Chapter 8
Graphics
CHAPTER 8 GRAPHICS 107
What is the dimension of the information you will illustrate? Do you need to
illustrate repeated information for several groups? Is a graphical illustration
the best vehicle for communicating information to the reader? How do you
select from a list of competing choices? How do you know whether the
graphic you produce is effectively communicating the desired information?
GRAPHICS SHOULD EMPHASIZE AND HIGHLIGHT SALIENT FEATURES. THEY
should reveal data properties and make large quantities of information
coherent. While graphics provide the reader a break from dense prose,
authors must not forget that their illustrations should be scientifically
informative as well as decorative. In this chapter, we outline mistakes in
selection, creation, and execution of graphics and discuss improvements
for each of these three areas.
Graphical illustrations should be simple and pleasing to the eye, but the
presentation must remain scientific. In other words, we want to avoid those
graphical features that are purely decorative while keeping a critical eye
open for opportunities to enhance the scientific inference we expect from
the reader. A good graphical design should maximize the proportion of the
ink used for communicating scientific information in the overall display.
THE SOCCER DATA
Dr. Hardin coaches youth soccer (players of age 5) and has collected the
total number of goals for the top five teams during the eight-game spring
2001 season. The total number of goals scored per team was 16 (team 1),
22 (team 2), 14 (team 3), 11 (team 4), and 18 (team 5). There are many
KISS--Keep It Simple, but Scientific
Emanuel Parzen
ways we can describe this set of outcomes to the reader. In text above, we
simply communicated the results in text.
A more effective presentation would be to write that the total number of
goals scored by teams 1 through 5 was 16, 22, 14, 11, and 18, respectively.
The College Station Soccer Club labeled the five teams as Team 1, Team 2,
and so on. These labels show the remarkable lack of imagination that we
encounter in many data collection efforts. Improving on this textual
presentation, we could also say that the total number of goals with the team
number identified by subscript was 222, 185, 161, 143, and 114. This
presentation better communicates with the reader by ordering the outcomes
because the reader will naturally want to know the order in this case.
FIVE RULES FOR AVOIDING BAD GRAPHICS
There are a number of choices in presenting the soccer outcomes in
graphical form. Many of these are poor choices; they hide information,
make it difficult to discern actual values, or inefficiently use the space
within the graph. Open almost any newspaper and you will see a bar chart
graphic similar to Figure 8.1 illustrating the soccer data. In this section,
108 PART II HYPOTHESIS TESTING AND ESTIMATION
0
5
10
15
20
25
1 2 3 4 5
FIGURE 8.1 Total Number of Goals Scored by Teams 1 through 5. The x
axis indicates the team number, and the y axis indicates the number of goals scored
by the respective team. Problem: The false third dimension makes it difficult to
discern values. The reader must focus on the top of the obscured back face to
accurately interpret the values plotted.
CHAPTER 8 GRAPHICS 109
we illustrate five important rules for generating correct graphics. Subsequent
sections will augment this list with other specific examples.
Figure 8.1 includes a false third dimension; a depth dimension that does
not correspond to any information in the data. Furthermore, the resulting
figure makes it difficult to discern the actual values presented. Can you tell
by looking at Figure 8.1 that Team 3 scored 14 goals, or does it appear
that they scored 13 goals? The reader must focus on the top back corner
of the three-dimensional rectangle since that part of the three-dimensional
bar is (almost) at the same level as the grid lines on the plot; actually, the
reader must first focus on the floor of the plot to initially discern the vertical
distance of the back right corner of the rectangular bar from the corresponding
grid line at the back (these are at the same height). The viewer
must then mentally transfer this difference to the top of the rectangular
bars in order to accurately infer the correct value. The reality is that most
people focus on the front face of the rectangle and will subsequently misinterpret
this data representation.
