15.4 Problem Solving Read and Make Line Graphs Answer Key

Forepart Psychol. 2015; 6: 1673.

Proficient interpretation of bar and line graphs: the role of graphicacy in reducing the consequence of graph format

Received 2022 Aug 26; Accepted 2022 Oct 16.

Abstruse

The distinction between informational and computational equivalence of representations, kickoff articulated past Larkin and Simon (1987) has been a central principle in the analysis of diagrammatic reasoning which has been supported empirically on numerous occasions. We nowadays an experiment that investigates this principle in relation to the performance of skilful graph users of 2 × two "interaction" bar and line graphs. The study sought to decide whether adept interpretation is afflicted by graph format in the aforementioned way that novice interpretations are. The findings revealed that, unlike novices—and contrary to the assumptions of several graph comprehension models—experts' performance was the same for both graph formats, with their estimation of bar graphs being no worse than that for line graphs. We discuss the implications of the study for guidelines for presenting such data and for models of expert graph comprehension.

Keywords: expertise, graph comprehension

i. Introduction

A widely established finding in the diagrammatic reasoning literature is that the interpretation and comprehension of data can be significantly affected by the format of its representation. The phenomenon of two graphical representations of the same information resulting in very dissimilar behavior has been reported on numerous occasions (e.k., Zacks and Tversky, 1999; Peebles and Cheng, 2003; Kosslyn, 2006; Peebles, 2008) and is typically explained in terms of the distinction between informational and computational equivalence of representations (Larkin and Simon, 1987). Co-ordinate to this account, observed variation in behavior is due primarily to the fact that different graphical representations facilitate the utilize of different cerebral and perceptual operators.

Take two widely used representations—bar and line graphs—as an case (see Effigy ​ i). These two formats share a fundamental structural feature; the graphical framework provided past the ten and y axes, which defines the Cartesian coordinate system. It has been argued that this framework is an essential element of people'southward mental representation (or schema) of these graphs stored in long-term memory that acts as a visual cue for the stored mental representation which is then used to translate the graph (Ratwani and Trafton, 2008).

The eight data sets used in the experiment.

Despite this common framework, the distinct features of bar and line graphs result in significant differences in their interpretation. Considering lines bind plotted points into single objects, people encode them in terms of their gradient (east.g., Simcox, 1983, reported by Pinker, 1990), interpret them as representing continuous changes on an ordinal or interval scale (Zacks and Tversky, 1999; Kosslyn, 2006), and are mostly better at identifying trends and integrating data using line graphs (Schutz, 1961).

This is not the example for bar graphs even so. Because data points are represented by individual separate bars, they are more likely to be encoded in terms of their acme, interpreted as representing distinct values on a nominal scale, and are therefore better for comparing and evaluating specific quantities (Culbertson and Powers, 1959; Zacks and Tversky, 1999).

In a series of experiments, we have investigated the effect of format on the interpretation of interaction graphs (Peebles and Ali, 2009; Ali and Peebles, 2011, 2013). Interaction graphs (in both bar and line form) are widely used in the analysis and interpretation of data from factorial design experiments, a complex skill that requires detailed knowledge and substantial practice to do correctly. The pervasiveness of factorial research designs in science, engineering, business organisation, and medicine places them centrally in the curricula of these disciplines and they are employed and studied by many thousands of people globally.

The production and interpretation of graphical representations of statistical analysis results is an important element of grooming to use factorial designs. For instance, the simplest, most common, and often earliest encountered design is the 2 × 2 factorial design which investigates the effects and interactions of two factors (each of which has two levels) on a dependent variable. Statistical analysis of this design typically results in a 2 × 2 matrix of the mean dependent variable values corresponding to the pairwise combinations of each cistron's levels and graphs of this matrix (examples of which are shown in Figure ​ 1) are frequently produced to help interpret the data.

In our studies we have investigated how the different graphical features of bar and line graphs touch on how people interpret data due to the operation of different Gestalt laws of perceptual organization (Wertheimer, 1938). The Gestalt principles of proximity, similarity, connectedness, continuity, and common fate make up one's mind how graphical features are grouped by the human visual system to grade coherent wholes and play a crucial part in determining how data are interpreted and the nature of the mental representations that users generate when using graphs (due east.g., Kosslyn, 1989; Pinker, 1990; Shah et al., 1999).

For instance, the x variable values in bar graphs are grouped together on the x axis and, as a result of the Gestalt principle of proximity (Wertheimer, 1938) each cluster of bars forms a dissever visual clamper (Peebles and Ali, 2009). People then use these chunks as the basis for comparing the levels of the legend variable (e.one thousand., in Effigy ​ 1D a user may say "if Quebec plants are non chilled, they have up less CO_ii than when they are chilled, only if Mississippi plants are not chilled, they take up more CO_two than when they're chilled").

