributed equally to writing–review and editing. Jonathan Redshaw served in a supporting role for writing–review and editing. Thomas Suddendorf served in a supporting role for methodology and writing–review and editing. Jessica Crimston, Jonathan Redshaw, and Thomas Suddendorf contributed equally to conceptualization. Jessica Crimston and Jonathan Redshaw contributed equally to formal analysis. Jonathan Redshaw and Thomas Suddendorf contributed equally to supervision. Correspondence concerning this article should be addressed to Jessica Crimston, Early Cognitive Development Centre, School of Psychology, The University of Queensland, St. Lucia, Queensland 4072, Australia. Email: firstname.lastname@example.org Developmental Psychology © 2023 American Psychological Association 2023, Vol. 59, No. 10, 1881–1891 ISSN: 0012-1649 https://doi.org/10.1037/dev0001587 1881 This document is copyrighted by the American Psychological Association or one of its allied publishers. This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. natural disasters before seeking an insurance policy. Indeed, the concepts of possibility and probability, in addition to long being the fodder of linguists and philosophers, are an integral part of our everyday decision-making lives (Carey et al., 2020). Yet, despite their importance to human cognition and behavior, we know very little about when and how children begin to account for the likelihood (i.e., the possibility and probability) of future events to guide their choices. The aim of the present studies, therefore, was to examine young children’s ability to prepare for future events with varying possibilities and probabilities of occurring. The first question, of course, is when children become capable of distinguishing between event outcomes with probabilities that are greater than or equal to zero—that is, possible and impossible events. A series of seminal studies suggested that infants could distinguish between such events between 3.5 and 5 months of age (Baillargeon, 1987; Baillargeon et al., 1985). In these studies, infants were presented with a drawbridge that moved in a 180° arc, either up to (possible) or through (impossible) an occluded box and found that infants reliably looked longer in the impossible condition. However, later findings suggested that infants may have been responding to the novelty of the event rather than its apparent or perceived impossibility (Bogartz et al., 2000; Cashon & Cohen, 2000; Rivera et al., 1999). Indeed, Jackson and Sirois (2022) found that if 9-month-old infants were habituated to the impossible event, they would subsequently look longer at the possible event. These infant studies may, therefore, not tell us as much as first thought about the development of children’s ability to reason about possibility. Proficiency in distinguishing between possible and impossible events has also been assessed in preschool- to school-aged children. For example, Gautam et al. (2021) found that children under 5 years performed at chance when selecting between three containers: one that had a 0% chance of concealing a reward and two that had a 50% chance of concealing a reward. Shtulman and Carey (2007) found that, although 4- to 8-year-olds correctly judged impossible events (e.g., eating lightning for dinner) as such, they frequently regarded improbable events (e.g., getting struck by lightning) as impossible too. Weisberg and Sobel (2012) likewise found that 4-year-olds would categorize improbable events as impossible. Interestingly, however, they found that children preferred to develop their own stories with improbable rather than impossible events. This would suggest that children did possess some level of sensitivity to or knowledge of the distinction but perhaps struggled to communicate this insight without the surrounding context. Thus, it is still unclear when children become capable of reasoning about the possibility or impossibility of given events. A corollary question is when children begin to consider the uncertainty of particular future events and imagine alternative possible futures. Some research suggests that children can consider “future hypotheticals” from around age 3 (Beck et al., 2006; Gautam et al., 2019; Perner et al., 2004; Riggs et al., 1998; Robinson & Beck, 2014). For example, Beck et al. (2006) presented children with a toy slide that had one entrance but forked into two exits. They then introduced a toy mouse that was going to run down the slide and asked children to lay out cottonwool mats to cushion the mouse’s landing. Results showed that after the mouse had run down one exit, 3- to 4-year children were able to correctly answer the question, “What if next time he goes the other way?” by placing a mat at the alternate exit. Interestingly, children younger than 5 struggled to prepare for both outcomes before the mouse ran (i.e., by preemptively placing mats at both exits). This study, however, involved several intermediate steps and complex linguistic demands, potentially preventing younger children from demonstrating competence. The “forked-tube” task, developed by Redshaw and Suddendorf (2016), was designed to assess children’s