Benefits of visualization in the Mammography Problem

The Impact of Visualizing Nested Sets. An Empirical Study on Tree Diagrams and Unit Squares

“…Our results suggest that the double-tree diagram makes the relevant subset relation more transparent compared to the tree diagram, because the set of all positively tested people is represented by one node in the double-tree which is missing in the tree diagram (see Figure 2 ). Moreover, frequency grids containing natural frequencies in a legend were equally effective when compared to double-trees containing the same numerical information in Khan et al (2015). Therefore, we would expect that frequency grids containing natural frequencies in a legend are more effective than tree diagrams with natural frequencies, as it is the case for double-trees.…”

“…The tree diagram representing a “Branch style” (Khan et al, 2015) does not visualize the subset-relation that is necessary for applying Bayes’ rule whereas the unit square representing a “Nested style” (ibid.) visualizes this subset-relation by neighboring areas.…”

“…We hypothesize that the area-proportionality of the unit square could have an additional beneficial effect compared to the advantage of the 2 × 2-table. It could be also an interesting question to compare the unit square (with natural frequencies) and frequency grids that Khan et al (2015, p. 96) called “Frequency style” and that proved to be effective for understanding Bayesian reasoning situations (Garcia-Retamero and Hoffrage, 2013; Khan et al, 2015). As mentioned above, we hypothesize that both forms of visualization show the same effectiveness.…”

“…Thus, following Khan et al (2015, p. 96) visualizations like the tree diagram represent a “Branch style” and emphasize relations of subsets in a logical way. By contrast, visualizations like the unit square, the roulette-wheel diagram, the Euler diagram and also the 2 × 2-table represent a “Nested style” and emphasize relations of subsets in a geometrical way.…”

“…Based on a theoretical analysis of visualizations representing the “Nested style,” Oldford and Cherry (2006, p. 3) argued that especially the unit square “visually grounds probability and naturally incorporates the rules of probability within its construction” due to the area-proportionality of the unit square compared to the related statistical data. Whereas 2 × 2-tables can be understood to represent the “Nested style” according to Khan et al (2015), they do not, in contrast to the unit square, include an area-proportionality. For this reason we hypothesize that a unit square represents in some sense an ideal way of visualizing nested sets.…”