Academic journal article Human Factors

Modeling the Effect of Task and Graphical Representation on Response Latency in a Graph Reading Task. (Special Section)

Academic journal article Human Factors

Modeling the Effect of Task and Graphical Representation on Response Latency in a Graph Reading Task. (Special Section)

Article excerpt

INTRODUCTION

The ability to interpret and reason with charts and graphs is increasingly important in this information-rich society. Charts, graphs, and other diagrams are used extensively in science, engineering, business, and the media. To be able to reason with charts and graphs effectively requires sophisticated perceptual and reasoning skills and a broad range of general and specific knowledge about diagrammatic representations. Understanding diagrammatic reasoning is an important goal for cognitive scientists, therefore, not only because of the ubiquity of diagrammatic representations but also because diagrammatic reasoning is a process in which behavior is a function of a complex interaction among three factors: the cognitive and perceptual skills of the reasoner, the graphical properties of the external representation being used, and the specific requirements of the task being undertaken. It is also likely that a deeper understanding of the relationships among these three factors will have implications for the desi gn of more effective graphical representations.

In the area of graph-based reasoning, we have carried out a number of investigations into how these three factors affect reasoning with different types of Cartesian coordinate (x,y) graphs (Peebles & Cheng, 2001, 2002; Peebles, Cheng, & Shadbolt, 1999) and have proposed the graph-based reasoning (GBR) model to characterize the complex interactions and resulting behavior. The goals of GBR are similar to those of the cognition-artifact-task (Gray & Altmann, 2001) and embodied cognition-artifact-task (Byrne, 2001; Gray, 2000; Gray & Boehm-Davis, 2000) frameworks proposed to characterize interactive behavior in human-computer interaction tasks.

Figure 1 shows the four graphs used in the experiment reported here. They depict the amount (in millions of units) of UK offshore oil and gas production over two decades. In the function graphs the argument variable (AV: time in years) is represented on the x axis and the quantity variables (QV: oil and gas) on the y axis, whereas in the parametric graphs the quantity variables are represented on the x and y axes and time is plotted as a parameterizing variable along the curve.

To evaluate the similarity between function and parametric graphs, we start with the notions of informational and computational equivalence of representations defined by Larkin and Simon (1987). According to their definition, two representations are informationally equivalent if no information can be inferred from one that cannot be inferred from the other and if each can be constructed from the information in the other. Conversely, two representations are computationally equivalent if they are informationally equivalent and if any inferences that can be drawn "quickly and easily" from the explicit information in one can be similarly drawn from the explicit information in the other, and vice versa. This latter term requires that not only the information content of the representations be taken into account but also the nature and speed of the various operators used to interact with them. According to Larkin and Simon's criteria, each pair of function and parametric graphs generated from the same data set for t his study can be considered to be informationally equivalent. The computational equivalence of the graphs, however, is one of the issues this research seeks to address.

Function and parametric graphs also share several important properties. They are both simple line graphs using a two-dimensional Cartesian coordinate system to relate quantities and represent magnitudes. Although the two graph types assign different variables to their axes, they are similar in that both represent specific values of plotted variables as points on the line. Because of these visual and representational similarities, many of the basic operators for accessing items of information are the same for both graph types. …

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