understanding of future uncertainty without such complex demands. Again, children were required to prepare for a single future event with two mutually exclusive potential outcomes. A vertical forked tube had one opening at the top and two exits at the bottom, such that a ball dropped from the top could exit from either the right or left side, and subjects were asked to catch it as it exited. The authors tested 2- to 4-year-old children and found that, over the course of 12 trials, 2-year-olds typically placed their hands under one of the exits (thus failing to catch the reward on around half of the trials). By contrast, many 3-year-olds and most 4-year-olds spontaneously and consistently covered both exits, demonstrating the capacity to prepare for mutually exclusive future event outcomes. These findings have since been replicated crossculturally (Redshaw et al., 2019) and with various modifications of this simple task (Redshaw et al., 2018; Suddendorf et al., 2017). Overall, the results from these studies suggest that, by the age of 3–4 years, many children can recognize that some future events are uncertain and prepare for alternative possibilities. It has not been ruled out, however, that some children may have passed forked-tube tasks even without the ability to reason about possibilities. For example, a child may simply remember that sometimes the ball has exited from the left, and sometimes the ball has exited from the right, and place a hand under each exit associated with such a memory, without conceiving of these as two alternative versions of the same event. Alternatively, a child may simply match the affordances of the two tube exits with the affordances of their two hands, and thus place a hand under each exit even without thinking about mutually exclusive possibilities. Such alternative explanations persist partly because the task assesses children’s spontaneous actions, rather than giving them a choice between actions that would either be consistent or inconsistent with an understanding of possibilities. Indeed, in a recent study where children were given the choice between placing a single container under one of three exits—one with a 100% chance of reward and two with a 50% chance of reward—3- and 4-year-olds performed poorly (B. Leahy, 2022). We therefore devised a similar choicebased task to assess whether children could discriminate between future events with merely possible outcomes (50% chance of reward) and future events with guaranteed outcomes: either 0% chance of reward or 100% chance of reward. Unlike B. Leahy (2022), however, we always presented children with a simple decision between two options: left or right. The Present Study Our task adapted elements from Redshaw and Suddendorf’s (2016) forked-tube task and also from a paddle-box task developed by Tecwyn et al. (2013, 2014). Tecwyn et al.’s task required children to navigate a route from a reward’s starting position, through up to three levels of rotatable paddles, toward particular locations at the bottom of an apparatus. Participants could turn each paddle to either the left or the right, such that the reward would fall in a predictable manner into the next level of the apparatus. We adopted this basic design to give participants the opportunity to determine in which of two tube apparatuses a target would fall. In our experiments, 1882 CRIMSTON, REDSHAW, AND SUDDENDORF This document is copyrighted by the American Psychological Association or one of its allied publishers. This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. turning a paddle in a particular direction would sometimes lead to a predictable positive outcome, sometimes lead to a predictable negative outcome, and sometimes lead to an unpredictable positive or negative outcome. That is, children were given the choice between turning the paddle in such a manner that would either lead to a guaranteed (positive or negative) outcome or an uncertain outcome with two possibilities. Experiment 1 Two- to 5-year-old children were presented with a clear acrylic apparatus containing a paddle that could be turned to either the left or the right (see Figure 1). On each side of the paddle was either a single tube (with one opening and one exit) or a forked tube (with one opening and two exits). A marble was placed on a paddle above the tubes and children were asked to try to send the marble through one of the tubes using a handle attached to the paddle, such that they could retrieve the marble from the bottom of the apparatus. Critically, some of the tube exits were blocked, altering the apparent probability of retrieving the marble if the paddle was turned to the corresponding side. In all four conditions, one of the two tubes was two-pronged, with one exit open and one exit blocked, such that children should have inferred that the chance of receiving the reward by turning the paddle in that direction was uncertain (i.e., 50%). Turning the paddle in the other direction always resulted in a certain outcome (100% or 0%) with either one or two causal paths (see Figure 2 in Results for a schematic depiction of example tube combinations): Condition A: one-pronged with the exit open (100% chance of reward) Condition B: two-pronged with both exits open (100% chance of reward) Condition C: one-pronged with the exit closed (0% chance of reward) Condition D: two-pronged with both exits closed (0% chance of reward) The conditions, therefore, varied on two dimensions: (a) whether the certain outcome was a reward (A and B) or a failure (C and D), and (b) whether the certain outcome had one causal chain (A and C) or two possible causal chains (B and D). In Conditions A and B, the optimal response was to turn the paddle toward the tube with a certain reward; whereas in Conditions C and D, the optimal response was to turn the paddle toward the tube with a 50% chance of reward. This allowed us to examine whether children would make a rational response across a variety of situations. Experiment 1 was largely exploratory, however, if children do begin to understand mutually exclusive possibilities around the age of 3–4 (Redshaw & Suddendorf, 2016; Redshaw et al., 2019; Suddendorf et al., 2017), then they should consistently turn the paddle in the direction that gives them the highest chance of reward. Method Participants A total of 75 children participated in this study, but 11 were ultimately excluded from the analyses: nine due to failing to pass the Figure 1 The Apparatus Setup From the Child’s Perspective Note. Here, a blocked single and half-blocked two-pronged tube are attached (i.e., Condition C). Children need to turn the handle to decide into which tube they wish to send the marble and, if successful, then retrieve it through the circular opening at the bottom of the apparatus. See the online article for the color version of this figure. Figure 2 Children’s Performance by Age Group Across Trial Conditions Note. Dashed bars indicate conditions for which the certain outcome was a reward (i.e., A and B), and solid bars for which it was a failure (i.e., C and D). Gray-colored bars indicate conditions for which the causal chain was certain (i.e., A and C) and black for which it was uncertain (i.e., B and D). The dashed line (score of 1) indicates chance performance, while the solid line (score of 2) indicates maximum performance. The schematic tube depictions are representative of each condition; however, different visual combinations may have been shown to children based on the counterbalancing sequence to which they were assigned. WHAT ARE THE ODDS? 1883 This document is copyrighted by the American Psychological Association or one of its allied publishers. This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. manipulation check (seven 2-year-olds and two 3-year-olds) and two due to experimenter error. Thus, the final sample included 64 children: 16 two-year-olds (Mage = 2.7 years, SD = 0.2), 16 three-yearolds (Mage = 3.5 years, SD = 0.2), 16 four-year-olds (Mage = 4.5 years, SD = 0.3), and 16 five-year-olds (Mage = 5.4 years, SD = 0.3); with an even gender split in each age group. This sample size was chosen in accordance with typical cell sizes in similar developmental psychology studies with children aged between 2 and 5 (e.g., Redshaw & Suddendorf, 2016; Sobel et al., 2009), and it also enabled one child of each age to be assigned to each of 16 counterbalancing conditions. A post hoc power analysis indicated that this sample gave us a 99.5% chance of detecting the hypothesized large age effect (equivalent to r = .50) in children’s overall performance. The majority of children (n = 61) were recruited and tested at a booth at the Queensland Museum in Brisbane, Australia. To balance groups, however, the final three were recruited through a participant database and tested at the Early Cognitive Development Centre at the University of Queensland. The study was approved as conforming to ethical standards by the university’s human research ethics committee (approval number: 2019000349). Materials The apparatus consisted of an acrylic screen, approximately 50 cm high and 50 cm wide, with a small circular opening at the bottom, approximately 9 cm in diameter (see Figure 1). The screen was secured to a large whiteboard, approximately 80 cm long by 50 cm wide, which sat on the ground. Near the top of the screen, on the children’s side, there was a handle, approximately 16 cm in length. This handle controlled a V-shaped paddle on the experimenter’s side of the apparatus, which held a marble. A semicircle was cut out of either end of the paddle so that, when turned, it would lead the marble into the tubes on either side of the apparatus. These tubes were secured via clips and Velcro and were made from 1 in. conduit. The entrance and exits to all tubes were made out of transparent plastic, but an opaque t-section was used to hide a platform inside the two-pronged tubes. An opaque coupler was also added to the middle of single tubes to make them perceptually analogous to the two-pronged tubes. The platform inside the two-pronged tubes determined the direction of the reward and was surreptitiously controlled by the experimenter using a small handle attached to the back of the tube. If a reward exited a nonblocked prong of the tubes, it would fall onto a large white ramp attached to the back of the apparatus