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Bars and Lines: A Study of Graphic Communication

Jeff Zacks and Barbara.Tversky

Psychology Department

Stanford University

Stanford, CA 94305-2130

{zacks,bt} @psych.stanford.edu

Abstract

Interpretations of graphic displays of information seem to be

rooted in principles of cognitive naturalness and information

processing rather than arbitrary correspondences. Both of

these considerations predict that people should more readily

associate bars with discrete information because bars are

discrete entities and facilitate point estimates. Similarly,

people should more readily associate lines with trends

because lines connect discrete entities and directly represent

slope. In two experiments, viewers tended to describe bar

graphs in terms of discrete comparisons between individual

data points, while they tended to describe line graphs in

terms of continuous trends. In a third experiment,

participants sketched graphic displays to illustrate verbal

descriptions of data; they tended to use bar graphs to convey

discrete comparisons, and line graphs to convey trends. The

strength of the bar/line convention seems to depend on the

communicative situation as well as the perceptual and

conceptual properties of the graphic displays.

Introduction

Graphs are a pervasive species of cognitive artifact, used

both to reason about data and to communicate them. Given

a particular data set, there are a large number of ways it

could be portrayed, and people develop conventions that

govern what techniques are used in a given situation. One

such convention is the use of bar graphs to depict

comparisons among discrete data points and line graphs to

depict trends. This convention is reflected in instructional

books (Kosslyn, 1993), publication manuals (American

Psychological Association, 1994), and in the frustrated

complaints of editors when it is violated. It does not seem

to be arbitrary. On the one hand, it fits with the way people

use space to convey meaning. On the other hand, it fits

with the ease with which people extract information from

graphics.

In the sections that follow, we will describe how the bar-

line convention could originate from biases in the

perceptual and cognitive abilities of graph viewers. We

will then present data documenting how the convention

functions both for viewers and authors of graphs. Based on

the strength of the effect, and on the relationship of

authors’ choices to viewers’ behavior, we conclude that the

convention can’t be fully understood just in terms of the

information-processing properties of graph viewers, but

requires thinking about the larger situation in which graphs

are used to communicate.

Cognitive Naturalness

Many conventions of graphic communication have been

invented and reinvented across cultures and by children,

suggesting that they derive from cognitively natural ways

of using space to convey meaning (Tversky, 1995). This

may be the case for bars and lines as well. Some support

for this comes from research on production and

comprehension of graphic displays. In producing graphic

representations of temporal, quantitative, and preference

relations, children across cultures line up dots they perceive

as representing levels of an underlying dimension but do

not line up dots they do not perceive as related

dimensionally (Tversky, Kugelmass & Winter, 1991).

selecting what graphic displays they would use for

conveying various sorts of information, adults prefer to use

bars for conveying discrete information and lines for

conveying trends (Levy, Zacks, Tversky & Schiano, 1996).

The Gestalt principles underlying figural perception

support the naturalness of bars for categorical information

and lines for ordinal or interval data. In bar graphs, each

value is represented as a separate bar, suggesting separate

entities or categories, whereas in line graphs, values are

connected by a single line, suggesting that all the values

belong to the same entity.

Information-processing Models Of Graphical

Perception

Pinker (1990) has developed the most detailed information-

processing theory of graph comprehension. In Pinker’s

model, a graph reader first builds up a visual description of

the visual display, similar to Marr’s (1982) 2 1/2 D sketch.

This representation is constrained by several factors,

including Gestalt laws of grouping and prior experience

with other graphs. From the visual description, a graph

reader constructs conceptual messages, which are

propositions about variables depicted in the graph. The

reader can also construct conceptual questions, which are

essentially conceptual messages with missing values.

High-level inferential processes are available to operate on

conceptual messages.

144

From: AAAI Technical Report FS-97-03. Compilation copyright © 1997, AAAI (www.aaai.org). All rights reserved.

Pinker argues, "different types of graphs are not easier or

more difficult across the board, but are easier or more

difficult depending on the particular class of information

that is to be extracted" (1990, p. 11). Based on the theory,

Pinker predicts that it should be easier to make discrete

comparisons between individual data points from bar

graphs and easier to make trend assessments from line

graphs.

~

The Gestalt principles again support this

prediction. Absolute values are easier to discern when the

values are presented separately, as in bars, whereas trends

are easier to discern when values are connected, as in lines.