In the case of line graphs however, data points are connected by lines which, by the Gestalt principle of connexion (Palmer and Rock, 1994), course private visual chunks (Peebles and Ali, 2009). People rapidly place these chunks, access the associated label in the legend by color (via the Gestalt law of similarity) and so utilize them equally the basis for comparing the levels of the x variable (e.g., in Figure ​ 1E a user may say "for bead diamonds, limestone produces more than cutting tool wearable than granite, but for wire diamonds the opposite is true").

Because of this, people are more than likely to describe relationships as a function of the variable plotted on the ten axis when using bar graphs merely more than likely to describe them equally a office of the legend variable when using line graphs (Peebles and Ali, 2009; Shah and Freedman, 2009; Ali and Peebles, 2013).

1.one. The human relationship betwixt graph format and graphical literacy

The event of graph format on interpretation is specially pronounced and deleterious for inexperienced users. In our experiments we have demonstrated that non-expert users perform significantly worse using line graphs than when using equivalent bar graphs (Peebles and Ali, 2009; Ali and Peebles, 2011, 2013). Our studies revealed that non-expert line graph users consistently ignore or are unable to interpret the variable plotted on the x centrality.

The reason for this is that bar graphs allow the operation of two Gestalt principles to take place which results in a more balanced representation of the data. In bar graphs, as a result of the Gestalt principle of proximity (Wertheimer, 1938), each cluster of confined forms a divide visual chunk anchored to the 10 centrality. When people nourish to these chunks, they are able to identify the nearby x value label quickly and hands and associate the bars with the variable plotted on the x axis. In addition, the confined are besides usually colored or shaded, with the fable containing like patches next to the level labels of the z variable. Co-ordinate to the Gestalt principle of similarity, this shared color or shade allows users to associate each bar with its associated level quickly and easily. The two principles combined ensure that users attend to both variables equally.

In line graphs yet, data points are usually represented by colored shapes connected by similarly colored lines. According to the Gestalt principle of connectedness (Palmer and Rock, 1994), each line with its two end points forms an individual visual clamper. As in the case of the bar graphs, line graph users are able to associate each line with a level of the legend variable by shared color and the Gestalt principle of similarity. Different the bar graphs however, there is no equivalent perceptual grouping process available in the line graphs to facilitate the clan between the points at the ends of the lines and the variable values on the x centrality. Although points and labels may be associated by vertical alignment, our studies showed that this association is non sufficient to counterbalance the colour-matching process, most likely because perceiving the line as the chief representational feature impairs users' power to differentiate the points from the line.

Based on these findings and our understanding of how Gestalt principles operate, we adult a modified version of the line graph that produces a more balanced representation and which significantly reduces the biases and errors found in novices' interpretations (Ali and Peebles, 2013).

Our research demonstrated how the graphical and representational features of different graphs can strongly affect the performance of individuals with relatively little experience. Nonetheless, a number of intriguing questions remain about how expert users interpret data using both graph formats. Specifically, information technology would be valuable to know precisely what knowledge and cognitive processes underlie expert performance and to determine to what extent (if at all) experts' interpretations are affected by the graph type used. If information technology is institute that expert performance is largely unaffected by graph format then identifying the knowledge that determines this full general skill will exist useful to meliorate the training and instruction of novices. Conversely, if it is establish that experts' abilities do differ between bar an line graphs and are more attuned to a specific format, so this will as well be valuable in evaluating the appropriateness of the two graph types for different tasks and classes of user.

In relation to graph estimation, expertise consists of 2 core elements; (a) noesis of the domain and the methods past which the information in the graph was obtained or created, and (b) full general graphical literacy, or "graphicacy" (Friel and Bright, 1996; Friel et al., 2001; Shah and Freedman, 2009). The latter consists of knowledge of how classes of diagrams piece of work, including the properties of coordinate systems (east.thou., the principle that the altitude betwixt two graphical elements encodes the magnitude of a relationship between the concepts represented by those elements), and the typical allocation of the dependent and independent variables to the axes and legend. This noesis allows users with high levels of graphical literacy to mentally manipulate and transform the data in the graph (for example by knowing how to identify or compute the mean value of a set of points) to generate inferences that not-adept users could not.

ane.2. Pattern recognition and expert graph comprehension

Another central aspect of expert graph apply is the ability to recognize and interpret common patterns, a characteristic of proficient operation plant in many domains, from chess playing (Chase and Simon, 1973; De Groot, 1978), medical diagnosis (Norman et al., 2007), to geometry trouble solving (Koedinger and Anderson, 1990).

In interaction graphs, a small number of quite distinct and relatively mutual patterns exist which experts learn to place rapidly, either through explicit instruction (e.g., Aron et al., 2006) or simply through repeated exposure. Four patterns indicating the existence (or otherwise) of interaction effects are especially common and readily identified: the "crossover interaction" shown in Effigy ​ 1E, the "less than" or "greater than" pattern shown in Figure ​ 1H, and a related "angle" pattern formed by a horizontal and a sloped line (Figure ​ 1B). In contrast, parallel lines (e.thou., Figure ​ 1A) signal that there is no interaction between the IVs.

