Reasoning from Data: The Effect of Sample Size and Variability on Children’s and Adults’ Conclusions
Reasoning from Data: The Effect of Sample Size and Variability on Children’s and Adults’ Conclusions
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从数据推理：样本量和变异性对儿童和成人结论的影响
DOI：
10.4324/9781315782379-146
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Bradley J. Morris
中科院分区：
文献类型：
--
作者：
Amy M. Masnick;Bradley J. Morris
从数据中推理：样本大小和变异性对儿童和成人结论的影响。Masnick（masnick@andrew.cmu.edu）卡内基梅隆大学心理学系匹兹堡PA 15213布拉德利J.莫里斯（bjmorris@pitt.edu）匹兹堡大学学习、研究与发展中心匹兹堡PA 15260摘要数据解释是科学实验的关键部分，因为它涉及将一个人的背景理论知识应用于数据的特征。虽然许多研究者已经研究了背景知识的影响，但很少有人考虑到数据特征对决策的影响。在这项研究中，我们提供了一系列的数据集，在不同的样本量，数据对的一致性和相对于平均值的变异性，三年级，六年级和大学本科生。我们发现，在所有年龄段，参与者对样本量以及比较数据集中是否存在重叠数据点都表现出敏感性，但在使用的理由和从数据中得出的结论方面存在年龄差异。数据解释是科学实验的关键部分。对数据特征的期望被认为是评估数据的一个重要组成部分（Kahneman & Tversky，1973）。这些期望基于所考虑的领域的理论知识和数据本身的特征。虽然科学思维中的大量研究考察了域理论对数据评估的影响（例如，Klahr，2000年; Koslowski，1996年; Kuhn，Garcia-Mila，Zohar，& Andersen，1995），关于数据的特征如何影响儿童和成人如何解释它知之甚少。科学的一个重要组成部分是区分真实的影响与错误，或由被探索的因素以外的因素引起的影响。在科学实验室，统计学是帮助做出这些决定的重要工具。当存在极不可能偶然发生的差异时，科学家可以更有信心地从数据中得出结论。在日常生活中，我们经常在没有正式统计数据的情况下对证据做出决定。在这种情况下，我们只能依靠理论和预期。然而，在许多情况下，我们没有强有力的背景信息，因此只有基于数据的证据。小学生在评估数据方面似乎有很大的障碍--他们对世界的知识基础比较小，对统计及其应用的正规知识也比较少。小学的学生开始学习实验和数据解释，三年级到六年级是对基础科学基本原理的理解有重要增长的时期，例如变量控制策略（例如，Chen & Klahr，1999）。此外，小学教师通常会让孩子们进行重复的事件试验，并解释说这就是科学的工作方式（Klahr，Chen & Toth，2001）。当孩子们不知道正式的统计技术时，在评估课堂内外的数据时，我们希望他们依靠他们在该领域的非正式知识。但是，什么构成了统计推理的“非正式”概念呢？我们建议两个组成部分：对数据分布的期望和对样本大小的影响的期望。一些研究对数据分布的预期进行了研究，研究了概率估计。例如，当给出一系列抛硬币的数据时，参与者预期每隔一次抛硬币都会有一枚硬币落在“正面”上（Gilovich，1991）。这表明，参与者对一系列抛硬币中的数据分布有一个隐含的预期，并且对“随机性”的判断（至少部分）是基于预期和数据模式之间的映射。最近，一些人认为，五岁或六岁的孩子对概率有功能性的理解（Schlottman，2001）。虽然在几个领域有相关的研究，但很少有研究明确关注数据的特征以及这种关注对结论的影响。有证据表明，不同年龄的儿童确实认识到数据集的不同属性，这种认识反过来会影响他们得出的结论。例如，Jacobs和Narloch（2001）发现，7岁的儿童可以使用样本大小和变异性信息来推断未来事件的可能频率。变异性的差异是基于对基本速率的先验知识（即，有多少大象有两只眼睛，有多少鸟有一种特定的颜色）。本研究中使用的样本量差异很大，在事件发生前有1、3或30个事件。
Reasoning from Data: The Effect of Sample Size and Variability on Children’s and Adults’ Conclusions Amy M. Masnick (masnick@andrew.cmu.edu) Department of Psychology, Carnegie Mellon University Pittsburgh PA 15213 Bradley J. Morris (bjmorris@pitt.edu) Learning, Research, & Development Center, University of Pittsburgh Pittsburgh PA 15260 Abstract Interpretation of data is a critical part of scientific experimentation because it involves applying one’s background theoretical knowledge to the characteristics of the data. Though many researchers have examined the impact of background knowledge, few have considered the impact of the characteristics of the data in making decisions. In this study, we presented 3 r d graders, 6 th graders, and college undergraduates with a series of datasets that varied in sample size, consistency in data pairs and variability relative to the mean. We found that at all ages, participants showed sensitivity to sample size and whether or not there were overlapping data points in comparative datasets, but that there were age differences in the justifications used and in conclusions drawn from the data. Interpretation of data is a critical part of scientific experimentation. Expectations about features of the data have been suggested as an important component in assessing data (Kahneman & Tversky, 1973). These expectations are based both on theoretical knowledge about the domain under consideration and on features of the data itself. While a large body of research in scientific thinking