Catherine Sophian & Martha E. Crosby
University of Hawaii
User interfaces often present quantitative information visually. We focus here on the visual representation of ratios, an aspect of interfaces that may be of particular importance since people often find ratios confusing. Most often, interfaces present quantitative information in linear form; for example, the scroll bar in computer windows uses the ratio between the portion of the scroll bar above versus below the marker to represent the ratio between the portion of the document that is above vs. below the cursor's current position. However, because ratios are fundamentally two dimensional -- they represent a relation between two quantities and their values are affected by alterations in either of those quantities -- we hypothesize that two-dimensional representations of them, in which the two components of a ratio are mapped onto the height vs. width of a spatial figure -- will be easier to process than linear ones. Experiment 1 tests this hypothesis by comparing judgments about the relation between pairs of ratios presented either linearly or two-dimensionally. Experiment 2 examines patterns of eye fixations in performing a ratio-based shape comparison task in order to learn more about the perceptual and cognitive processes underlying the interpretation of spatial representations of ratio information.
In Experiment 1, adults were asked to judge whether two visually presented ratios were the same. Linear problems presented ratios in the form of pairs of vertical line segments, positioned one directly above the other. Both of the line segments comprising one pair were longer than those comprising the other, but the ratio between the upper and lower line segments might or might not be the same for both pairs. For the two-dimensional problems, the stimuli were rectangles whose heights and widths matched the lengths of the two line segments in corresponding linear problems. It was predicted that, even though