# Moritz j b watson j m 2002 representing and

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Moritz, J. B. & Watson, J. M. (2002). Representing and questioning statistical associations . Manuscript in preparation. JONATHAN MORITZ University of Tasmania GPO Box 252-66, Hobart 7001, Australia
41 11. DEVELOPING AND ASSESSING STUDENTS’ REASONING IN COMPARING STATISTICAL DISTRIBUTIONS IN COMPUTER SUPPORTED STATISTICS COURSES ROLF BIEHLER Universität Gesamthochschule Kassel, Germany The paper summarizes results from some of our studies of students’ reasoning with data. We interviewed students after a computer supported course in statistics, which had an emphasis on exploratory data analysis (EDA). Our major goal was to support students’ thinking in terms of “distributions”. One of the issues we looked at was strategies and tools students used for comparing two data sets. Students had learned various displays and summaries including dot plots, box plots, histograms, mean, median, quartiles, interquartile range, variance and standard deviation. We consider a cultural practice of using just means for group comparison as critical and often misleading. The origin of EDA is closely related to this criticism. Before one uses certain summary statistics for comparisons, distributional assumptions have to be checked, data displays have to be used for becoming aware of distributional behaviour. Box plots were introduced as an exploratory tool which provide a multifaceted initial distributional summary including a robust measure of the center and information about the amount of spread above and below the center. The difference : + = 2 1 | ~ ~ 3 n i x x median x q i where x ~ is the median of the whole data set can be interpreted as an average deviation from the median in the upper half (similarly the difference 1 ~ q x ). In this sense the box plot is intended a center ± spread display. In our research we identified many “non-standard” uses of box plots. Students often frame group comparison tasks as hypothesis testing tasks such as: Is X larger in group 1 than in group 2? Example: Do boys (tend to) watch longer TV per week than girls? The expectation that this question has a definite answer is one of the obstacles that have to be overcome. Students are looking for a single comparison number, are irritated when quantiles in the box plot do not all point into the same direction. An interpretation of quartiles as medians of the lower (upper) half that could help is often not available. Students have difficulties in relating spread information to aspects of the context of the data. We think that the conscious introduction of the “uniform shift model”(group 2 distribution is just group 1 distribution uniformly shifted by a fixed amount) might help students. Looking for deviations from a shift model can draw attention to more complex distributional relation can occur.

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