and become retrievable through the opening of the apparatus. Thick sponges were used to block the tube’s prongs and impede the marble in the relevant conditions. Procedure Exposure/Training Phase Stage 1: Demonstration of Paddle Mechanism. Children were asked to watch as the experimenter attached two transparent single tubes to the apparatus and placed a marble on the paddle. The experimenter then demonstrated that turning the paddle left or right would drop the marble into the corresponding tube. After falling through the tube, the marble became retrievable from the bottom of the apparatus via a small opening on the child’s side. Stage 2: Paddle Practice. Children were then given the opportunity to practice and instructed to try turning the handle, dropping the marble once each way. Stage 3: Demonstration of Blocking Principle. In some conditions, tubes were blocked by a sponge. The experimenter took a piece of sponge, stuck it into the end of one of the single tubes, and demonstrated that the marble could still fall freely through the unblocked tube but that if it fell into the blocked tube, it would become stuck. The other tube was then blocked, and the demonstration was repeated. Stage 4: Training Phase. The apparatus was again set up with one unimpeded and one blocked single tube; the child was told it was their turn and asked which way they should turn the handle to retrieve the marble. In addition to acting as a training phase, this stage also allowed us to ensure that children understood the basic premise of the task (i.e., to avoid blocked tube exits) before moving on to the experiment. Children, therefore, were given three chances to pass four trials in a row (the experimenter swapping the blocked side each time); if they failed to pass four trials in a row they were excluded. Stage 5: Introduction of Two-Pronged Tube. Finally, the experimenter attached 2 two-pronged tubes to the apparatus and told the child that these tubes were special because you could never tell which way the marble would exit. The experimenter then demonstrated the marble coming out of each of the four exits (two exits for each tube) in a pseudorandom order and reiterated the unpredictability of the outcome. Experimental Phase. Each child received eight test trials, comprising two trials of each condition. We counterbalanced the trial order, tube arrangement, and direction of optimal response, resulting in 16 possible sequences of trials (see the online supplemental material). If children passed the training phase, they were assigned to one of these 16 sequences (counterbalanced within each age group). At the beginning of the trials, children were informed the real game was starting and that from hereon they would be able to exchange each marble retrieved for a sticker of their choosing. On each trial, the tubes were set up and children were asked to look at them before the experimenter put the marble on the paddle. Regardless of whether they turned the paddle in the correct/logical or incorrect/illogical way, if they retrieved the marble, the experimenter would say “You got it!” and offer them a sticker. If they went the incorrect way and the marble became stuck, the experimenter would simply say “Uh oh, it got stuck!” While, if they went the correct way but the marble got stuck (i.e., in a half-blocked two-pronged tube), the experimenter would say “Uh oh, you never know with those ones!” The experimenter live-coded all testing sessions. An independent rater, blind to the study’s hypotheses, later performed reliability coding on video-recorded responses from approximately 20% of the sample (i.e., 12 participants), with a percentage coding agreement of 97%. Results Group-Level Performance Across Conditions Children’s performance was analyzed across trials at a group level using a generalized estimating equation (GEE) analysis, summarized in Table 1. We chose to use a GEE analysis because we had a categorical dependent variable (i.e., pass/failure performance) which was repeated across multiple trials (Stroup, 2012). This analysis revealed the main effects of age and certain outcome types (i.e., whether the certain outcome in the pairing was a reward [conditions 1884 CRIMSTON, REDSHAW, AND SUDDENDORF This document is copyrighted by the American Psychological Association or one of its allied publishers. This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. A and B] or a failure [conditions C and D]), but no effect of the causal chain (i.e., whether the certain outcome had one potential exit [A and C] or two [B and D]) and no interactions. For the main effect of age, children were more likely to provide an apparently rational response as they increased with age. Notably, however, follow-up of one-sample t tests revealed that children from all age groups performed significantly above a chance level of 50% when collapsed across conditions, all M . 