Figure 8.2 also includes a false third dimension. As before, the resulting
illustration makes it difficult to discern the actual values presented. This
illusion is further complicated by the fact that the depth dimension has
been eliminated at the top of the three-dimensional pyramids so that iťs
nearly impossible to correctly ascertain the plotted values. Focus on the
result of Team 4, compare it to the illustration in Figure 8.1, and judge
whether you think the plots are using the same data (they are). Other
types of plots that confuse the audience with false third dimensions
include point plots with shadows and line plots where the data are connected
with a three dimensional line or ribbon.
The lesson from these first two graphics is that we must avoid illustrations
that utilize more dimensions than exist in the data. Clearly, a better
presentation would indicate only two dimensions where one dimension
identifies the teams and the other dimension identifies the number of
goals scored.
Rule 1: Don't produce graphics illustrating more dimensions
than exist in the data.
Figure 8.3 is an improvement over three-dimensional displays. It is
easier to discern the outcomes for the teams, but the axis label obscures
the outcome of Team 4. Axes should be moved outside of the plotting
area with enough labels so that the reader can quickly scan the illustration
and identify values.
Rule 2: Don't superimpose labeling information on the graphical
elements of interest. Labels can add information to the plot, but
should be placed in (otherwise) unused portions of the plotting
region.
Figure 8.4 is a much better display of the information of interest. The
problem illustrated is that there is too much empty space in the graphic.
Choosing to begin the vertical axis at zero means that about 40% of the
plotting region is empty. Unless there is a scientific reason compelling you
to include a specific baseline in the graph, the presentation should be
limited to the range of the information at hand. There are several
instances where axis range can exceed the information at hand, and we
will illustrate those in a presentation.
Rule 3: Don't allow the range of the axes labels to significantly
decrease the area devoted to data presentation. Choose axis limits
wisely and do not automatically accept default values for the axes
that are far outside of the range of data.
110 PART II HYPOTHESIS TESTING AND ESTIMATION
0
5
10
15
20
25
1 2 3 4 5
FIGURE 8.2 Total Number of Goals Scored by Teams 1 through 5. The x
axis indicates the team number, and the y axis indicates the number of goals scored
by the respective team. Problem: The false third dimension makes it difficult to
discern the values in the plot. Since the back face is the most important for interpreting
the values, the fact that the decorative object comes to a point makes it
impossible to correctly read values from the plot.
Figure 8.5 eliminates the extra space included in Figure 8.4 where the
vertical axis is allowed to more closely match the range of the outcomes.
The presentation is fine, but could be made better. The data of interest in
this case involve a continuous and a categorical variable. This presentation
treats the categorical variable as numeric for the purposes of organizing
the display, but this is not necessary.
Rule 4: Carefully consider the nature of the information underlying
the axes. Numeric axis labels imply a continuous range of
values that can be confusing when the labels actually represent
discrete values of an underlying categorical variable.
Figures 8.5 and 8.6 are further improvements of the presentation. The
graph region, area of the illustration devoted to the data, is illustrated with
axes that more closely match the range of the data. Figure 8.6 connects
the point information with a line that may help visualize the difference
between the values, but also indicates a nonexistent relationship; the
CHAPTER 8 GRAPHICS 111
0
5
10
15
20
25
0 1 2 3 4 5 6
FIGURE 8.3 Total Number of Goals Scored by Teams 1 through 5. The x
axis indicates the team number, and the y axis indicates the number of goals scored
by the respective team. Problem: Placing the axes inside of the plotting area effectively
occludes data information. This violates the simplicity goal of graphics; the
reader should be able to easily see all of the numeric labels in the axes and plot
region.
horizontal axis is discrete rather than continuous. Even though these
presentations vastly improve the illustration of the desired information, we
are still using a two-dimensional presentation. In fact, our data are not
really two-dimensional and the final illustration more accurately reflects
the true nature of the information.
Rule 5: Do not connect discrete points unless there is either (a) a
scientific meaning to the implied interpolation or (b) a collection
of profiles for group level outcomes.
