CAGBT is a new framework for analyzing the cognitive requirements of conducting graph-based tasks. The framework can be used to make predictions of task complexity and, indirectly, of task completion time and task performance. These predictions are also sensitive to graph structure and graph complexity. Only static, common graphs and common (everyday) graph reading tasks are considered. However, tasks may be more complex than was possible hitherto with existing frameworks described elsewhere in the literature.
From an analysis of the literature on graph comprehension (Lohse, 1993; Gillan & Lewis, 1994; Ratwani et al., 2008), and from two previous empirical studies using similar graphs and questions (Hurts, 1998; Hurts & Van Leeuwen, 1998), we arrived at the list of ten elementary operations mentioned in the table below (each followed by the psychological type the operation belongs to - and a brief description of the operation).
We assume most questions extracting and integrating information from simple line and bar graphs can be answered by applying these operations sequentially. Each operation may occur more than once in each sequence, each time instantiated to a different part (point, line, text label) of the graph.
Name of operation
Search Label/Line (Visual Search)
Read Off Height (Visual Search)
Estimate Slope (Visual Arithmetic)
Determine Vertical Orientation (Visual Arithmetic)
Determine Horizontal Orientation (Visual Arithmetic)
Determine Intersection (Visual Arithmetic)
Establish Line Parallelism (Visual Arithmetic)
Establish Slope Pattern (Visual Arithmetic)
Compare Heights (Mental arithmetic)
Compare Differences between Heights (Mental arithmetic)
Description of operation
Search for label of bar (bar graps) or data point (line graphs), or identify a line.
Read off (vertical) length of specific bar
Estimate slope of line segment, starting from a data point contained by that line
Determine whether one data points is above or below another
Determine whether one data points is to the right (left) of another
Determine whether two line segments are intersecting
Determine whether two lines with known slopes are parallel or no
Determine whether two lines are converging or diverging, going from left to right (or the other way around)
Estimate size of difference between two heights
Determine whether one (absolute) difference between two heights is larger or smaller than another
Additionally, each operation acts on certain graphical input information and/or computational information obtained in previous steps. In turn, it generates itself computational information with which to control future processing steps.
It can be seen that the following types of operation were distinguished: visual search, mental arithmetic (including logical reasoning), and visual arithmetic. The six visual arithmetic operations were defined in order to better capture the visual nature of higher cognitive processes that are invoked when more complex,integrated questions have to be answered about graphs (Ratwani et al., 2008).
Despite the similarities between our visual arithmetic operations and the spatial comparisons distinguished in the MA-P model (Gillan & Lewis, 1994), some of the operations listed in the table below capture more detailed aspects of the graph reading behaviour. In addition, unlike the component processes of the MA-P model, the operations of our framework are, to a certain extent, graph-dependent.
Hurts, K. (2010). Line parallelism, graph memory, and detecting statistical interactions. Published in: Theoretical Issues in Ergonomics Science.