In addition to these interaction patterns, two patterns indicating substantial main effects can also exist recognized by experts (and are ofttimes rapidly identified by novices due to their visual salience). These patterns are shown in Figure ​ 1. The large gap between the mid-points of the ii lines in Figure ​ 1A shows a large main effect of the legend variable while the big departure between the mid-points of the two values representing each ten axis level in Effigy ​ 1G reveals a large main consequence of the 10 axis variable.

These ii examples highlight an additional source of bottom-upwardly, information-driven effects on interpretation not associated with the features of a specific graph format but which influences the patterns formed similarly in both graph formats. Specifically, the relative sizes of the principal and interaction effects in a particular data set determine the patterns formed in the graph and the relative salience of the effects. Information technology is possible that this could influence the order in which experts interpret effects as larger effects are represented past wide gaps between lines or bars which may be more perceptually salient than smaller gaps. The possibility that graph comprehension performance is determined by the interaction between the patterns formed past diverse relationships in the information and the size of those relationships will be discussed and investigated further below.

1.ii.1. A blueprint recognition based cognitive model of good graph comprehension

Following the novice written report conducted past Ali and Peebles (2013), Peebles (2013) carried out a detailed cognitive task assay of the comprehension of 2 × 2 interaction graphs to produce a cognitive model implemented in the Act-R cognitive architecture (Anderson, 2007). The model is informed by foundational work on graphical perception (Cleveland and McGill, 1984) and includes a precise specification of the declarative and procedural noesis required to produce a complete and accurate interpretation of 2 × 2 interaction graphs and a set of assumptions and hypotheses about the processes by which experts interpret them. Specifically, the model contains representations in long-term retentiveness that associate private patterns or visual indicators in the graph with item interpretations. The model besides contains strategies for visually scanning the graph (encoded as a set of product rules) equally well as a ready of production rules to identify patterns. When a pattern is identified, a chain of subsequent productions is triggered which obtains further information from the graph and declarative memory until an interpretation is produced. This process continues until all patterns take been identified and interpreted appropriately, and an accurate mental model of the state of affairs depicted in the graph has been generated.

The Deed-R model is able to produce a complete and accurate interpretation of any data presented in iii-variable line graphs at the level of a human being expert and tin can explain its interpretations in terms of the graphical patterns it uses¹. Equally such it can exist considered a course of expert system built inside the constraints of a theoretically grounded cognitive compages. It remains an open question however, to what extent the behavior of human experts conforms to this ideal model and if not, what constitutes and underlies sub-optimal operation.

Information technology is also not clear to what extent the assumptions underlying the expert model utilize equally to the comprehension of line and bar graphs. Although the model has only currently been applied to line graphs, the key information that the model encodes from the brandish is the fix of x-y coordinate locations of the 4 information points and the distances betwixt them. Therefore, the pattern matching rules used by the model exercise non rely on specific features of the line graph just are divers in relation to the patterns formed by the coordinate points. It would be footling to present the model with a set of equivalent bar graphs and the model would predict no pregnant divergence in behavior.

If empirical studies were to reveal withal that experts do in fact conduct differently with the two formats (or past the relative sizes of the various effects in a data set), and so the assumptions of the model would take to exist revised to incorporate these processes.

one.three. Aims of the study

As alluded to earlier, two contrasting hypotheses may exist produced concerning the relationship between levels of graphical literacy and the interpretation of different graph types. The first is that users with high graphicacy should be afflicted less by graph format because they should be able to identify and mentally dispense relevant information in the graph and generate appropriate inferences irrespective of the graphical features used to represent it (Pinker, 1990).

The 2nd hypothesis is that experts' greater exposure to the different graph formats and their learning of common patterns creates a set of expectations well-nigh the functions and properties of each format. For case, expert users may develop the expectation that the function of line graphs is to display interactions while that of bar graphs is to present main effects (Kosslyn, 2006). This may bias experts' interpretations and result in experienced users beingness every bit, if non more, affected by presentation format than non-experts.

Using a student sample divided into "high" and "depression" graphicacy groups, Shah and Freedman (2009) examined these competing predictions and establish that expectation did not influence interpretation in a straightforward fashion. Rather, they found that loftier graphicacy students were merely influenced past format expectations when the graph depicted information from a known domain. Specifically, high graphicacy students were more likely to identify main effects in bar graphs just when the subject field matter was familiar to them. When the domain was unfamiliar, there was no difference in operation between graph formats. The authors did observe however that the identification of interactions from both loftier and depression graphicacy participants was affected by graph format in the predicted fashion (i.east., more descriptions every bit a part of the 10 centrality variable with bar graphs and more descriptions as a office of the legend variable with line graphs).