Rules 4 and 5 are aimed at the practice of substituting numbers for
labels and then treating those numeric labels as if they were in fact
numeric. Had we included the word "Team" in front of the labels, there
would be no confusion as to the nature of the labels. Even when nominative
labels are used on an axis, we must consider the meaning of values
between the labels. If the labels are truly discrete, data outcomes should
not be connected or they may be misinterpreted as implying a continuous
rather than discrete collection of values.
112 PART II HYPOTHESIS TESTING AND ESTIMATION
0
5
10
15
20
25
0 1 2 3 4 5 6
FIGURE 8.4 Total Number of Goals Scored by Teams 1 through 5. The x
axis indicates the team number, and the y axis indicates the number of goals scored
by the respective team. Problem: By allowing the y axis to range from zero, the
presentation reduces the proportion of the plotting area in which we are interested.
Less than half of the vertical area of the plotting region is used to communicate
data.
Figure 8.7 is the best illustration of the soccer data. There are no false
dimensions, the range of the graphic is close to the range of the data,
there is no difficulty interpreting the values indicated by the plotting
symbols, and the legend fully explains the material. Alternatively, we can
produce a simple table.
Table 8.1 succinctly presents the relevant information. Tables and
figures have the advantage over in-text descriptions that the information is
more easily found while scanning through the containing document. If the
information is summary in nature, we should make that information easy
to find for the reader and place it in a figure or table. If the information is
ancillary to the discussion, it can be left in text.
Choosing Between Tabular and Graphical Presentations
In choosing between tabular and graphical presentations, there are two
issues to consider: the size (density) of the resulting graphic and the scale
CHAPTER 8 GRAPHICS 113
10
12
14
16
18
20
22
24
0 1 2 3 4 5 6
FIGURE 8.5 Total Number of Goals Scored by Teams 1 through 5. The x
axis indicates the team number, and the y axis indicates the number of goals scored
by the respective team. Problem: This graph correctly scales the y axis, but still uses
a categorical variable denoting the team on the x axis. Labels 0 and 6 do not correspond
to a team number and the presentation appears as if the x axis is a continuous
range of values when in fact it is merely a collection of labels. While a
reasonable approach to communicating the desired information, we can still
improve on this presentation by changing the numeric labels on the x axis to
String labels corresponding to the actual team names.
of the information. If the required number of rows for a tabular presentation
would require more than one page, the graphical representation is
preferred. Usually, if the amount of information is small, the table is preferred.
If the scale of the information makes it difficult to discern otherwise
significant differences, a graphical presentation is better.
114 PART II HYPOTHESIS TESTING AND ESTIMATION
10
12
14
16
18
20
22
24
1 2 3 4 5
FIGURE 8.6 Total Number of Goals Scored by Teams 1 through 5. The x
axis indicates the team number, and the y axis indicates the number of goals scored
by the respective team. Problem: The inclusion of a polyline connecting the five
outcomes helps the reader to visualize changes in scores. However, the categorical
values are not ordinal, and the polyline indicates an interpolation of values that
does not exist across the categorical variable denoting the team number. In other
words, there is no reason that Team 5 is to the right of Team 3 other than we
ordered them that way, and there is no Team 3.5 as the presentation seems to
suggest.
Team 2Team 4 Team 3 Team 1 Team 5
10 12 14 16 18 20 22 24
FIGURE 8.7 Total Number of Goals Scored by Teams 1 through 5. The
x axis indicates with a square the number of goals scored by the respective team.
The associated team name is indicated above the square. Labeling the outcomes
addresses the science of the KISS specification given at the beginning of the
chapter.
ONE RULE FOR CORRECT USAGE OF
THREE-DIMENSIONAL GRAPHICS
As illustrated in the previous section, the introduction of superfluous
dimensions in graphics should be avoided. The prevalence of turnkey solutions
in software that implement these decorative presentations is alarming.