5.43/8, p , .001. The main effect of certain outcome types indicated that children performed significantly better when the certain outcome was a failure in conditions C and D (mean trials passed = 1.73/2, SE = .05) than when it was a reward in conditions A and B (mean trials passed = 1.56/2, SE = .04; see Figure 2). Individual-Level Performance Across Conditions Children’s individual performance across trials was also analyzed and is summarized in Table 2. As the a priori chance of passing at least seven out of eight trials is 3.2%, or p = .032 (Binomial test), we considered a child to be performing significantly above chance if they passed either seven or eight trials out of eight. According to this criterion, 1/16 two-year-olds (6.25%), 3/16 three-year-olds (18.75%), 13/16 four-year-olds (81.25%), and 16/16 five-year-olds (100%) performed significantly above chance. Importantly, however, one must keep in mind that 3.2% of children would be expected to pass by chance alone. Although the proportions of passing 3-yearolds, p = .013, 4-year-olds, p , .001, and 5-year-olds, p , .001, were above this chance level, the proportion of passing 2-year-olds was not, p = .406. At the individual level, therefore, there was evidence that some 3-year-olds and many 4- and 5-year-olds were more likely to select the rational option than would be expected by chance. Notably, no children performed significantly below chance (i.e., 0 or 1 out of 8), suggesting that children were not simply motivated to make the marble get stuck by directing it to the blocked exits. Discussion As expected, children’s performance significantly improved with age. At an individual level, only one 2-year-old and three 3-year-olds performed above chance, compared to the vast majority of 4- and 5-year-olds. At face value, this pattern suggests that children do not typically begin to distinguish merely possible future outcomes from guaranteed future outcomes until around age 4. However, when considered at a group level, all age groups performed above chance, consistent with the possibility that even some 2- and 3-yearolds had some minimal capacity to solve the task, albeit they could not reliably demonstrate this capacity across eight trials. Indeed, the suggestion that a minority of such younger children possess a rudimentary capacity to reason about possibilities is consistent with the pattern of results from the forked-tube paradigm (Redshaw & Suddendorf, 2016; Suddendorf et al., 2017). Interestingly, we also found that although the complexity of the causal chain did not affect children’s performance, the nature of the guaranteed outcome did. That is, children were better at avoiding certain losses (i.e., avoiding tubes with a 0% probability of returning the marble), rather than gaining certain rewards (i.e., pursuing tubes with a 100% probability of returning the marble). Of course, while these results appear to provide evidence that preschoolers can distinguish between possible and guaranteed future outcomes in a choice-based task, it is possible that children may have been relying on simpler heuristics to solve the problem. The two most straightforward of such heuristics would be opting for the side with more open exits and/or avoiding the side with more blockages. It also remains unclear when children become capable of distinguishing between possible future outcomes with varying degrees of probability. Notably, there is a wealth of research suggesting that infants are already sensitive to probabilistic outcomes between 6 and 15 months of age (e.g., Denison & Xu, 2010a, 2010b, 2012, 2014; Denison et al., 2013, 2014; Gweon et al., 2010; Téglás et al., 2007, 2011; Xu & Denison, 2009; Xu & Garcia, 2008). For example, infants typically show a heightened level of interest when a white ball is drawn from a box they know to contain predominantly red balls (Xu & Garcia, 2008). Twelve-month-olds even seem sensitive to dynamic shifts in probabilistic outcomes over time, such that they are more likely to expect a particular-colored ball to emerge from a lottery device when they have reason to expect that more balls of that color are close to the exit of the device (Téglás et al., 2007). However, such studies typically fall short of showing that infants can make rational decisions between actions that have different probabilities of leading to a positive outcome. A few studies have also shown that infants (e.g., Denison & Xu, 2010a), toddlers (e.g., Goddu et al., 2021; Waismeyer et al., 2015), and preschoolers (e.g., Denison et al., 2010; Gualtieri & Denison, 2019; Kushnir & Gopnik, 2005; Sobel et al., 2009) can provide apparently rationally responses on the basis of relative probabilities for outcomes that have already occurred. For instance, Denison and Xu (2010a) found that 12- to 14-month-old infants preferred to select a hidden candy that was pulled from a jar containing mostly liked candies, rather than a hidden candy pulled from a jar of mostly disliked candies. It should be noted, however, that when Girotto et al. Table 2 Number of Children From Each Age Group Passing Each Proportion of Eight Trials Age group 3/8a 4/8 5/8 6/8 7/8 8/8 Above chance?b 2 years 0 3 4 8 1 0 1 (6.25%) 3 years 2 0 2 9 1 2 3c (18.75%) 4 years 0 0 1 2 3 10 13c (81.25%) 5 years 0 0 0 0 5 11 16c (100%) a No children passed fewer than three trials. b This represents the total number of children who passed at least seven trials (p = .032). c Proportion of children