Journal of Statistics Education, VION3: Garfield http://www .amstat.orglpubl ications/jse/v 1On3/garfieJd.html ---- Journal of - . sta tis tic s -- __ ' .:: : _ Education The Challenge of Developing Statistical Reasoning Joan Garfield University of Minnesota Journal of Statistics Education Volume 10, Number 3 (2002), www.amstat.orgipublications/jse/vlOn3 /garfield.htrnl Copyright �� 2002 by Joan Garfield, all rights reserved. This text may be freely shared among individuals, but it may not be republished in any medium without express written consent from the author and advance notification of the editor. Key Words: Assessment Statistical reasoning. Abstract This paper defmes statistical reasoning and reviews research on this topic. Types of correct and incorrect reasoning are summarized, and statistical reasoning about sampling distributions is examined in more detail. A model of statistical reasoning is presented, and suggestions are offered for assessing statistical reasoning. The paper concludes with implications for teaching students in ways that will facilitate the development of their statistical reasoning. 1. What is Statistical Reasoning? Statistical reasoning may be defmed as the way people reason with statistical ideas and make sense of statistical information (Garfield and Gal 1999). This involves making interpretations based on sets of data, graphical representations, and statistical summaries. Much of statistical reasoning combines ideas about data and chance, which leads to making inferences and interpreting,statisticahesults. Underlying this reasoning is a conceptual understanding of important ideas, such as distribution, center, spread, association, uncertainty, randomness, and sampling. Statistical reasoning is a topic of interest to many types of people, including: ��� Psychologists, who study how people make judgments and decisions involving statistical information (often using incorrect intuitions or misconceptions), ��� Doctors and others in the medical profession, who need to understand and interpret risks, chances of different medical outcomes, and test results, ��� Journalists and science writers, who are interested in how to best explain and critique statistical I of 12 11112/201010:52 AM

Journal of Statistics Education, VION3: Garfield http://www .amstat.orglpublications/j se/v 1On3/garfield.html information in the media, ��� Political analysts, who are interested in studying and interpreting polls and elections, and ��� Statistics teachers, who want to teach students not only a set of skills and concepts but also how to reason about data and chance. The expression "statistical reasoning" is widely used and appears in many different contexts. A Web search using the phrase" Statistical Reasoning" produced a list of almost three thousand Web pages that contain the words "statistical" and "reasoning." This list revealed the following categories of Web pages: ��� Advertisements for statistics textbooks (that have "statistical reasoning" in their titles or promotional materials), ��� Materials from Colleges' or instructors' Web pages for statistics courses offered in a variety of different disciplines (such as mathematics, statistics, psychology, education, engineering, physical therapy, and the health sciences), and ��� Presentations, grant proposals, and papers that include discussions of statistical reasoning. The Web search also produced the home pageof the electronic Journal of Applied Statistical Reasoning and a book (not a statistics textbook) deyoted to the topic of improving statistical reasoning (Sedlmeier 1999). A quick scan of the materials on the Web that describe courses or textbooks suggests that people are using the term "statistical reasoning" to represent the desired outcomes of a statistics course, and that this expression is used interchangeably with "statistical thinking." There were no clear definitions offered regarding what statistical reasoning means and there did not appear to be clear connections between what was in a course or textbook and the development of particular reasoning skills. For example, some courses were traditional statistics courses with a focus on computations and no use of computing packages. Some courses were more focused on concepts and big ideas, while other courses combined concepts, computation, and computing. Overall, there did not appear to be a consensus in the .broad statistics community as to what statistical reasoning means and how to develop this type of reasoning in statistics courses. The next section reviews some of the research literature on statistical reasoning and the ways this term has been used in research studies. 2. Statistical Reasoning in the Research Literature Chervaney, Collier. Fienberg, Johnson, and Neter (1977) and Chervaney, Benson. and lver (1980) defmed statistical reasoning as what a student is able to do with statistical content (recalling, recognizing, and discriminating among statistical concepts) and the skills that students demonstrate in using statistical concepts in specific problem solving steps. They viewed statistical reasoning as a three-step process: ��� Comprehension (seeing a particular problem as similar to a class of problems), ��� Planning and execution (applying appropriate methods to solve the problem), and ��� Evaluation and interpretation (interpreting the outcome as it relates to the original problem). The authors proposed a systems approach for teaching and assessing statistical reasoning based on this 20f12 11/12/201010:52 AM