On the Usefulness and Limitations of Diagrams in Statistical Training

On the Usefulness and Limitations of Diagrams in Statistical Training,Atsushi Terao

On the Usefulness and Limitations of Diagrams in Statistical Training  
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The purpose of this study was to examine the use- fulness and limitations of vector diagrams, con- sisting of lines with arrows representing variables, in statistical training. Nineteen undergraduates learned advanced level statistics either with vec- tor diagrams or in the conventional way and solved three problems. Vector diagrams sometimes helped the students understand descriptions in the text which were difficult in conventional explanations, but caused other difficulties. Vector diagrams were useful for solving one of the three problems, but not the other two. It is concluded that a property of di- agrams or formulae can be a double-edged sword. Students who are majoring in psychology or other relevant disciplines have to study statistics. Despite substantial effort by teachers, understanding statis- tics is often difficult for many students. This paper reports the results of a practical experiment in which the students learned to employ either "vector dia- grams" or a conventional formula-based approach to the basics of regression analysis. The students were then asked to solve three problems using the given technique they learned. Unlike many previous studies on using diagrams in educational settings, which focus only on the useful- ness of diagrams, this study also investigates limita- tions of diagrams. Research on diagrammatic rea- soning has found many "good" properties of dia- grams (e.g., Barwise & Etchmendy, 1996; Cheng & Simon, 1995; Larkin & Simon, 1987). The re- searchers seem to consider these properties as if they are always support (at least do not impair) under- standing and problem solving. The results of this study suggest that the same property, which defi- nitely makes the solution of a problem easy, some- times makes another problem difficult. Similarly, the results suggest that formulae do not necessarily have "bad" properties. The vector diagrams used in this study consist of several vectors drawn as lines with arrows, each of which corresponds to a variable. For example, the correlation coefficient is defined as cosθ where θ is the angle between two vectors, ~
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