While it is unclear to what extent high graphicacy students can be considered experts, Shah and Freedman'southward experiment tin can be seen equally providing at least tentative prove that could claiming previous recommendations to employ line graphs considering of experts' ability to recognize interactions using common patterns created by the lines (e.g., Pinker, 1990; Kosslyn, 2006). Shah and Freedman found no effect of graph skill on interaction descriptions and while they did show that both high and low graphicacy participants were affected past graph format, they found no prove that line graphs supported identification of interactions more than bar graphs in either group. It may be the instance therefore, that once users take obtained a certain level of graphical literacy, they are able to apply their knowledge to override differences in Gestalt group or visual salience between graph types to interpret data accordingly whatever graph they use.

The experiment reported here aims to answer the questions raised in the in a higher place discussion by focusing more closely on the types of individuals we study. Different previous research in this area (including our ain) that has predominantly used undergraduate students, nosotros recruited participants from academic faculty in the areas of scientific psychology and cognitive science who have sufficient feel (either through instruction or research or a combination of both) of ANOVA designs to exist considered expert users of interaction graphs.

The sample was representative of the range of expertise typically institute in academia and ranged from early career researchers and banana professors to full professors. Feel in the field at post-doctoral level ranged from a few years to decades. The sample was gathered from multiple centers and participants included British and international academics who could exist considered experts in the field. Using this participant group, we aim to decide whether experts' interpretations of unfamiliar data differ depending upon whether the information is presented in bar or line graph form. In so doing we also aim to ascertain the relative effects of bottom-upwards and top-downward processes (i.e., to decide the relative effects of user expectations and graphical features). This will allow us to quantify the amount of benefit, if any, that line graphs provide for skilful users (equally suggested by Kosslyn, 2006) and to decide whether this is outweighed by other factors (e.g., event sizes in the data).

The 2nd aim of this experiment is to determine whether the processes by which experts reach their interpretations differ using the two graphs. Although it may be the case that experts are able to produce accurate and roughly equivalent interpretations of bar and line graphs, the processes past which they do and then may exist quite different and affected significantly past graphical features. Specifically, previous studies using non-expert samples accept shown that graph format affects the social club in which people translate the graph; people typically interpret the fable variable earlier the x centrality variable when using line graphs (Shah and Carpenter, 1995) but the opposite order when using bar graphs (Peebles and Ali, 2009). In add-on, line graphs may facilitate design recognition processes that bar graphs do not which may lead to more rapid identification of interaction effects.

A tertiary, related aim of the experiment is to determine whether interpretation order is afflicted significantly by the relative size (and as a effect salience) of the patterns formed past the various relationships in the information.

By recording a range of behavioral measures such as the number of correct interpretations, the sequential order of interpretations, and task completion times, together with concurrent verbal protocols, we aim to construct detailed hypotheses relating to the processes underlying expert graph comprehension and to utilize the data obtained to evaluate the assumptions of the cerebral model, specifically the hypothesis that adept performance tin exist accounted for by a sequence of pattern recognition and cognition retrieval processes.

Exact protocol analysis is a technique widely used in cognitive science to obtain information about the processes being employed to perform tasks (Newell and Simon, 1972; Ericsson and Simon, 1984) which has successfully brought to light a wide range of phenomena including nonverbal reasoning (Carpenter et al., 1990), diagrammatic reasoning (Koedinger and Anderson, 1990), and graph comprehension (Shah et al., 1999). The "recollect aloud" method we employ in this study is one of the nigh commonly used techniques for obtaining verbal protocols and at that place is considerable empirical evidence that it is relatively unobtrusive and does not significantly affect cerebral processing (Crutcher, 1994; Fox et al., 2011).

Taken as a whole, the verbal protocol and other behavioral data volition allow united states of america to make up one's mind the extent to which experts' operation differs from the optimal predictions of the model and provide valuable information to inform revisions of the currently assumed mechanisms and processes.

ii. Methods

2.1. Participants and design

The participants were 42 (11 female person, 31 male) university faculty (i.due east., assistant, acquaintance, and full professors) or post-doctoral researchers in cognitive psychology or cognitive science. 40 were educated to PhD level while 2 were in the latter stages of working toward a PhD while beingness employed every bit academy teaching fellows. Participants were gathered from iii locations. The bulk of participants were faculty specializing in cognitive psychology and quantitative inquiry methods from the universities of Keele and Huddersfield in the UK. The remaining participants were cognitive scientists attending an international conference on cognitive modeling.

The experiment was an independent groups design with ane between-subject field variable: the type of diagram used (bar or line graph) and 21 participants were allocated to each condition using a random process.

2.two. Materials

The stimuli were 16 iii-variable interaction graphs—eight line and 8 bar—depicting a wide range of fictional content using variables taken from a variety of (non-psychology related) sources. Each of the eight data sets (shown in Effigy ​ 1) used to produce the graphs depicted the effects of two independent variables (IVs) on a dependant variable (DV) equally would be produced by a 2 × 2 factorial inquiry design.

The data sets were generated to create the main effects and interactions commonly encountered in these designs in a range of sizes. The y centrality for all graphs started at nil and had the same 11 tick marks in the same locations (although the values on the scales varied) and data values were chosen so that all plotted points corresponded to a tick mark.