The prediction of an interaction between graph type (bar

vs. line) and ease of making discrete comparisons or trend

assessments is also supported by empirical results. Simcox

(1984, described in Pinker, 1990) found that viewers were

faster to make judgments about the absolute value of data

points with bar graphs than with line graphs, but faster to

make judgments of slope with line graphs than with bar

graphs. This pattern held both for a sorting task and a

classification task. In related (as yet unpublished) work,

we found that viewers were faster to make discrete

comparisons from bar graphs than from line graphs. For

trend judgments, there was no difference between the two

graph types. Interestingly, this pattern held even when the

graphs contained only two data points. In this case, the

discrete comparison and the trend assessment are formally

equivalent (Zacks, Levy, Tversky & Schiano, 1996).

Finally, Simkin and Hastie (1987) compared bar graphs (of

a type slightly different from that used in our experiments)

with pie graphs for discrete comparison judgments and

proportion-of-the-whole judgments. They found viewers

were more accurate making discrete comparisons with the

bar graphs than the pie graphs, while the opposite was true

for proportion-of-the-whole judgments. Also, they

reported that in a survey, viewers tended to spontaneously

describe bar graphs in terms of discrete comparisons, and

to describe pie graphs in terms of proportions of the whole.

Origins of the Bar-Line Convention

Together, the theory and results described above suggest

that people should be more likely to interpret information

presented in bars as deriving from discrete variables and

information presented in lines as deriving from continuous

underlying variables. This should be evident in the way

they describe the depicted relations. Information presented

as bar graphs should be described categorically, in terms of

discrete comparisons between individual data points, using

terms such as "higher," "lower," "greater than," and "less

than." On the other hand, information presented as lines

should be described as continuous trends between the data

I Graphical perception, including the comprehension of

trends and discrete comparisons from line and bar graphs,

has also been modeled quantitatively by Lohse (1993).

However, specific predictions about the interaction of

graph type (bar vs. line) and task were not reported.

points, using terms like "rising," "falling," "increasing,’"

and "decreasing." The first two experiments examine

people’s spontaneous descriptions of data graphed as bars

or lines.

Mirroring the predictions for comprehension of graphics

are the predictions for production of graphics. When asked

to graphically represent information described

categorically, using terms like "greater than," people

should produce relatively more bars than lines. When

asked to graphically represent information described

continuously, using terms like "increases," people should

produce relatively more lines than bars. The last

experiment examines people’s constructions of graphs for

representing data described discretely or continuously.

Experiment 1

In the first experiment, we presented participants with

simple bar or line graphs and asked them to describe what

they saw. We predicted that viewers would be more likely

to describe the bar graphs in terms of discrete comparisons

between the individual data points. On the other hand, we

predicted they would be more likely to describe the line

graphs in terms of continuous trends.

Method

Participants. 69 Stanford University undergraduates

participated in this experiment to partially fulfill a course

requirement.

Stimuli and procedure. Simple graphs were drawn of a

two-point data set. The two points were always drawn so

as to be appreciably different; which point was higher was

counterbalanced across viewers. The horizontal axis was

labeled "X" and the vertical axis was labeled "Y." The

data point on the left was labeled "A," and the one on the

right labeled "B." One critical factor was manipulated:

viewers either saw a version of the graph drawn as a bar

graph or as a line graph. Examples of the stimuli are

shown in Figure 1.

Below each graph was the instruction: "Please describe

in a sentence what is shown in the graph above:". The

graph and instructions took up half a page; the other half

was printed with another unrelated question about graphs.

The graphs were printed on 8.5" x 11" paper and

distributed as part of a packet of questionnaires. (A note:

though equal numbers of each version of the graph were

distributed, not all the questionnaire packets were fully

completed, so the numbers of participants viewing each

graph version was not equal. The same was true for the

two studies described below.)

145

A

Y

A

x

Figure 1: Examples of the bar and line graph stimuli used

in Experiment I.

Results

Three judges (the first author and two judges who were

naive to the hypotheses and blind to the conditions)

classified each response as either a "discrete comparison"

between the two points or a "trend assessment". Their

instructions were:

"Classify the way the sentence characterizes the data as a

comparison or a trend description. Comparisons use terms

like more/less, more/fewer, higher/lower, larger/smaller,

stronger/weaker; they tend to refer to discrete values.

Trend descriptions use terms like function, relationship,

correlation, varies, trend; the tend to refer to continuous

changes in the variables. Not all the sentences will have

unambiguous assignments; use your judgment. "

All three judges agreed on 59 of the 69 responses. For

those 59 responses, every bar graph was described with a

discrete comparison and every line graph was describe with

a trend assessment, ~2(1) = 54.9, p < .001. Table 1 shows

this pattern.

Bar graph Line graph

Discrete comparison

24 0

Trend assessment

0

35

Table 1: Frequency of data characterization responses as a

function of graph type.

