Typicality effect in data graphs

Graph schema

Several cognitive models of graph comprehension (e.g. Lohse, 1993; Padilla et al., 2018; Pinker, 1990) suggest that people have a graph schema stored in their long-term memory. The basic idea is that viewers’ comprehension of a given graph requires that the visually encoded stimulus is matched to a specific graph schema (Kosslyn, 1989). For example, vertical bar graphs, horizontal bar graphs and line graphs all belong to an ‘L-shaped’ graph schema characterized by horizontal and vertical axis defining a Cartesian coordinate system. In contrast, pie charts and doughnut graphs belong to an ‘O-shaped’ graph schema characterized by a circular space defined by polar coordinates (angle and distance from centre). Quick and efficient mapping of visual stimuli to the correct graph schema facilitates comprehension. Working from the assumption that differences in reaction time (RT) reflect differences in recognition and cognitive processing of graphs, Ratwani and Trafton (2008) found that individuals extracted information from graphs more quickly when a schema consistent with the current stimulus was activated through prior exposure (i.e. during blocks of non-switch trials, bar graph followed by bar graph) than when a schema inconsistent with the current stimulus was activated (i.e. during blocks of switch trials, pie chart followed by bar graph). The results suggest that individuals do indeed make use of specific graph schemas when interpreting a given data graph.

Pinker (1990) proposed that graph schemas are part of a hierarchical structure – similar to how the cognitive representations of other semantic categories are organized (Rosch, 1975; Rosch et al., 1976). As shown in Figure 1, general schemas are mapped to collections of more specific schemas or visual descriptions. For example, the general schema for bird is activated as the visual descriptions of particular types of birds (e.g. robin, ostrich) are perceived and encoded. Ideally, the general schema helps organize the visual information in ways that support comprehension. Similarly, a general schema that supports comprehension of information embedded in data graphs is activated when the visual descriptions of specific graphs (e.g. vertical bar graphs, horizontal bar graphs, line graphs) are perceived and encoded.

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Figure 1.

Applying typicality research to data graphs.

Graph typicality

Notably, the general schema may be activated more quickly by specific instances that are especially typical or common – a phenomenon known as the typicality effect (Rosch, 1975). For example, as indicated by the bold line on the left side of Figure 1, a robin may be perceived as a more typical case of the bird schema than an ostrich. When true, visual descriptions of robins will more quickly activate a general bird schema that would support comprehension of the stimuli (Rosch et al., 1976). By analogy, as indicated by the bold line on the right side of Figure 1, vertical bar graphs may activate the data graphs schema more quickly than horizontal bar graphs or line graphs. When true, the typicality effect would suggest that vertical bar graphs may be especially useful for communicating quantitative information.

Two kinds of models have been proposed to account for typicality effects. In prototype models (Rosch and Mervis, 1975), typicality is determined by the extent to which a stimulus has the specific features that define the prototype. In exemplar models (Storms et al., 2000), typicality is determined by the degree of similarity of a stimulus to one or more of all the exemplars stored in memory. In both models, frequency of exposure to specific instances plays a critical role for the development of cognitive representations – either by supporting formulation of the feature set that defines the prototype or by expanding the quantity or quality of exemplars stored in memory. This suggests that, whether using prototype or exemplar models, graphs that are encountered more often should become more typical, and in turn be interpreted more quickly. Indeed results from two studies indicate that individuals can pick out specific values or the higher of two values more quickly when viewing vertical bar graphs than when viewing horizontal bar graphs (Fischer et al., 2005) or line graphs (Ratwani and Trafton, 2008). The implication is that vertical bar graphs may be seen more often and thus be deemed more typical than horizontal bar graphs or line graphs.

The present study

In this study, we investigate if and how typicality effects manifest across a variety of data graphs. Specifically, we examine typicality of three types of L-shape graphs that are both ubiquitous (Friendly and Denis, 2005) and serve as key examples in graph comprehension models (Kosslyn, 1989; Pinker, 1990; Ratwani and Trafton, 2008): vertical bar graphs, horizontal bar graphs and line graphs; and three types of data patterns that are commonly depicted in these graphs: rising, neutral and falling patterns. Our results inform both scientific and practical knowledge about data graphs. First, our results provide new knowledge about the structure of the graph schema, specifically whether they may be organized in a hierarchical structure (Pinker, 1990; Ratwani and Trafton, 2008). Second, the results will inform decisions about which graph types might best facilitate viewers’ understanding as well as the design of icons in human–machine interactions (where fast graph recognition is crucial). Third, in the long run, knowledge of typicality effects will help designers create more memorable visualizations, since unique stimuli seem to be easier to remember (Borkin et al., 2013).