To classify the size of the furnishings nosotros used the same procedure every bit used in the ACT-R model of Peebles (2013). We calculated the distance between the relevant plot points as the proportion, p, of the distance of the overall length of the y axis and then categorized the distance co-ordinate the post-obit scheme: "no" (p = 0), "very small" (0 < p < 0.2), "modest" (0.2 ≤ p < 0.4), "moderate" (0.4 ≤ p < 0.half dozen), "large" (0.half-dozen ≤ p < 0.8), and "very large" (0.8 ≤ p ≤ i.0). The resulting classifications of the eight graphs are shown in Table ​ i.

Table 1

Size of main effects and interactions for the eight graph stimuli.

Graph	Main effect X	Main result Z	Interaction
1	Modest	Large	No
2	Medium	Medium	Big
iii	Large	Large	Small
4	Medium	No	Large
5	No	No	Large
6	No	Big	Medium
7	Very large	No	Small
8	No	Medium	Large

When matching data sets to graph content, care was taken to ensure that the effects depicted did not corresponded to unremarkably held assumptions about relationships between the variables (although this would be unlikely given the specialized nature of the graphs' bailiwick matter).

The graphs were presented on A4 laminated cards and were drawn blackness on a calorie-free grey background with the legend variable levels colored green and bluish. A portable digital sound recorder was used to record participants' speech as they carried out the experiment.

ii.3. Procedure

The study was carried out in accordance with the ethical conduct recommendations of the British Psychological Society and was canonical by the Academy of Huddersfield'due south Schoolhouse of Human and Health Sciences Research Ethics Committee. All subjects gave written informed consent in accordance with the Proclamation of Helsinki.

Participants were seated at a table with eight bar or line graphs randomly ordered and face downward in front of them and informed that their task was to effort to understand each one as fully every bit possible while thinking aloud. In add-on to concurrent verbalization during interpretation, participants were also asked to summarize the graph before proceeding to the side by side one.

During the experiment, if participants went quiet the experimenter encouraged them to keep talking. When participants had interpreted and summarized a graph, they were instructed to place the graph face up down to one side and go on by turning over the next graph. Participants were non allowed to revisit graphs.

3. Results

3.one. Coding the exact descriptions

A 2 × two experiment design results in 3 central potential effects: a chief effect of the 10 axis 4, a main effect of the legend IV, and an interaction effect between the two. Information analysis involved coding whether each of the effects was identified and noting the time taken to interpret each graph. Audio recordings were transcribed prior to information coding with information identifying graph format existence removed to ensure that coders were blind to graph format.

To meet the requirements for identification of primary effects, participants had to state explicitly that at that place was an effect (eastward.1000., from Figure ​ 1F "There is a primary outcome of curing method") or describe the consequence of one of the IVs on a DV irrespective of the 2nd Iv (e.g., "Photocuring consistently produces a much college fixtural strength than autocuring irrespective of cement type").

To meet the requirements for identification of an interaction effect a participant had to land that there was an interaction effect (e.g., from Figure ​ 1E "This shows a crossover interaction") or describe how the effect of one of the IVs was moderated past the other (eastward.k., from Effigy ​ 1D "Treatment has a differential effect on CO_ii uptake depending on plant type; when handling is chilled, plant CO₂ uptake is the same for both plant types but when treatment is non-chilled, constitute CO₂ uptake is lower in Quebec and higher in Mississippi."

To illustrate the general speed and efficiency of many of the adept participants' interpretations, the example verbal protocol below is a verbatim transcription of a (non atypical) expert participant interpreting the line graph version of Figure ​ 1G.

1. (Reads) "Glucose uptake every bit a office of fasting and relaxation preparation"

2. Alright, so we have…you're either fasting or you're not.

3. You have relaxation grooming or you don't.

4. And so…not fasting…er…

5. So there'southward a large consequence of fasting.

6. Very footling glucose uptake when you're not fasting.

7. And lots of glucose uptake when you are fasting.

8. And a comparatively pocket-sized result of relaxation preparation.

9. That actually interacts with fasting.

The protocol (which lasted 43 south) reveals the speed with which the variables and their levels are established and the central relationships inside the information identified. Accuracy is non always perfect withal; in improver to correctly identifying the main result of the 10 variable and the interaction betwixt the 2 IVs, the participant also incorrectly states that in that location is a (small) primary effect of the legend variable.

The exact protocols were coded by the 2nd writer and a sample of randomly selected codings (approximately 15% from each graph blazon) was independently scored past the first author. The level of agreement between the two coders was 96% for the bar graphs and 92% for the line graphs. When disagreements were found the raters came to a consensus as to the correct code.

3.2. Identification of furnishings

Our initial analysis sought to determine whether experts' identification of main and interaction effects was affected past graph format. Figure ​ 2 shows the mean number of identifications of the main effect of the x axis 4 (henceforth referred to as "principal effect x"), the primary upshot of the legend Iv (henceforth referred to as "chief issue z"), and interaction event as a office of graph format.