The particular content of the responses was quite

variable. Most respondents provided conceptual

descriptions of the relationship between the data point A

and B, but some gave physical characterizations of the

graph, and others invented fictional situations to explain

the data. The following are three typical "discrete

comparison" responses, and-three typical "trend

assessment" responses:

Discrete comparisons:

"Y is greater in a than B"

"A is a larger Y quantity than B"

"B is bought more often than A"

Trend assessments:

"A line, drawn on the XY plane, descending from A to B

along the X axis"

"As x increases in value y increases"

"As X increases, Y decreases"

To summarize, the deployment of the bar-line convention

had an unambiguous affect on the disposition of the readers

to respond. When they saw bar graphs, they described

discrete contrasts in the data; when they saw line graphs,

they described trends.

Experiment 2

Experiment 1 demonstrated the existence of a bar-line

convention effect on conceptual structure. Is this effect a

"hot house" laboratory phenomenon, or does it reflect

processes that have real impact on our interactions in the

world? One way to get at this question is to add a salient

source of real-world variation in conceptual structure and

check to see that the bar-line convention effect holds up.

Experiment 2 did this by manipulating the conceptual

domain of the graph along with the graph type. The

dependent variable was always continuous (height). For

the independent variable, the discrete conceptual domain of

gender was contrasted with the continuous domain of age.

This produced situations in which the bar-line convention

conflicted with the content of the data. Most interesting is

the case where line graphs were used with gender as the

conceptual domain. Here the convention implies that a

continuous trend is being depicted, but the domain is

clearly discrete. In this situation, how will people describe

the graph?

Method

Participants. 106 Stanford University undergraduates

participated in this experiment to partially fulfill a course

requirement.

146

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40-

c

~" 30"

20-

"v

10-

0

Female Male

50-

40.-

¢-

~=’30-

°~

~ 20-

10-

0

Female Male

6O

50-

10

6O

50-

40-

e-

t-’-

~30-

e-

._~

~. 20-

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0 0

10-year-olds 12-year-olds 10-year-olds 12-year-olds

Figure 2: Examples of the bar and line graph stimuli, and the continuous and discrete conceptual domains used in

Experiment 2.

Stimuli and procedure. The stimuli were quite similar to

those used in Experiment 1. Simple graphs were drawn of

a two-point data set. The two points were always drawn so

as to be appreciably different; the second point was always

higher than the first.

In this experiment, two factors were manipulated. As in

Experiment I, viewers either saw a version of the graph

drawn as a bar graph or as a line graph. Also, the

conceptual domain of the data was manipulated by varying

the labeling of the points and axes. Two domains were

selected such that the dependent variable could be held

constant while the nature of the independent variable was

manipulated. In one version (the "gender" domain), the

two points were labeled "Female" and "Male." In the other

version, (the "age" domain) the points were labeled "10-

year-olds" and "12-year-olds." The vertical axis was

always labeled "Height (inches)." In the first version, the

two labels identified (more-or-less) discrete categories;

thus the labels denoted a discrete conceptual domain. For

the second version the labels denoted a continuous

variable, age, and therefore a continuous conceptual

domain. To summarize, a given graph stimulus was either

associated with a discrete or continuous conceptual

domain, and either was drawn as a bar graph or line graph.

Examples of the stimuli are shown in Figure 2.

In the previous experiment, it had been noted that a

minority of the responses did not describe the data shown

by the graph. Several described the physical appearance of

the figure, and several created fictional explanations of the

depicted data. To reduce the number of these types of

responses, the instructions were changed slightly. Below

each graph was the instruction: "Please describe in a

sentence the relationship shown in this graph:" (rather than

simply asking for a description of what is shown). The

graph and instructions took up half a page; the other half

was printed with another unrelated question about graphs.

The graphs were printed on 8.5" x 11" paper and

distributed as part of a packet of questionnaires.

Results

Because there was good agreement among the judges about

the graph descriptions in Experiment 1, only the first author

147

Gender (discrete domain) Age (continuous domain)

Bar graph

Line graph Bar graph Line graph

Discrete comparison

28 22 28 9

Trend assessment

0

3 2 14

Table 2: Frequency of data characterization responses as a function of graph type (bar graph or

line graph) and conceptual domain (gender or age).

rated the descriptions. During rating, he was blind to the

type of graph presented.

Effects of graph type and conceptual domain on viewers’

propensity to make a discrete comparison or a continuous

trend assessment were investigated by fitting log-linear

models. We tested the effect of a factor by comparing the

simplest model that contained its interaction with the

dependent variable (description type) with a model with

that interaction removed. In each case, we estimated both

Pearson’s X

2

and the likelihood ratio Z

2,

and report the

more conservative of the two (which in this case was

always Pearson’s E2).