At one time, these graphics were limited to business-oriented software
and presentations, but this is no longer true. Misleading illustrations are
starting to appear in scientific talks. This is partly due to the introduction
of business-oriented software in university service courses (demanded by
the served departments). Errors abound when increased license costs for
scientific- and business-oriented software lead departments to eliminate the
more scientifically oriented software packages.
The reader should not necessarily interpret these statements as a
mandate to avoid business-oriented software. Many of these maligned
packages are perfectly capable of producing scientific plots. Our warning is
that we must educate ourselves in the correct software specifications.
Three-dimensional perspective plots are very effective, but require specification
of a viewpoint. Experiment with various viewpoints to highlight
the properties of interest. Mathematical functions lend themselves to
three-dimensional plots, but raw data are typically better illustrated with
contour plots. This is especially true for map data, such as surface temperatures,
or surface wind (where arrows can denote direction and the length
of the arrow can denote the strength).
In Figures 8.8 and 8.9, we illustrate population density of children for
Harris County, Texas. Illustration of the data on a map is a natural
approach, and a contour plot reveals the pockets of dense and sparse pop-
ulations.
While the contour plot in Figure 8.8 lends itself to comparison of maps,
the perspective plot in Figure 8.9 is more difficult to interpret. The
surface is more clearly illustrated, but the surface itself prevents viewing all
of the data.
CHAPTER 8 GRAPHICS 115
Team 4 Team 3 Team 1 Team 5 Team 2
11 14 16 18 22
TABLE 8.1 Total Number of Goals Scored by Teams 1
through 5 Ordered by Lowest Total to Highest Totala
a
These totals are for the Spring 2001 season. The
organization of the table correctly sorts on the numeric
variable. That the team labels are not sorted is far less
important since these labels are merely nominal; were it
not for the fact that we labeled with integers, the team
names would have no natural ordering.
116 PART II HYPOTHESIS TESTING AND ESTIMATION
No. children per
region
0-1000 1000-2000 2000-3000 3000-4000 4000-5000
FIGURE 8.8 Distribution of Child Population in Harris County, Texas.
The x axis is the longitude (-96.04 to -94.78 degrees), and the y axis is the
latitude (29.46 to 30.26 degrees).
0
500
1000
1500
2000
2500
3000
3500
4000
4500
4000-4500
3500-4000
3000-3500
2500-3000
2000-2500
1500-2000
1000-1500
500-1000
0-500
FIGURE 8.9 Population Density of the Number of Children in Harris
County, Texas. The x axis is the longitude (-96.04 to -94.78 degrees), and the
y axis is the latitude (29.46 to 30.26 degrees). The x­y axis is rotated 35 degrees
from Figure 8.10.
Rule 6: Use a contour plot over a perspective plot if a good viewpoint
is not available. Always use a contour plot over the perspective
plot when the axes denote map coordinates.
Though the contour plot is generally a better representation of mapped
data, a desire to improve Figure 8.8 would lead us to suggest that the grid
lines should be drawn in a lighter font so that they have less emphasis
than lines for the data surface. Another improvement to data illustrated
according to real-world maps is to overlay the contour plot where certain
known places or geopolitical distinctions may be marked. The graphic
designer must weigh the addition of such decorative items with the
improvement in inference that they bring.
ONE RULE FOR THE MISUNDERSTOOD PIE CHART
The pie chart is undoubtedly the graphical illustration with the worst reputation.
Wilkinson (1999) points out that the pie chart is simply a bar
chart that has been converted to polar coordinates.
Focusing on Wilkinson's point makes it easier to understand that the
conversion of the bar height to an angle on the pie chart is most effective
when the bar height represents a proportion. If the bars do not have
values where the sum of all bars is meaningful, the pie chart is a poor
choice for presenting the information (cf. Figure 8.10).
CHAPTER 8 GRAPHICS 117
16
22
14
11
18
1
2
3
4
5
FIGURE 8.10 Total Number of Goals Scored by Teams 1 through 5. The
legend indicates the team number and associated slice color for the number of
goals scored by the respective team. The actual number of goals is also included.