Mean number of main effect x, main upshot z, and interaction descriptions (with 95% confidence intervals) for the ii graph conditions.

Three independent sample t-tests revealed that graph format had no significant effect on participants' ability to identify the main effect ten [t _(twoscore) = one.183, p = 0.246, d = 0.36], main effect z [t ₍₄₀₎ = 0.21, p = 0.832, d = 0.07], or interaction effect [t ₍₄₀₎ = 1.56, p = 0.127, d = 0.48]. The consequence sizes vary from very small for chief outcome z to approaching medium for the interaction effect. In all cases, the pattern of responses was in favor of the bar graph condition merely, in general, the results betoken that whatever lesser-upwardly or top-down effects that may be are not strong plenty to bias experts' interpretations significantly in favor of one graph format over another. The nowadays study therefore has not detected any event of graph format on experts' ability to place the key relationships in the data.

Some other measure of the upshot of graph format on functioning is task completion fourth dimension because this may indicate differences in interpretation strategy. A t-test on the mean task completion time for bar graphs (one min, 25 s) and line graphs (1 min, xi south) showed that this was not the case however [t _(29.783) = 1.077, p = 0.290, d = 0.iii].

3.3. Main effect/interaction identification gild

Although graph format does non atomic number 82 to significant differences in the number of effects and interactions identified or the time taken to interpret a graph, it may exist the case that the format of the graph affects the processes by which experts interpret them. For case, Shah and Carpenter (1995) constitute that people'south understanding of the ten-y human relationship in three-variable line graphs was more than comprehensive than their understanding of the z-y relationship due to the activeness of Gestalt processes whereas Peebles and Ali (2009) institute the reverse effect in bar graphs. This typically leads to users focusing initially on the fable variable in line graphs and the ten axis variable in bar graphs.

If expert users are susceptible to the same visual influences as novices, and so information technology could exist expected that they would be more likely to identify the main consequence of the legend first in the line graph but the x axis master effect get-go in the bar graphs. Alternatively, experts' well-practiced strategies may override any such influences. To determine between these two hypotheses, we took trials where participants identified both master effects (xx% of line graph trials and 23% of bar graph trials) and recorded which main upshot was identified first.

The proportions of users selecting the ten main consequence before the z main effect was roughly equal between graph formats (line = 45.5%, bar = 44.7%) as was the case for the alternative order (line = 54.5% bar = 55.iii%), indicating that, in contrast to novice users, experts are unaffected past Gestalt processes in this regard.

The two graph formats likewise differ in terms of the perceptual cues they provide to betoken the existence of an interaction. Line graphs provide a salient perceptual cue (cross pattern or non parallel lines) which is non as salient in bar graphs (Pinker, 1990; Kosslyn, 2006). In addition, there may exist an expectation issue—experts may be influenced past their knowledge that line graphs are most often used to represent interactions and may therefore be primed to look for them (Shah and Freedman, 2009).

If this is the example, it could be expected that experts will identify interaction effects beginning in line graphs but main furnishings starting time in bar graphs. To exam this, we took trials where participants identified both a chief effect and an interaction (21% of line graph trials and 26% of bar graph trials) and recorded which one they identified first.

As with the previous analyses, in that location was no significant deviation in the order of interaction and main effect identification between graph format conditions. The proportions of people selecting a master effect earlier the interaction result was roughly equal betwixt graph formats (line = 47%, bar = l%) as was the example for the culling club (line = 53%, bar = 50%). This shows that experts are influenced neither by an expectation that certain effects volition be present in particular formats nor the more than salient perceptual line graph cue indicating an interaction issue.

three.4. Interaction identification

Although we take found no differences in the patterns of identification due to Gestalt principles, user expectations, or dissimilar visual cues, the different perceptual cues in the two graphs may result in different patterns of inference to institute the existence of an interaction upshot in bar graphs compared to line graphs. Specifically, interaction identification in line graphs may exist triggered by the rapid identification of a salient pattern such as a cross and parallel lines [as assumed in the Act-R model (Peebles, 2013)] whereas in bar graphs this blueprint recognition procedure may not be equally prevalent or influential.

To determine whether this is the case, we counted whether experts described the nature of the interaction prior to identifying the interaction issue in bar graphs and vice versa in line graphs. An example verbal protocol illustrating the first example recorded from a participant using the bar graph version of the graph in Figure ​ 1B is presented below.

1. (Reads) "Maize yield as a office of plant density and nitrogen level"

2. When plant density is meaty maize yield is higher.

3. Otherwise information technology's the same in all other conditions.

4. So information technology's an interaction betwixt nitrogen level and plant density.

In contrast, an example verbal protocol illustrating the latter case recorded from a participant using the line graph in Figure ​ 1E is listed below.

