Academic journal article Human Factors

Visual Arithmetic, Computational Graphics, and the Spatial Metaphor

Academic journal article Human Factors

Visual Arithmetic, Computational Graphics, and the Spatial Metaphor

Article excerpt

INTRODUCTION

A spatial metaphor underlies the design of graphs (e.g., Wainer, 1984). The term metaphor often refers to figurative language in which the metaphor transfers meaning from one object (the vehicle) to another (the tenor), typically through an implicit comparison. For example, "the killer had a heart of ice" transfers the attribute cold from "ice" to "killer's heart." In recent years nonlinguistic metaphors - especially user interface metaphors - have been a major concern in the human factors of computing systems (e.g., Carroll, Mack, and Kellogg, 1988; see also Dent-Read, Klein, and Eggleston, 1994, for a more general discussion of visual display metaphors). The spatial metaphor in a graph, also a nonlinguistic metaphor, transfers meaning by relating the spatial extent or the position of the indicators in the graph (i.e., the graphic elements that indicate the values of variables, such as bars in a bar graph and points in a line graph) to the amount of the indicated variable. In contrast, other graphical displays are primarily literal in that they use display space to represent real-world space: Maps stand for a larger real-world space, whereas schematic diagrams stand for a smaller real-world space. All of these graphical displays have the potential to engage a user's perceptual and cognitive processes, including identification of emergent features (e.g., Bennett and Flach, 1992; Sanderson, Flach, Buttigieg, and Casey, 1989) and performance of mental rotation or other manipulations of parts (Gillan and LaSalle, 1994; Simkin and Hastie, 1987). However, among these graphical displays, only graphs use space metaphorically.

Recent research with typical graph users (engineers, scientists, and students) indicates that despite the underlying spatial metaphor in graphs, users do not employ the spatial metaphor when they interact with graphs in a variety of circumstances. Specifically, task and protocol analyses conducted during the development of a model of graph comprehension, the Mixed Arithmetic-Perceptual (MA-P) model (e.g., Gillan, 1993; Gillan and Lewis, 1994; Gillan, Lewis, and Rudisill, 1990; Gillan and Neary, 1992), indicate that when people use common graphs (a line or bar graph) to perform many quantitative tasks (determining a mean, adding the values of indicators, determining the ratios of indicators), they focus on the quantitative characteristics of the graph. However, they appreciate graphs and will display data in a graphical format for aesthetic reasons.

Based on the task and protocol analyses of people using graphs, the MA-P model proposes that five functional component processes underlie a user's interactions with common graphs to perform various tasks: (1) searching for the spatial location of an indicator, (2) encoding the value of the indicator, (3) performing arithmetic operations on the encoded values, (4) comparing the spatial relations (e.g., the relative heights or lengths) of two or more indicators, and (5) responding. According to the model, the components and the order in which the user applies them depend on the task and graph: For such tasks as determining a sum, mean, or difference, the user applies the search, encoding, and arithmetic operation components, whereas for tasks requiring comparisons and trends, the user applies the search and spatial comparison component processes. A variety of tests of the MA-P model have provided support for its analysis of graph comprehension. For example, Gillan and Lewis (1994) showed that the model could account for as much as 85% of the variance in the time subjects took to read a graph in order to answer questions. Gillan and Neary (1992) empirically supported predictions from the model concerning the effects of manipulating the spatial relations among elements within graphs. The model and supporting data indicate that when people use graphs to determine means, sums, or differences, they focus on the quantitative character of graphs. …

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