Drawing on prior work, we study typicality effects using two methods (Rosch et al., 1976). In Study 1, we followed the traditional approach where participants are asked to provide subjective ratings of the typicality of specific instances of the general category (e.g. pictures of different types of birds). Here, ratings indicate relative typicality of the different graph types and data patterns. In parallel, we obtained participants’ perceptions of the relative frequency of their prior exposure to the different graph types and data patterns. In Study 2, we used a verification time task approach wherein participants are asked to judge whether or not specific instances belong to the general category. Here, faster reaction times indicate greater typicality of specific graph variants. In line with prior work (Ratwani and Trafton, 2008), we expected that participants had encountered vertical bar graphs more frequently and that these graphs would be deemed, both subjectively and behaviourally, as the most typical of the data graphs studied here.

Method

Material and procedure

The study was conducted online using Unipark (Questback GmbH, 2019). Each person was presented with 9 stimuli in a randomized order which consisted of 3 graph types (vertical bar graph, horizontal bar graph and line graph) and 3 data patterns (rising, neutral, falling). The nine data graphs (created using Excel) are depicted in Figure 2. Each data graph showed 6 data points. For the rising patterns, the first number was randomly chosen from 0 – 10 (6.26), the second from 10 – 20 (16.65), the third from 20 – 30 (26.31), the fourth from 30 – 40 (39.88), the fifth from 40 – 50 (47.49) and the sixth from 50 – 60 (50.66). For the falling patterns, we used the generated numbers from the rising patterns in a reversed order. For the neutral pattern, six numbers were randomly chosen from a range between from 25 – 35 (resulting in 33, 31.95, 32.94, 30.02, 31.80 and 33.76). We chose this range to avoid creating a rising or falling pattern. The axis showing the value of the data points was always labelled with tick-marks from 0 to 60 with 10-point intervals. The pixel size of each data graph was 379 × 379. First, all graphs were presented one by one in an individually randomized order and participants rated how typical the shown graph was for a data graph using a 1 (very untypical) to 6 (very typical) response scale. Second, participants used the mouse to sort the stimuli in descending order in accordance with their estimation of how often they had seen a similar graph in their life before. The most frequently encountered graph was to be placed at the top (first place was coded as 1) and the least frequently encountered graph was to be placed at the bottom (last place was coded as 9). All stimuli images and data are available at https://osf.io/7ZM2D

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Figure 2.

Data graph stimuli of the studies.

Typicality ratings

A 3 × 3 ANOVA with the within-subject factors graph type (vertical bar graph, horizontal bar graph, line graph) and data pattern (rising, neutral, falling) showed a significant main effect for graph type, F(2, 112) = 20.92, p < .001, η_p² = .27, and a significant main effect for data pattern, F(1.80, 100.66) = 9.18, p = .011, η_p² = .14 (Greenhouse-Geisser corrected). No interaction effect was found, F(4, 224) = 0.81, p = .518, η_p² = .01.

In regard to the graph type, higher typicality ratings were observed for vertical bar graphs (M = 4.68, SD = 1.15) and line graphs (M = 4.63, SD = 1.20), than for horizontal bar graphs (M = 3.81, SD = 1.41). The difference between vertical bar graphs and horizontal bar graphs was significant (t(56) = 5.26, p < .001), as well as the difference between line graphs and horizontal bar graphs (t(56) = 5.14, p < .001). The difference between vertical bar graphs and line graphs was not significant (t(56) = 0.42, p = .676).

In regard to the data pattern, higher typicality ratings were observed for the rising pattern graphs (M = 4.66, SD = 1.08), followed by the falling pattern (M = 4.41, SD = 1.26), followed by the neutral pattern (M = 4.06, SD = 1.27). The difference between rising patterns and falling patterns was significant (t(56) = 2.19, p = .033), as well as the difference between rising patterns and neutral patterns (t(56) = 3.96, p < .001), and the difference between falling patterns and neutral patterns (t(56) = 2.29, p = .026).

Discussion

Despite using common (L-shaped) data graph formats that can be used interchangeably to display many variants of data, Study 1 documented substantial differences in rated typicality and consistent frequency ratings. Vertical bar graphs seem to dominate the representation. The correlation showed that typicality ratings were related to perceived frequency of exposure. Thus, the more often a specific kind of data graph has been observed in the past, the more typical it is perceived. Overall, perceived typicality was highest for vertical bar graphs, followed by line graphs followed by horizontal bar graphs. This order is largely in line with Ratwani and Trafton’s (2008) finding based on participants’ reaction times for reading off a value, where vertical bar graphs were read fastest, followed by horizontal bar graphs and then line graphs.

