## 1. Introduction

A well-designed graph can be a vivid, memorable, and easy-to-understand depiction of quantitative information (Larkin & Simon, 1987; Shah, Freedman, & Vekiri, 2005; Smith, Best, Stubbs, Archibald, & Roberson-Nay, 2002; Tufte, 2001). For those reasons, graphs are used extensively in textbooks, scientific journals, and the popular print media (Shah et al., 2005; Zacks, Levy, Tversky, & Schiano, 2002). In fact, there has been a dramatic rise in the prevalence of graphs depicting quantitative data. In one analysis, Zacks et al. (2002) found that between 1984 and 1994 the mean number of graphs in academic journals nearly doubled, and the number of graphs in newspapers more than doubled. Corresponding to the increased prevalence of graphs, research on graph comprehension has grown substantially in the last several years (see e.g., Canham & Hegarty, in press; Mautone & Mayer, 2007; Ratwani & Trafton, 2008; Ratwani, Trafton, & Boehm-Davis, 2008).

Despite the fact that graph comprehension is better understood, research has primarily focused on the comprehension of two-variable data (e.g., sex vs. height) with a small number of data points (e.g., 2 or 4). Less is understood about more complex data. However, conclusions from studies of relatively simple graphs and tasks frequently do not scale up to the comprehension of more complex information (Canwan & Hegarty, in press; Ratwani & Trafton, 2008; Shah et al., 2005; Trafton et al., 2000). The current study addresses two as yet unresolved questions about the comprehension of two common graph formats, line and bar graphs, depicting data of medium complexity (see Fig. 1):

- 1 How does an individual’s prior knowledge (both topic familiarity and graphicacy, or graphical literacy skills) interact with format to influence viewers’ interpretations?
- 2 To what extent does graph format affect fact-retrieval and inference generation in multivariate data comprehension?

An understanding of how prior knowledge interacts with bottom-up features should lead to a better understanding of the design of graphs and other visual displays. Specifically, by focusing on individuals' familiarity with the topic of information in a graph and their graphical literacy skills, we can draw conclusions about what formats benefit different individuals.

We take as our starting point Hegarty’s (2005) model of display comprehension. According to this model, a version of which is depicted in Fig. 2 (Kriz & Hegarty, 2007), top-down processes interact with bottom-up information in the comprehension of all external displays. We have proposed that this type of interactive model applies to graph interpretation as it does for other less abstract visual displays (e.g., Freedman & Shah, 2002; Shah, 1997; Shah et al., 2005), yet there is little empirical evidence demonstrating the interaction of top-down and bottom-up processes in the context of graphs. In this study we test an extension of interactive models to consider the effects of two types of prior knowledge: domain-specific familiarity with the content depicted in a graph, and domain-general knowledge about graphs per se (e.g., graphicacy skills, including Pinker’s *graph schema*; Pinker, 1990). We expect that these two types of knowledge may have an impact on inference generation processes in graph comprehension.

Inference generation is more likely to be relevant for complex graphs compared to simple graphs. Simple graphs typically require individuals to retrieve a small number of facts that can easily be remembered, whereas complex graphs frequently require making decisions about what information to encode and mental computations and inferences to simplify the information depicted. Consider the graph in Fig. 1. If an individual attempted to encode and remember three values (word familiarity, reading level, and reading time) for each of the nine data points, the information would far exceed his or her working memory capacity. To reduce the amount of information encoded requires selective processing, and, quite likely, mentally transforming the information depicted. A related difference between simple and complex data is that complex data allow for a greater number of possible comprehension goals that may be selected by a graph viewer. Each goal might require different component processes, mental transformations, or inferences. For example, a graph viewer may compute average differences between high- and low-ability children because his goal is to see whether, as they expected, high-ability third graders read faster than low-ability third graders. Or she may be more interested in the role of word familiarity, or the possibility that there might be a nonlinear relationship between ability and reading speed. Although the nine data point, medium complexity graphs in our study are not as complex as graphs in other studies (e.g., Trickett & Trafton, 2007), they are complex enough to support multiple goals and to require some simplification or inference generation.

