Do infants and preschoolers quantify probabilities based on proportions?

Most statistical problems encountered throughout life require the ability to quantify probabilities based on proportions. Recent findings on the early ontogeny of this ability have been mixed: For example, when presented with jars containing preferred and less preferred items, 12-month-olds, but not 3- and 4-years-olds, seem to rely on the proportions of objects in the jars to predict the content of samples randomly drawn out of them. Given these contrasting findings, it remains unclear what the probabilistic reasoning abilities of young children are and how they develop. In our study, we addressed this question and tested, with identical methods across age groups and similar methods to previous studies, whether 12-months-olds and 3- and 4-years-olds rely on proportions of objects to estimate probabilities of random sampling events. Results revealed that neither infants nor preschoolers do. While preschoolers’ performance is in line with previous findings, infants’ performance is difficult to interpret given their failure in a control condition in which the outcomes happened with certainty rather than a graded probability. More systematics studies are needed to explain why infants succeeded in a previous study but failed in our study.

Methods
Children were recruited from a database of families who had voluntarily registered and agreed to participate. They were from mixed socioeconomic backgrounds and some family were plurilingual.

Each child underwent a preference test, a probability condition and a baseline condition. In the preference test, the experimenter presented children with two different Kinder eggs capsules, one empty and white and the other containing a fingerpuppet and blue. She hid both objects in separate cups and let subjects choose a cup (only subject choosing the cup containing the blue egg were kept in the final sample). In the probability condition, the experimenter presented subjects with two populations of Kinder eggs, one containing a higher proportion of blue eggs and the other a higher proportion of white eggs. She secretly drew one object out of each population, hid them in separet cups and let subjects choose between both cups. The same procedure was repeated in the baseline condition, in which one population only contained blue eggs and the other only white eggs. 

Every session was video recorded. Children's choices were coded from the videos. We coded it as a success when children chose the sample drawn out of the population with a higher proportion of blue eggs and as a failure when they chose the other sample.

日常生活中遇到的绝大多数统计问题，都需要具备基于比例量化概率的能力。关于这一能力的早期个体发育的现有研究结论并不一致：例如，当向被试展示装有偏好物品与非偏好物品的罐子时，12月龄婴儿似乎会依据罐内物体的比例，来预测随机从中抽取的样本内容，但3至4岁儿童并未表现出这一能力。鉴于这些相互矛盾的研究结果，目前仍不清楚幼儿的概率推理能力究竟具备何种特征，以及该能力是如何发展的。
本研究针对这一问题展开，采用跨年龄组一致的实验方法，并沿用与前人研究相似的实验范式，检验12月龄婴儿与3-4岁儿童是否会依据物体比例来估算随机抽样事件的概率。结果显示，两类被试均未表现出基于比例的概率推理能力。尽管学龄前儿童的表现与前人研究结果相符，但婴儿的表现却难以解释：他们在一项控制实验中出现了失误——该控制实验的结果是确定的，而非分级概率。未来仍需开展更多系统性研究，以解释为何婴儿在既往研究中表现出概率推理能力，而在本研究中却未能做到。
研究方法
被试来自自愿注册并同意参与实验的家庭数据库，其家庭社会经济背景多样，部分家庭为多语言家庭。
每名被试均需完成偏好测试、概率条件实验与基线条件实验。在偏好测试环节，主试向儿童展示两款不同的健达奇趣蛋胶囊（Kinder eggs capsules）：一款为白色空壳，另一款内含蓝色手指玩偶（fingerpuppet）。主试将两款物品分别藏入不同的杯子中，让儿童选择其一（最终样本仅保留选择了装有蓝色奇趣蛋的杯子的被试）。
在概率条件实验中，主试向被试展示两组健达奇趣蛋（Kinder eggs）：一组蓝色奇趣蛋的比例更高，另一组白色奇趣蛋的比例更高。主试分别从两组中偷偷抽取一件物品，将其藏入不同杯子后，让儿童在两个杯子间进行选择。基线条件实验采用相同流程，但两组奇趣蛋分别仅包含蓝色与白色的奇趣蛋。
所有实验环节均进行录像，后续从录像中编码儿童的选择结果：若儿童选择了来自蓝色奇趣蛋比例更高的组的抽取样本，则记为成功；若选择另一组的抽取样本，则记为失败。