examines the influence of domain theory on the evaluation of data (e.g., Klahr, 2000; Koslowski, 1996; Kuhn, Garcia-Mila, Zohar, & Andersen, 1995), little is known about how the characteristics of data influence how children and adults interpret it. An important component of science is distinguishing real effects from error, or effects caused by factors other than the ones being explored. In the science laboratory, statistics is a vital tool to help make these decisions. When there are differences that are highly unlikely to occur by chance, scientists can feel more confident about drawing conclusions from data. In daily life, we regularly make decisions about evidence without the aid of formal statistics. In such cases, we resort to relying on theory and expectations. However, there are many situations in which we do not have strong background information, and thus only have evidence based in the data. Elementary school students seem likely to have an especially large handicap in evaluating data – they have a smaller knowledge base about the world and also have less formal knowledge about statistics and its applications. Students in elementary school are beginning to learn about experimentation and data interpretation, and third through sixth grade is a time of important increases in understanding of basic science fundamentals, such as the control of variables strategy (e.g., Chen & Klahr, 1999). In addition, elementary school teachers routinely assign children to perform repeated trials of events, explaining that this is how science is done (Klahr, Chen & Toth, 2001). In evaluating data in and out of the classroom when children do not know formal statistical techniques, we expect them to rely on their informal knowledge of the area. But what constitutes “informal” notions of statistical reasoning? We suggest two components: expectations about data distribution and expectations about the influence of sample size. Some research that has examined expectations for the distribution of data has looked at probability estimates. For example, when given data about a series of coin flips, participants expected that a coin would land on “heads” every other flip (Gilovich, 1991). This suggests that the participants had an implicit expectation of the distribution of data in a series of coin flips and that the judgment of “randomness” was (at least in part) based on a mapping between expectations and data patterns. More recently, some have argued that children as young as five or six have a functional understanding of probability (Schlottman, 2001). Although there is related research in several areas, few studies focus explicitly on the characteristics of the data and the effects this focus has on conclusions. There is some evidence that children at different ages do recognize different properties of datasets, and that this recognition in turn affects the conclusions they draw. For example, Jacobs and Narloch (2001) found that children as young as seven could use sample size and variability information in inferring the likely frequency of a future event. The differences in variability were based on prior knowledge of base rates (i.e., how many elephants have two eyes, compared to how many birds are a specific color). The sample sizes used in this study varied dramatically, with either 1, 3, or 30 instances of an event before the
影响因子：
4.6
作者：
Chen, Z;Klahr, D
通讯作者：
Klahr, D