Content familiarity, we argue, will support the likelihood that viewers will generate inferences from the data for several reasons. First, content familiarity will have an influence on the viewers’ comprehension goals. For example, viewers may attempt to confirm or disconfirm relationships that they expect to find. When data are complex, those *expected* relationships are more likely to be simpler than the actual data in the graph. In the graphs in Fig. 1, a viewer might expect and wish to confirm that high-ability third graders read faster than low-ability third graders in the data. Although it may seem like a relatively simple inference from the bar graph in Fig. 1, this goal requires mentally averaging the three bars representing words of low-, middle-, and high-familiarity words for high-ability readers and comparing those averages to those for low-ability readers. Or it requires checking and confirming that low-ability readers are systematically slower than high-ability readers for all three groups of bars. That is, identifying the main effect requires mental computation while keeping track of information already encoded such as the fact that the dark bars represent low reading skill individuals. Second, content familiarity knowledge may help viewers keep track of information in the service of the mental computation required in inference generation. Content familiarity may help viewers keep track of that information because they have expectations about which bars are likely to be associated with which condition. Finally, content familiarity may help the viewer identify potential errors. Viewers might double-check results of their computation if the results did not match their expectations.

Graph comprehension skills should support making such inferences for a different reason. Specifically, graph comprehension skills are required to understand how to mentally transform the data to generate the relevant inferences for particular graph formats. High-skilled graph viewers may know how to average across one variable to compute a main effect, for example, but low-skilled graph viewers may not. A consequence of their ability to mentally manipulate information in the graph would be that the presentation format should have *less* impact on comprehension for high-skilled viewers than low-skilled viewers. That is, high graph skilled individuals may have the ability make the appropriate inferences regardless of format. An alternative possibility is that because graphicacy skills include the ability to automatically associate visual patterns with interpretations (e.g., Pinker, 1990), highly skilled/experienced individuals may actually be *more* affected by presentation format. Specifically, viewers may have expectations that multivariate line graphs are intended to convey interactions, and multivariate bar graphs are intended to convey categorical differences. This line of reasoning suggests a pattern of results that might be the opposite of many interactive models of comprehension: High-skilled graph viewers may be more, rather than less, affected by format. The current study considers both possible interactions of graphicacy and format on viewers’ interpretations of data. The nature of the interaction has implications for graph and display design: Does graphic format matter more for novice viewers or for experts?

In sum, the primary goal of the present study is to examine the influence of two kinds of top-down knowledge on graph comprehension: topic familiarity and graph comprehension skills. We predict that both content familiarity and graph comprehension skills may affect inference generation. A secondary goal of our study is to consider how bottom-up processes, too, affect inference generation in graph comprehension.

In graph comprehension, the initial step is that visual elements (e.g., the symbols, colors, types of lines, shape fills) are identified and grouped together into chunks (Pinker, 1990), and these visual chunks influence viewers’ interpretations of the data. As discussed below, bottom-up factors such as format (line or bar graph) influence the nature of those visual chunks. Specifically, the display is chunked based on the Gestalt principles of proximity, good continuity, and similarity (Pinker, 1990). We acknowledge that format is not strictly a bottom-up factor because skilled viewers may have knowledge of these formats, but in the context of this study we focus on the visual characteristics of line versus bar graphs and their influence on comprehension.

Previous research establishes that, for simple data, bar graphs and line graphs facilitate the comprehension of different information in fact-retrieval tasks. Viewers are faster at reading individual data points when viewing bar graphs compared to line graphs, and they are faster at making trend judgments when viewing line graphs compared to bar graphs (Simcox, 1984). Likewise, viewers can more accurately identify individual data points from bar graphs than from line graphs (Carswell & Wickens, 1987; Carswell, 1992). Furthermore, individuals are more likely to spontaneously make discrete comparisons (i.e., *x*_{1} is greater than *x*_{2}) when viewing data in bar graphs and more likely to describe trends (i.e., as *x* increases *y* increases) when viewing line graphs in open-ended description tasks (Carswell, Emery, & Lonon, 1993;Zacks & Tversky, 1999). In fact, even when two discrete data points are plotted in a line graph, viewers sometimes describe the data as continuous. For example, a common interpretation of a line graph depicting height of males and females might be, “The more male a person is, the taller he/she is” (Zacks & Tversky, 1999).

