HEURISTIC REASONING IN INTERPRETING BOX PLOTS: THE INFLUENCE OF ORIENTATION

Abstract

Abstract: We studied how graph design principles can predict specific reasoning mechanisms that occur when misinterpreting box plots, and, more specifically, the misinterpretation of the area as a representation of frequency or proportion of observations, instead of density. In previous studies this misinterpretation has been shown to be heuristic in nature and is elicited by the fact that box plots do not use space in a natural way. Graph design principles provide a theoretical framework for assuming that the orientation of a box plot could influence its interpretation. By analyzing reaction times and accuracy rates for different item types, we explored whether there indeed is an influence of the orientation of a box plot on the way it is interpreted. Results indicate that the misinterpretation manifests itself in both orientations to the same extent, suggesting that the orientation of a box plot does not influence the reasoning mechanisms it provokes.Key wo rds: du al-process theory, gra ph design, misinterpretation, heuristic, box plotsINTERPRETACIA RAMCEKOVÝCH GRAFOV: VPLYV PRIESTOROVEJ ORIENTACIES. L e m, C. V a n d e b e e k, P. O n g h e n a , L. V e r s c h a f f e l, W. V a n D o o r e nSuhrn: Sk umali sme ako principy navrhu grafov predikuju specificke mechanizmy usudzovania, k u k torým dochadza pri sk reslenej interpretacii ramcekových grafov, presnejsie, pri ich sk reslenej interpretacii a ko reprezentacie frekvencie alebo miery pozorovani, a nie hustoty. Predchadzajuce studie uk aza li, ze skreslena interpretacia ma heuristický charakter a vyvolava ju sk utocnost, ze ramcekove grafy nevyuziva ju priestor prirodzeným sposobom. Principy navrhovania grafov posk ytuju teoretický ramec pre predpoklad, ze priestorova orientacia ramcekoveho gra fu moze ovplyvnit jeho interpreta ciu . Pomocou analýzy reakcných casov a miery presnosti pre rozne typy poloziek sme zistova li, ci priestorova orientacia ramcekoveho grafu sku tocne vplýva na sposob, ak ým je interpretova ný. Výsledky naznacuju, ze skreslena interpretacia sa vyskytova la v rovnak ej miere v oboch priestorových orientaciach, na zaklade coho mozno predpokladat, ze priestorova orienta cia ra mcekoveho gra fu neovplyvnuje mechanizmy usudzovania, ktore vyvolava.Lem, Onghena, Ver scha ffel, and Van Dooren (2013b) recently showed that box plots are misinterpreted frequently and that the incorrect interpretation of the area of the box plot can be assigned to incorrect heuris- tic reasoning. A limitation of this study is, however, that it only used horizontally po- sitioned box plots, while it is also common practice to make use of vertically positioned box plots, particularly when multiple groups are being compared (e.g., McGill, Tukey, Larsen, 1978; Williamson, Parker, Kendrick, 1989). Based on graph design principles (Tversky, 1997), some arguments can be given that make it likely that less interpreta- tion difficulties will occur when the box plot is represented vertically. In the present study, we compared the way horizontally and verti- cally positioned box plots are interpreted, using a dual processing perspective.The Heuristic Misinterpretation of Box PlotsThe misinterpretation, which is the focus in this study, was documented first by Bakker, Biehler, and Konold (2005). They found that the area of the box plot is often perceived by students as displaying the fre- quency or proportion of observations in that interval, instead of the density. Bakker et al. ascribed this misinterpretation to the fact that students link the use of box plots to the use of graphical r epresen tations previously learned in school (e.g., histograms and bar graphs, see also Lem, Onghena, Verschaffel, Van Dooren, 2012). In box plots the area of the box indicates how dense the observa- tions are in that interval: The smaller an area, the higher the density of observations in that interval. This makes box plots very different from other graphical representations, such as bar graphs and histograms, in which a larger area of the bar reflects a higher fre- quency of observations. …