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ERIC Number: ED502272
Record Type: Non-Journal
Publication Date: 2008-Aug
Pages: 22
Abstractor: ERIC
Students' Conceptual Metaphors Influence Their Statistical Reasoning about Confidence Intervals. WCER Working Paper No. 2008-5
Grant, Timothy S.; Nathan, Mitchell J.
Wisconsin Center for Education Research (NJ1)
Confidence intervals are beginning to play an increasing role in the reporting of research findings within the social and behavioral sciences and, consequently, are becoming more prevalent in beginning classes in statistics and research methods. Confidence intervals are an attractive means of conveying experimental results, as they contain a considerable amount of information in a concise format. The objectives of this study are to (1) show that the theory of conceptual metaphor as delineated in contemporary embodied cognition is a useful framework for describing statistics students' conceptions of confidence intervals; and (2) provide empirical evidence from discourse and gesture that graduate students in social science use at least two competing conceptual metaphors for confidence limits that have important implications for the understanding and application of statistics and for the reform of statistics education. In the first metaphor--Confidence Intervals Are Changing Rings Around a Fixed Point ("Changing Ring metaphor")--confidence intervals are moving disks of various diameters covering a fixed but unknown point, like horseshoes of varying widths pitched at a fixed stake. Key to this correct conceptual metaphor is that the interval is a property of a sample but not of the population. Here, the diameter of the disk (i.e., the length of the confidence interval) changes from sample to sample, whereas the location of the stake (i.e., the population parameter or population mean) is fixed across samples but generally unknown. In contrast, the second metaphor--Confidence Intervals Are Changing Points on a Fixed Disk ("Fixed Disk metaphor")--conceptualizes confidence intervals as fixed-diameter disks onto which successive points are placed. In this incorrect metaphor, the population parameter can change from sample to sample. The interval is of a fixed length, and each experiment results in placing a new parameter somewhere onto the fixed-diameter disk. One possible source of this second metaphor is a suspected confusion between acceptance regions in hypothesis testing and confidence intervals, concepts that tend to be taught in close proximity to one another in statistics textbooks. The Fixed Disk metaphor will generally lead to a misinterpretation of the confidence interval that results in inaccurate problem solving. By better understanding students' mental representations of confidence intervals and appealing to the metaphors they convey, the authors hope to improve both statistics instruction and education researchers' uses of statistical tests. Interview items are appended. (Contains 5 tables and 4 figures.)
Wisconsin Center for Education Research. School of Education, University of Wisconsin-Madison, 1025 West Johnson Street Suite 785, Madison, WI 53706. Tel: 608-263-4200; Fax: 608-263-6448; e-mail:; Web site:
Publication Type: Reports - Evaluative; Tests/Questionnaires
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: Wisconsin Center for Education Research
Grant or Contract Numbers: N/A