Shah, Mayer, and Hegarty (1999) extended studies of bar versus line graphs work to characterize how Gestalt principles might affect comprehension of more complex graphs depicted in high school social studies textbooks. One main conclusion from this work can be illustrated by consideration of the graphs in Fig. 1. In the bar graph, the proximity principle predicts that for bar graphs a viewer would encode the grouped sets of bars representing levels of word familiarity (low, medium, and high). In the line graph, the principle of good continuity suggests that individuals would encode three visual chunks formed by the lines representing reading skill (low, medium, and high). Viewers’ descriptions, if based on the visual chunks, would differ depending on format. For the bar graph, a visual chunk-based description may be, “For the least familiar words, children with high reading skills are much faster than children with low reading skills; for medium familiar words, children with high reading skills are moderately faster than children with low reading skills; and for highly familiar words, children with high reading skills are only a little faster than children with low reading skills.” Thus, descriptions focus on the effect of the variable plotted on the *z*-axis legend (reading skill) on read-aloud time for each set of bars on the *x*-axis (word familiarity). For ease we refer to this type of description as a *z*–*y* interaction because it refers to the *z*-*y* relationship (where “*z*” is the variable depicted in the legend) and how it is moderated by the variable depicted along the *x*-axis. For line graphs, a visual chunk-based description might be, “As word familiarity increases, reading time is slightly faster for high-skilled readers, moderately faster for medium-skilled readers, and much faster for low-skilled readers.” For simplicity, we refer to this as an *x*–*y* interaction because it describes the *x–y* relationships and how it is moderated by the “*z*” variable. Although these descriptions are, technically, descriptions of interactions, we note that they also require very little processing of the data depicted. As such, for the novice graph viewer such a description does not necessarily imply a deep understanding of an interaction, but it may reflect merely a minimally digested interpretation. Indeed, our previous work suggested that viewers who provided such descriptions were focusing on the surface features and could not recognize the same data when plotted differently (Shah & Carpenter, 1995).

The earlier work on line and bar graph comprehension outlined above primarily examined how format affects fact-retrieval processes in graph comprehension. The current study addresses how format might affect inference generation such as the identification of main effects in the graphs in Fig. 1. In the bar graph, the main effect of familiarity for read-aloud time (the *x–y* main effect) is computed by mentally averaging the three groups of bars representing low, medium, and high reading skill. The grouping of the bars (using the Gestalt principle of proximity) can support comprehension in two ways: First, each group may be encoded as a single entity and one might easily visually extract a trend. Second, the grouped bars may reduce working memory load in mentally computing averages because the three bars to be averaged in each set are together. In a line graph, computing the *x–y* main effect requires ignoring the highly salient interaction depicted in the three lines. Thus, we predict that viewers may be more likely to compute and describe *x–y* main effects when viewing bar graphs than when viewing line graphs.

Generating *z–y* main effect may be less affected by format. For the bar graph in Fig. 1, the *z–y* main effect is computed by mentally averaging the three black bars, the three gray bars, and the three white bars. The visual cues provided by the colors of the bars (Gestalt principle of similarity) may help reduce working memory load in keeping track of the bars to be mentally averaged. Computing the *z–y* main effect for line graphs is supported by the fact that the three sets of points to be mentally averaged are connected in lines. Thus, one might expect that both bar graphs and line graphs, to some extent, support interpretation of this main effect.

In sum, we make the following predictions regarding the influence of bottom-up characteristics on the interpretation of line and bar graphs: Viewers will provide *x–y* interaction descriptions more frequently for line graphs and for bar graphs, and *z–y* interaction descriptions approximately equally for bar graphs and line graphs. We also predict that viewers will be more likely to make inferences about *x–y* main effects for bar graphs than for line graphs.

To examine the influence of format, content knowledge, and graph skills on the comprehension of bar and line graphs, we presented different groups of participants with line graphs or bar graphs depicting the same data. We tested participants on an independent measure of graph comprehension skill. To assess the effect of content knowledge, we varied familiarity of the content depicted in graphs rather than using an individual differences approach. Thus, half the graphs depicted familiar data to this subject population, and half depicted unfamiliar data.