1. (Reads) "Cutting tool wearable equally a function of rock type and diamond blazon"

2. Direct abroad I run across an interaction.

3. The effect of this gene is opposite depending on the rock type conditions.

4. If y'all have bead diamond type cutting tool wear is highest nether limestone whereas bead under granite condition cutting tool wearable is lower.

5. Bead works best in limestone and worse in granite.

6. In the wire information technology's the opposite trend. Cutting tool wear is lower in limestone and much college in the granite.

7. Definite interaction. The other thing is the issue is very consequent; the two higher bars are 8 and the lower ones are at 5.

8. My summary is that if you're cutting limestone you lot want a dewdrop type cutter, if it's granite then wire.

Only trials where participants described both the nature of the interaction and stated explicitly the existence of the interaction were included in the analysis. This amounted to 27% of line graph trials and 32% of bar graph trials. The proportion of participants who explicitly identified the interaction before going on to draw the nature of the effect was significantly larger in the line graph condition (lxxx%) than in the bar graph condition, (54%, χ² = xv.287, df = 1, p < 0.001). Analysis of the exact protocols revealed that expert line graph users predominantly land the interaction immediately and and so continue to describe the nature of the interaction whereas expert bar graph users would be equally likely to ascertain the nature of the relationship between the variables through a process of interrogation and reasoning followed past an explicit identification of the interaction.

Explaining this variance in behavior in terms of experts' different expectations is implausible as the previous process analysis found no differences in preference for identification of main consequence and interaction order betwixt the graph formats. The more convincing caption in our view is that this observation is due to the bottom upward influence of the salient patterns available in line graphs. It is of import to note that this process difference does not result in a more than superficial interpretation in the line graph status; the richness of the descriptions was the same, but in a different gild.

3.5. The influence of effect size

The analyses higher up demonstrated that graph format has no significant event on the number of chief or interaction effects identified by experts or the club in which they are interpreted. They have too provided no evidence that expectation has an influence upon the patterns and processes of experts' interpretations. We identified a third possible influence on proficient interpretation nonetheless that may sally from the relative sizes of the main and interaction effects in a particular data set up.

To observe whether this factor determined the relative salience of furnishings (and thereby the order in which experts interpreted them) we took the distance values between plot points used to classify the effect sizes shown in Table ​ 1 and tested whether these numerical values correlated with the gild in which the effects were identified^two. The analysis revealed a significant positive human relationship between upshot size and identification order—the larger the event size, the greater the likelihood that the effect would be identified outset, in both line [r ₍₂₁₎ = 0.647, p < 0.001] and bar [r ₍₂₁₎ = 0.730, p < 0.001] graphs.

4. Discussion

This study was designed to achieve iii inquiry goals related to issues concerning the nature of—and influences upon—expert comprehension functioning. The starting time aim was to provide evidence that would allow us to adjudicate between two contrasting hypotheses concerning the relationship between levels of graphical literacy and the effect of graph format on estimation. Ane hypothesis is that high levels of graphicacy will result in a reduction in the effect of graph format due to the increased ability to identify and mentally dispense relevant data in the graph and generate advisable inferences irrespective of the graphical features used to stand for information technology (e.one thousand., Pinker, 1990). The alternative hypothesis is that increases in graphicacy volition result in an increase in the upshot of graph format because graphicacy consists, at least in part, of a set of expectations and biases for dissimilar graph formats regarding their specific functions and backdrop (eastward.g., Zacks and Tversky, 1999; Shah and Freedman, 2009).

Although there was some prove of expert expectation (a couple of participants commented that the bar graphs they were using should take been line graphs), the results of our experiment showed that whatever expectations some participants may have had, they had no significant consequence on their interpretations. In fact the findings provide strong support for the former proposition by showing that experts' interpretations are, to all intents and purposes, identical for the two graph formats. There were no significant differences in the number of main effects or interactions that expert users were able to identify, nor in the time taken to place them, related to the format of the graph (as indicated by the very minor issue sizes).

The second aim of the study was to make up one's mind whether the processes or strategies by which experts achieve their interpretations using the two graphs differed in any pregnant fashion. Specifically we aimed to ascertain whether graph format affected the club in which experts interpreted the graph. In contrast to previous studies which have revealed a systematic interpretation social club of legend variable followed by 10 axis variable in line graphs (Shah and Carpenter, 1995) and the opposite order in bar graphs (Peebles and Ali, 2009), experts in this study exhibited no such patterns of beliefs, either in relation to the two main furnishings or in relation to the interaction and the main effects.

In addition, nosotros sought to make up one's mind whether line graphs were more likely to result in a faster identification of certain relationships due to pattern recognition processes as argued by Kosslyn (2006). The results did support the hypothesis by showing that the graphical features of the line graphs did result in a more rapid identification of interactions than the bar graphs. More than specifically, the verbal protocols suggested that participants in the line graph condition were indeed using pattern recognition processes to identify relationships in the data.