passing above chance is itself above a chance level of p , .05. Table 1 GEE Analysis of Factors Influencing Children’s Performance in Experiment 1 Factor χ2 p w Main effects model Age 28.08 ,.001 0.66 Certain outcome type 6.58 .010 0.32 Casual chain 0.15 .696 0.05 Interaction Age × Certain Outcome Type 0.85 .357 0.12 Note. GEE = generalized estimating equation. WHAT ARE THE ODDS? 1885 This document is copyrighted by the American Psychological Association or one of its allied publishers. This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. (2016) tried replicating Denison and Xu’s (2010a) finding with 3- to 5-year-old children, the participants’ verbal judgments of the task did not reveal probabilistic understanding until age 5—and the authors therefore suggested that infants may solve such tasks via simpler means. Such results also shed no light on the question of whether children can reason about the varying probabilities of alternative future outcomes and select the course of action that provides them with the optimal chance of success. Examining this and investigating children’s potential use of simpler heuristics, such as counting the number of exits or blocks, was therefore the aim of Experiment 2. Experiment 2 In Experiment 2, we introduced a three-pronged tube to our apparatus configuration (see Figure 3). The three-pronged tube allowed us to include apparent probabilities of 33% and 67% in the experimental trials; meaning that, among other combinations, we could now present trials where both tubes would have exactly one exit blocked but with different probabilities of the marble making it through (e.g., 50% vs. 67%). The three-pronged tube also allowed us to examine whether children were relying on the heuristics discussed above to solve the task (i.e., opting for the side with more openings and/or avoiding the side with more blockages). This was achieved by creating combinations where such strategies would not lead to success. For example, children would be led astray if they focused simply on the number of open exits when presented with an open single tube on one side (100%) and a three-pronged tube with two exits open and one blocked on the other (67%). Likewise, if children were presented with a two-pronged tube with one exit blocked (50%) and a three-pronged tube with one exit blocked (67%), then they could not simply rely on the number of blocked exits (1 vs. 1) to derive the optimal response. Experiment 2 was split into two parts, with the same children completing both parts sequentially. In Part 1, we examined the 8 three- versus one- and three- versus two-pronged configurations with different probabilities made possible by the addition of the three-pronged tube: 0% versus 33%, 0% versus 50%, 0% versus 67%, 33% versus 50%, 33% versus 100%, 50% versus 67%, 50% versus 100%, and 67% versus 100% (see Figure 4 in Results for a schematic depiction of all example tube combinations presented in Experiment 2). This also allowed us to examine several factors potentially contributing to children’s performance, including whether the type of certain outcome (i.e., 0%, 100%, or no certain outcome), total number of exits or prongs (i.e., four or five), difference between probabilities of reward (i.e., 16.7%, 33.3%, 50%, and 66.7%), or the cumulative probability of reward (i.e., 33.3%, 50%, 66.7%, 83.3%, 116.7%, 133.3%, 150%, and 166.7%) on a given trial affected performance. One potential problem of introducing the three-pronged tube was that children may have considered the tube’s central prong as a more likely exit point than the other two. If this was the case, children may have preferentially selected three-pronged tubes with an unimpeded central prong and avoided those with a blocked central prong (similar to a “gravity bias,” Hood, 1998). To assess this, in Part 2, we decided to give children three versions of the same three- versus three-pronged probability pairing (i.e., 33% vs. 67%), manipulating how the central prongs were blocked on each trial. One configuration had both central prongs blocked, another configuration had both central prongs open, and the third configuration had one central prong open and one blocked. Experiment 2 was preregistered on the Open Science Framework in October 2019, before the analysis of data (https://osf.io/x8as4/). The raw data, analytic code, and the online supplemental materials for both experiments can also be found at Anonymous: https://osf.io/x8as4/?view_only=642d869148a84373b1 3343c3eddb3a9b. Original: https://osf.io/x8as4. Method Participants A total of 77 children participated in this experiment, with five 3-year-olds excluded from the analyses for failing to pass the manipulation check. Thus, the final sample included 72 children: 24 three-year-olds (Mage = 3.5 years, SD = 0.3, 11 girls), 24 four-year-olds (Mage = 4.6 years, SD = 0.3, 6 girls), and 24 five-year-olds (Mage = 5.5 years, SD = 0.3, 11 girls). We decided to keep the overall sample size similar to that from Experiment 1, given that it was sufficient to detect a significant and large age effect. Accordingly, a post hoc power analysis indicated that our final sample of 72 gave us a 99.8% chance of detecting the hypothesized large age effect (equivalent to r = .50) in children’s overall performance. Given that we found no effect of gender in Experiment 1, we decided that an even gender split was not necessary for Experiment 2. As in Experiment 1, participants were recruited and tested through a booth at the Queensland Museum in Brisbane, Australia. The study was Figure 3 Three-Pronged Tube Added to the Apparatus for Experiment 2 Note. See the online article for the color version of this figure. 