Stephanie Lem

On the misinterpretation of histograms and box plots

Recent studies have shown that the interpretation of graphs is not always easy for students. In order to reason properly about distributions of data, however, one needs to be able to interpret graphical representations of these distributions correctly. In this study, we used Tversky’s principles for the design of graphs to explain how 125 first-year university students interpreted histograms and box plots. We systematically varied the representation that accompanied the tasks between students to identify how the design principles affected students’ reasoning. Many students displayed misinterpretations of histograms and box plots, despite the fact that they had the required knowledge and time to interpret the representations correctly. We argue that the combination of dual process theories and Tversky’s design principles provides a promising theoretical framework, which leads to various possibilities for future research.

Experts’ Misinterpretation of Box Plots – a Dual Processing Approach

Recent studies have shown that students often misinterpret the area of the box in box plots as representing the frequency or proportion of observations in that interval, while it actually represents density. This misinterpretation has been shown to be based on the saliency of this area and can be explained by heuristic reasoning as defined by dual process theories. In this study we tested whether expert users of box plots also display this misinterpretation and show signs of the same heuristic reasoning as found in students. Using a reaction time test, we found signs of heuristic reasoning in experts, both with respect to accuracy and reaction times. If even experts have difficulty interpreting box plots, one can question whether these are an appropriate form of representation to use when reporting data and deserve the prominent place they currently have in the statistics curriculum.

Refutational text and multiple external representations as a method to remediate the misinterpretation of box plots

Abstract The ability to interpret graphs is highly important in modern society, but has proven to be a challenge for many people. In this paper, two teaching methods were used to remediate one specific misinterpretation: the area misinterpretation of box plots. First, we used refutational text to explicitly state and invalidate the area misinterpretation of box plots. Second, we used multiple external representations (MERs): Histograms were used as an overlay on box plots in order to give students a better insight in the way box plots represent data distributions. Third, we combined refutational text and MERs. We found that refutational text was successful in improving students’ interpretation of box plots, but that the use of MERs did not improve students’ interpretation of box plots. The addition of MERs also did not increase the effect of refutational text.