Both the graph type and the conceptual domain exerted

effects on viewers’ descriptions of the graphs (see Table 2).

As in Experiment 1, participants were more likely to use a

discrete comparison for a bar graph than for a line graph,

and more likely to make a trend assessment for a line graph

than a bar graph, X2(I) = 21.5, p < .001. Also,

participants were more likely to make a discrete

comparison when the conceptual domain was gender, and

more likely to use a trend judgment when the conceptual

domain was age, Z2(1) = 14.3, p < .001. (We should

somewhat skeptical of the accuracy of the Z2

approximation, given that one of the cells in Table 2

contains a zero. As a check, we performed an analysis in

which we collapsed over graph type and domain in turn and

computed Z2 tests of independence; it gave the same

results.)

Responses were in general less variable than those in the

first experiment. Descriptions were usually of the depicted

variables, with few physical characterizations or fictional

stories. Examples of the discrete comparisons and trend

assessments follow.

Discrete comparisons:

"Male’s height is higher than that of female’s"

"The average male is taller than the average female."

"Twelve yr. olds are taller than 10 yr olds."

Trend assessments:

"The graph shows a positive correlation between a

child’s increases in age and height between the ages of

10 and 12."

"Height increases with age. (from about 46 inches at 10

to 55 inches at 12)"

"The more male a person is, the taller he/she is"

The last example deserves particular comment. The fact

that some participants were willing to use a continuous

trend assessment to describe a domain that was clearly

discrete illustrates the power of the bar-line convention. (3

of the 25 participants who saw that stimulus gave such a

response.) Comparing the odds ratios for the two effects

(15.4 for graph type, 7.2 for domain) shows that the effect

of graph type was about twice as big as that of conceptual

domain. This indicates that the biasing effect of graph type

is something to be reckoned with even in more

"ecologically valid" situations.

The effect of conceptual domain on qualitative

descriptions agrees well with research showing that

manipulating the conceptual domain can lead to

quantitative distortion in the perception of graphs. In one

experiment, Tversky and Schiano (1989) showed that

labeling a figure as a graph led to distortion of a diagonal

line, while labeling the same figure as a map did not.

Experiment 3

The two previous experiments showed that the bar-line

convention systematically influenced readers’ conceptual

understanding of a graph. If readers are sensitive to this

convention, are authors as well? Experiment 3 was

designed to answer this question.

Method

Participants. 99 Stanford University undergraduates

participated in this experiment to partially fulfill a course

requirement.

Stimuli and procedure. The stimuli for this experiment

were essentially the inverse of those used in the previous

experiment. Participants were given a description of a data

pattern together with a frame for a graph, and asked to

draw a graph. The conceptual domain and the labeling of

the frames was just as it had been in Experiment 2. In one

version (the "gender" domain), the two points were labeled

"Female" and "Male." In the other version, (the "age"

domain) the points were labeled "10-year-olds" and "12-

year-olds." The vertical axis was always labeled "Height

(inches)". The descriptions were either discrete

continuous. The discrete descriptions were:

148

Gender (discrete domain) Age (continuous domain)

Discrete Trend Discrete Trend

description description description description

Bar graph

14 7 11

0

Line graph

6 13

14 24

Table 3: Frequency of graph type drawn as a function of description type and conceptual

domain.

"In the frame above, draw a graph that depicts the

following relationship:

Height for males is greater than for females."

or,

"Height for 12-year-olds is greater than for 10-year-

olds."

The continuous descriptions were:

"In the frame above, draw a graph that depicts the

following relationship:

Height increases from females to males."

Or,

"Height increases from 10-year-olds to 12-year-olds."

The graph and instructions took up half a page; the other

half was printed with another unrelated question about

graphs. The graphs were printed on 8.5" x I I" paper and

distributed as part of a packet of questionnaires.

Results

Of the 99 forms that were returned, most of the drawings

were line graphs (57) or bar graphs (32). Of the remaining

10, 6 could be described as scatter plots. Only the bar

graph and line graph responses were analyzed further.

We analyzed the data in the same fashion as for

Experiment 2, by fitting log-linear models to test

differences in goodness-of-fit. Again, the presence of an

empty cell in the frequency table is problematic for the Z

2

approximations. As a check, we again computed Z

2

tests

of independence, which gave the same results as the log-

linear analysis reported below.

The results of Experiment 3 mirror those of the previous

experiments. Given a discrete description, participants

tended to draw bar graphs; given a continuous description,

the), tended to draw line graphs, Z2(1) = 15.3, p < .001.

