Martin, M. A. (2003), "'Itís like...you know': The Use of Analogies and Heuristics in Teaching Introductory Statistical Methods," Journal of Statistics Education, 11(2). (www.amstat.org/publications/jse/v11n2/martin.html)
Link to a response from the author: http://www.amstat.org/publications/jse/v11n3/martin_letter_response.html
As my explorations (Lesser 1994; Lesser 2002) of the appropriate use of counterintuitive examples have always also been accompanied by the use of intuitive analogies, I read with great interest Michael Martinís article on this latter topic in the July 2003 issue of JSE. While I know it is nearly impossible for an article to be exhaustive, the quest to offer a more complete set of analogies is important because, as Duit (1991, p. 665) notes, "[a] main problem with the approach is that there may not be enough good anchoring situations and bridging analogies available." Towards this end, allow me to supplement Martinís substantial and well-articulated collection with five additional examples discussed in Lesser (1994) that I have found useful in my teaching:
First, the rich crime-and-punishment metaphor for hypothesis testing can be extended (see, for example, Evans 1986) to a detective searching for clues in that chances of discovering significant evidence against the null hypothesis increase if the search can be narrowed by a priori considerations (that is, a one-tailed test), but decrease if the search must extend to both possible locations of significant evidence (that is, a two-tailed test).
Evans (1986) also offers an analogy on the topic of correlation between two variables. He describes how the possible relative vertical positions of neighboring merry-go-round horses illustrate patterns of positive, negative and no correlation.
When teaching confidence intervals, I enjoy using the analogy of falling leaves, as described by Weaver (1992, p.178): "As the trees shed their leaves, piles form around the trunks ... . Imagine standing next to a treeís trunk [estimated population mean] and picking up a leaf [sample mean] from the [normal-shaped] pile... . How sure are you that this leaf came from the same tree and not a neighboring one?"
An analogy (that might be even more student-friendly than signal-to-noise ratio) for introducing experimental design is the game of basketball, as used by Polyson and Blick (1985), who articulate counterparts to hypotheses, variables, replication, and counterbalanced design. Most of this analogy is not limited to basketball and can be applied to the team sport of one's choice.
Finally, Freedman, Pisani, Purves, and Adhikari (1991, p.339) offer an accessible analogy to understand how sample quality (that is, randomness) can be far more important than sampling fraction: "Suppose you took a drop of liquid from a bottle, for chemical analysis. If the liquid is well mixed, the chemical composition of the drop would reflect quite faithfully the composition of the whole bottle, and it really wouldnít matter if the bottle was a test tube or a gallon jug."
Lawrence M. Lesser
Armstrong Atlantic State University
11935 Abercorn Street
Savannah, GA 31419-1997
Duit, R. (1991), "On the role of analogies and metaphors in learning science," Science Education, 75(6), pp. 649-672.
Evans, G. F. (1986), "Getting through statistics with the help of metaphors," Journal of Education for Business, 62(1), pp. 28-30.
Freedman, D., Pisani, R., Purves, R., and Adhikari, A. (1991), Statistics (3rd ed.), New York: W. W. Norton.
Lesser, L. M. (1994), "The Role of Counterintuitive Examples in Statistics Education," unpublished Ph.D. dissertation, University of Texas at Austin.
Lesser, L. M. (2002), Letter to the Editor, Journal of Statistics Education [Online], 10(1). (www.amstat.org/publications/jse/v10n1/lesser_letter.html)
Polyson, J. A., and Blick, K. A. (1985), "Basketball game as psychology experiment," Teaching of Psychology, 12(1), pp. 52-53.
Weaver, K. A. (1992), "Elaborating selected statistics concepts with common experience," Teaching of Psychology, 19(3), pp. 178-179.
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