Finally, the experiment was conducted to determine whether the strategies that experts used to interpret data in these graphs were influenced by the relative effect sizes in the data and, if so, whether this differed betwixt the graph conditions (perhaps as a upshot of differences in visual salience of the patterns formed by the graphical features in the two graph formats). The results revealed that experts are indeed sensitive to outcome size and tended to identify large effects more apace than smaller effects, whichever graph format they used.

To summarize these results, while it does seem that experts are able to utilise the patterns in line graphs to more rapidly identify interactions, in that location is no overall benefit for experts of using line graphs over bar graphs. Although expert bar graph users may sometimes arrive at their interpretations via a different road, they accept the same fourth dimension and are no less likely to generate a total, right analysis of the data than if they were to utilise a line graph.

This reveals that experts' greater experience allows them to ignore or override the pitfalls produced past Gestalt grouping processes in line graphs that novice users fall foul of (Peebles and Ali, 2009; Ali and Peebles, 2011, 2013) simply does not result in experts constructing a set of expectations virtually the functions and properties of bar and line graphs that biases them detrimentally. Set in the broader context of the distinction between informational and computational equivalence of representations (Larkin and Simon, 1987), the experiment demonstrates how experts' knowledge of the possible relationships to look for in the data and the patterns that indicate them guides their search and reduces the effects of computational inequivalences and procedural constraints imposed past graphical format.

Taken together, these findings have a number of of import implications for the presentation of data of this form, in particular regarding the question of which might be the best format to utilise for the nigh widespread use (i.east., for both novice and skilful users). Currently line graphs are used more than frequently then bar graphs. A survey of graph use in a broad range of psychology textbooks by Peden and Hausmann (2000) showed that 85% of all information graphs in textbooks were either line graphs or bar graphs but that line graphs (64%) were approximately 3 times more common than bar graphs (21%). A similar only more recent survey which nosotros carried out (Ali and Peebles, 2013) revealed that in leading experimental psychology journals, there was a slight preference for line graphs (54%) over bar graphs (46%) simply a more than pronounced preference in pop psychology textbooks; line graphs were favored 20% more than than bar graphs.

In our previous piece of work (Peebles and Ali, 2009; Ali and Peebles, 2013) yet, we demonstrated that non-skilful users performed significantly worse with line graphs compared to equivalent bar graphs and recommended that bar graphs (or an enhanced line graph that nosotros designed) should exist employed in cases where the aim is for authentic interpretation for a general audience of both novice and practiced users.

Proponents of line graphs (e.yard., Kosslyn, 2006) have argued, however, that the run a risk and costs of misinterpreting line graphs are outweighed by the benefit of lines for producing easily recognizable patterns that experts tin can acquaintance with item effects or interactions. The results of this report prove however that although the patterns in line graphs are rapidly identified by experts, this does non lead to significantly better functioning; experts are no less likely to identify primal patterns in bar graphs equally they are in line graphs, undermining the argument for the latter as a preferred representation.

The results of the study likewise take implications for models of expert graph comprehension. The current computational model of Peebles (2013) is based on a unproblematic set of assumptions regarding blueprint matching and memory retrieval which relate to the patterns formed past the ten-y coordinates of the four data points (and are therefore not specific to any particular graph format). Currently the model does not accept the size of effects into account when selecting a design to interpret. Instead patterns are selected at random.

The experiment has revealed that although experts can interpret bar and line graphs equally well, the processes by which they interpret them are affected by the format of the graph and also by the relative sizes of the effects in the data (irrespective of format). So while the data are broadly consequent with the assumptions of the model to the extent that experts do conduct an exhaustive search for the possible effects that may be present, a more than accurate model will have to contain these additional factors. Once these factors are included, the resulting model will provide the most detailed and precise account of the noesis and processes underlying expert comprehension performance for a widely used class of graphs in ii formats.

Across the goal of extending the model to account for the full range of observed behavior with ii graph formats lies the larger aim of developing and broadening the model to explain comprehension for a broader grade of graphs. Interaction graphs embody a specific gear up of interpretive rules that are not shared by other more conventional graphs still because the data represent pairwise combinations of the IV levels and then that the variables plotted are chiselled, regardless of whether the underlying scale could exist considered equally continuous (east.g., hot/cold) or categorical (e.g., male/female).

The current model clearly identifies and characterizes these rules and distinguishes them from the knowledge and procedures that tin can exist applied to other graphs. In so doing, the model simplifies the job of identifying graph-specific operators and forms a basis upon which to explore a range of comprehension models for other graph types.

In improver to furthering the development of formal models, the current piece of work has also indicated farther avenues for empirical investigation. Specifically, the significant influence of relative result size found in the experiment suggests that expert interpretation is not allowed from the constraints imposed past the visual salience of various patterns created by data. Time to come research on these factors will provide further valuable insights into the dynamic interplay between bottom-up and peak-downwardly processes on graph comprehension.

Conflict of interest statement

The authors declare that the inquiry was conducted in the absence of any commercial or fiscal relationships that could be construed equally a potential disharmonize of interest.

Footnotes

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Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4626626/

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