Also, they were more likely to use a bar graph for the

discrete conceptual domain and more likely to use a line

graph for the continuous domain, Z2(1) = 9.83, p = .002.

The data are given in Table 3.

These results show that creators of graphs are sensitive to

the bar-line convention in a fashion that parallels that of

readers. Also mirroring the results of Experiment 2, the

effect of description type was more powerful (odds ratio

6.61 ) than that of domain (odds ratio = 3.82), suggesting

that the convention exerts a significant influence in real-

world situations.

Discussion

In two experiments, participants wrote descriptions of

relations portrayed in bar or line graphs. There was a

strong tendency to describe data portrayed as bars

discretely, for example, "A is higher than B," and to

describe data portrayed as lines in terms of trends, for

example, "X increases from A to B." The second

experiment also examined effects of discrete or continuous

variables in the data. The influence of graphic display was

far greater than that of the underlying variable. In a third

experiment, participants were given the reverse task.

Given relations described discretely or continuously, they

were asked to construct graphic displays. There was a

strong tendency to portray discrete descriptions as bars and

continuous descriptions as lines.

Thus, people’s comprehension and production of graphs

conform to the principles of cognitive naturalness and

information processing ease discussed in the introduction.

They also correspond to graphic convention. Where do

graphic conventions like the bar-line convention come

from? It seems likely that they originate in these same

perceptual and cognitive propensities. However, it seems

unlikely that the perceptual-cognitive biases alone could

give rise to the striking effects observed here. The

differences in ease of information extraction between bar

and line graphs are small (Zacks et al., 1996) as are the

effects of cognitive naturalness (Tversky et al., 1991).

We believe that small perceptual-cognitive biases are

parlayed into large effects due to positive feedback exerted

by communicative convention. Conforming to the biases

would initially make graphic communications more readily

understood and the information in them more easily

extracted. Once a disposition to privilege a given

relationship between graphic displays and conceptual

messages is exploited by authors, viewers can rely on that

regularity. This further enhances the disposition and

thereby its use. This process can be likened to the way

speech conventions develop in a community of users

(Clark, 1996).

149

While the origins of the bar-line convention can be

traced to cognitive naturalness and information processing

ease, a fuller understanding emerges when we consider the

larger situation in which authors and viewers use graphs to

communicate. Cognitive scientists interested in graphic

perception have traditionally looked at perceptual-cognitive

processes form the point of view of the solitary observer.

A complete account requires expanding the picture to

include processes of communication.

Zacks, J., Levy, E., Tversky, B., & Schiano, D. (1996).

Ease of Processing with Spatial Representations:

Interaction of Rendering Technique and Conceptual Task.

Unpublished manuscript.

Acknowledgments

The authors would like to thank Interval Research

Corporation for its support of this research and the National

Science Foundation Graduate Fellowship Program for its

support of the first author. Thanks also to Duncan Hill,

Rehan Khan, and Shelly Wynecoop for their assistance

rating the responses and Terry Winograd for his valuable

comments on an earlier draft.

References

American Psychological Association. (1994).

Publication Manual of the American Psychological

Association. Washington, DC: Author.

Clark, H. H. (1996). Using language, (pp. xi, 432).

Cambridge England ; New York: Cambridge University

Press.

Kosslyn, S. (1993). Elements of graph design. New

York: W.H. Freeman and Company.

Levy, E., Zacks, J., Tversky, B., & Schiano, D. (1996,

April 13-18, 1996). Gratuitous graphics? Putting

preferences in perspective. Paper presented at the ACM

conference on human factors in computing systems,

Vancouver.

Lohse, G. L. (1993). A cognitive model for

understanding graphical perception. Human-Computer

htteraction, 8(4), 353-388.

Marr, D. (1982). Vision. New York: W.H. Freeman and

Company.

Pinker, S. (1990). A Theory of graph comprehension.

R. Freedle (Ed.), Artificial Intelligence and the future of

testing, (pp. 73-126). Hillsdale, NJ: Lawrence Erlbaum

Associates.

Simkin, D., & Hastie, R. (1987). An information-

processing analysis of graph perception. Journal of the

American Statistical Association, 82 (398), 454-465.

Tversky, B. (1995). Cognitive origins of graphic

conventions. In F. T. Marchese (Ed.), Understanding

images, (pp. 29-53). New York: Springer-Verlag.

Tversky, B., Kugelmass, S., & Winter, A. (1991). Cross-

cultural and developmental trends in graphic productions.

Cognitive Psychology, 23, 515-557.

Tversky, B., & Schiano, D. J. (1989). Perceptual and

conceptual factors in distortions in memory for graphs and

maps. Journal of Experimental Psychology: General,

118(4), 387-398.

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