Typicality was also influenced by the data pattern depicted in the graph, albeit with a smaller effect size than the effect size of the graph type. Rising patterns were perceived as more typical than falling patterns. Neutral patterns seem to be less typical than rising or falling pattern. The finding of the high perceived frequency of rising trends is in line with previous findings from related fields. For example, research on function learning (Brehmer, 1971, 1974; Busemeyer et al., 1997: Kalish et al., 2004, 2007; McDaniel and Busemeyer, 2005) and graph perception (Ciccione et al., 2022) has shown that people have a bias for linear functions with a positive slope, that increasing linear functions are among the most easily learned functions, and that people extrapolate more easily from linear rising trends than from exponential ones.

In a second study, we used a verification time approach to check whether the conclusions obtained from self-report measures used in Study 1 might also manifest in behavioural measures.

Method

Materials and procedure

Participants were tested individually in a laboratory on a laptop computer with a 12.5-inch screen. The program was controlled by psychopy (Peirce et al., 2019). We used the same design and stimuli as in Study 1, except with a few changes. The nine data graphs were supplemented with a set of ‘shredded’ stimuli that might not be considered data graphs. These stimuli were created by taking each graph of Figure 2 and manipulating the image using image effects in the freeware IrfanView. For vertical bar graphs and line graphs, a vertical shift effect with a strength of 50 was introduced. For the horizontal bar graphs, a horizontal shift effect with a strength of 50 was used. Figure 5 shows the nine ‘shredded’ stimuli. During the study, each of 9 data graphs was presented 5 times so that RT could be averaged across multiple presentations of the same stimulus. Specifically, the stimuli were presented in an individually randomized order of 90 trials (9 data graph stimuli × 5 presentation times, and 9 shredded stimuli × 5 presentation times). On each trial, participants were asked to indicate as quickly as possible by pressing a key whether the presented stimulus was a data graph (right arrow key) or a shredded variant of a graph (left arrow key).

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Figure 5.

Shredded stimuli used in the study.

A fixation cross in the middle of the screen appeared before each stimulus for 1 second. At the beginning of the experiment, participants conducted a practice trial with six example stimuli. Three stimuli were data graphs (each data graph type with a neutral pattern) and three stimuli were shredded stimuli. The dependent variable, reaction time for correct recognition, was measured at each trial.

Results

Two criteria led to the exclusion of small amounts of reaction time data: wrong answers (0.011% of the data) and reaction times larger than 3000ms (0.001% of the data). For each of the nine data graphs, the mean value across the five (or less in case of excluded data) reaction times was calculated.

Figure 6 shows the mean reaction times for each data graph.

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Figure 6.

Mean reaction times for each data graph.

The 3 × 3 ANOVA showed a significant main effect for graph type, F(2, 58) = 4.92, p = .011, η_p² = .15, and a significant main effect for data pattern, F(2, 58) = 3.61, p = .033, η_p² = .11. No interaction effect was found, F(3.2, 92.7) = 1.43, p = .237, η_p² = .05 (Greenhouse-Geisser corrected).

In regard to the graph type, the shortest reaction time was observed for vertical bar graphs (M = 720 ms, SD = 224 ms), followed by horizontal bar graphs (M = 757 ms, SD = 250 ms), followed by line graphs (M = 773 ms, SD = 255 ms). The difference between vertical bar graphs and horizontal bar graphs was significant (t(29) = −2.50, p = .020), as well as the difference between vertical bar graphs and line graphs (t(29) = −3.15, p = .004). The difference between horizontal bar graphs and line graphs was not significant (t(29) = −0.82, p = .418).

In regard to the data pattern, the fastest reaction time was observed for the rising pattern graphs (M = 729 ms, SD = 239 ms), followed by the neutral pattern (M = 746 ms, SD = 227 ms), followed by the falling pattern (M = 774 ms, SD = 261 ms). The difference between rising patterns and falling patterns was significant (t(29) = −2.42, p = .022). The difference between rising patterns and neutral patterns was not significant (t(29) = −1.00, p = .328), neither was the difference between falling patterns and neutral patterns (t(29) = 1.90, p = .067).

The mean RT for shredded stimuli was 778 ms (SD = 463 ms) and for data graphs was 776 ms (SD = 500 ms). The difference was not significant (t(1346) = −0.11, p = .910).

Discussion

The results from Study 2 showed that graph type had a significant influence on the verification time. In Study 1, the vertical bar graphs were rated most typical and ranked with most frequent exposure. In Study 2, the vertical bar graphs were recognized significantly faster than horizontal bar graphs and line graphs, with the same ordering of reaction times seen in a previous study by Ratwani and Trafton (2008). In that study, participants had to identify data values in the graphs. Thus, it was ambiguous as to whether the RT differences reflected differences in recognition of the graph type (cf. Pinker, 1990) or aspects of the data extraction process (or both). Our finding, using a much simpler and more process pure task where participants only had to decide whether or not the stimulus is a data graph, thus provides an important replication and clarification. We add the new finding that reaction times for recognition were also influenced by the data pattern, with rising pattern graphs being recognized faster than neutral and falling pattern graphs.