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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 |