1886 CRIMSTON, REDSHAW, AND SUDDENDORF This document is copyrighted by the American Psychological Association or one of its allied publishers. This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. conducted under the same ethics project approval as Experiment 1 (approval number 2019000349). Materials The materials for Experiment 2 were the same as for Experiment 1, with the addition of three-pronged tube, displayed in Figure 3. Procedure Exposure/Training Phase. The first three stages of Experiment 2—demonstrating the function of the paddle mechanism, allowing children to practice using the paddle, and demonstrating the blocking principle—were exactly the same as in Experiment 1. Stage 4: Introduction of Two- and Three-Pronged Tubes. The experimenter attached 1 two- and 1 three-pronged tube to the apparatus and informed the child that these tubes were special because you could never tell which way the marble would exit. The experimenter then demonstrated the marble coming out of each of the five possible exists across the two tubes in a pseudorandom random order, while reiterating the unpredictability of the outcome. Stage 5: Training Phase. The child was then presented with four trials to test their understanding of the blocking principle and the nature of each of the tubes. The experimenter attached various pairings of either one-, two-, or three-pronged tubes to the apparatus. In each pairing, one tube had a 0% chance of reward and the other a 100% chance of reward and the child was asked which way they should turn the paddle to retrieve the marble on each trial. As in Experiment 1, children were required to pass four consecutive trials and were given three attempts to do so; if they failed, they were excluded from the experiment. Experimental Phase. In order to reasonably counterbalance factors such as which exits were blocked, which direction was the “optimal response” and whether children were rewarded or not on a given trial, 16 approximately counterbalanced sequences were devised (perfect counterbalancing would have required hundreds of trials; see the online supplemental material). If children passed the practice trials, they were pseudorandomly assigned to one of these sequence pairs and the experimenter ran them through their respective trials as in Experiment 1. Children’s responses were filmed while also being live-coded by the experimenter. Blind interrater reliability coding on approximately 20% of the sample (i.e., 15 participants) indicated a percentage agreement of 100%. Results Part 1 Children’s performance was analyzed using a GEE, as in Experiment 1. As preregistered, we initially ran a model with all examined independent variables included (see Table 3). Because of the high degree of multicollinearity between the fixed effects, however, we then used backward model selection to eliminate nonsignificant or highly colinear (variance inflation factor . 10) variables one-by-one. This left us with a model with significant variables of age and outcome type (i.e., whether there was a 0%, 100%, or no certain outcome in the pairing). Children performed significantly better when there was a certain outcome in the pairing as opposed to when both outcomes were uncertain (see Figure 4). This was true whether that certain outcome was a guaranteed reward (χ2 = 26.06, p , .001) or a guaranteed loss (χ2 = 35.67, p , .001);
CRIMSTON, J.; REDSHAW, J.; SUDDENDORF, T. What are the odds? Preschoolers’ ability to distinguish between possible, impossible, and probabilistically distinct future outcomes. Developmental Psychology, [s. l.], v. 59, n. 10, p. 1881–1891, 2023. DOI 10.1037/dev0001587.supp (Supplemental). Disponível em: https://search.ebscohost.com/login.aspx?direct=true&AuthType=ip,sso&db=psyh&AN=2024-12582-009&site=ehost-live. Acesso em: 4 out. 2023.
Read the article and answer the following questions:
a) What is the Research Question the article is trying to address?
b) Which Domain (Physical, Cognitive, Psychosocial) would this article fit into?
c) How does this article address age (control, measure, group)?
i) If they age for grouping, it this Longitudinal, Cross-Sectional, or Sequential
d) What are the IVs
e) What are the DVs
10) Write a 1-2 page review of the article including
a) Why did you choose this article/what were you interested in learning
b) What did the article find
c) What did you learn about the topic and research question being addressed in this study
d) What would you be interested in finding more out about with regard to this study?
Submission should include:
a) Title page
b) Q&A from question 9
c) 1-2 page review
d) Reference page
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