Problem: The sum of the individual values is not of interest so that the treatment
of the individuals as proportions of a total is not correct.
Rule 7: Do not use pie charts unless the sum of the entries is scientifically
meaningful and of interest to the reader.
On the other hand, the pie chart is an effective display for illustrating
proportions. This is especially true when we want to focus on a particular
slice of the graphic that is near 25% or 50% of the data since we humans
are adept at judging these size portions. Including the actual value as a
text element decorating the associated pie slice effectively allows us to
communicate both the raw number along with the visual clue of the
proportion of the total that the category represents. A pie chart intended
to display information on all sections where some sections are very small is
very difficult to interpret. In these cases, a table or bar chart is to be
preferred.
Additional research has addressed whether the information should be
ordered before placement in the pie chart display. There are no general
rules to follow other than to repeat that humans are fairly good at identifying
pie shapes that are one-half or one-quarter of the total display. As
such, a good ordering of outcomes that included such values would strive
to place the leading edge of 25% and 50% pie slices along one of the
major north­south or east­west axes. Reordering the set of values may
lead to confusion if all other illustrations of the data used a different
ordering, so the graphic designer may ultimately feel compelled to reproduce
other illustrations.
THREE RULES FOR EFFECTIVE DISPLAY OF
SUBGROUP INFORMATION
Graphical displays are very effective for communication of subgroup information--for
example, when we wish to compare changes in median family
income over time of African-Americans and Hispanics. With a moderate
number of subgroups, a graphical presentation can be much more effective
than a similar tabular display. Labels, stacked bar displays, or a tabular
arrangement of graphics can effectively display subgroup information.
Each of these approaches has its limits, as we will see in the following
sections.
In Figure 8.11, separate connected polylines easily separate the subgroup
information. Each line is further distinguished with a different plotting
symbol. Note how easy it is to confuse the information due to the
inverted legend. To avoid this type of confusion, ensure that the order of
entries (top to bottom) matches that of the graphic.
Rule 8: Put the legend items in the same order they appear in the
graphic whenever possible.
118 PART II HYPOTHESIS TESTING AND ESTIMATION
CHAPTER 8 GRAPHICS 119
0.5
0.55
0.6
0.65
0.7
0.75
0.8
1974 1976 1978 1980 1982 1984 1986 1988 1990
Year
Familyincomeratio
African-American
Hispanic
FIGURE 8.11 Median Family Income of African-Americans and Hispanics
Divided by the Median Family Income for Anglo-American Families for Years
1976­1988. Problem: The legend identifies the two ethnic groups in the reverse
order that they appear in the plot. It is easy to confuse the polylines due to the
discrepancy in organizing the identifiers. The rule is that if the data follow a
natural ordering in the plotting region, the legend should honor that order.
0
2
4
6
8
10
1 2 3
Fat type
Volume
Surfactant 1 Surfactant 2 Surfactant 3
FIGURE 8.12 Volume of a Mixture Based on the Included fat and Surfactant
Types. Problem: As with a scatterplot, the arbitrary decision to include zero
on the y axis in a bar plot detracts from the focus on the values plotted.
120 PART II HYPOTHESIS TESTING AND ESTIMATION
5
5.5
6
6.5
7
7.5
8
8.5
9
1 2 3
Fat type
Volume
Surfactant 1 Surfactant 2 Surfactant 3
FIGURE 8.13 Volume of a Mixture Based on the Included fat and Surfactant
Types. Drawing the bar plot with a more reasonable scale clearly distinguishes
the values for the reader.
Clearly, there are other illustrations that would work even better for this
particular data. When one subgroup is always greater than the other subgroup,
we can use vertical bars between each measurement instead of two
separate polylines. Such a display not only points out the discrepancies in
the data, but also allows easier inference as to whether the discrepancy is
static or changes over time.
The construction of a table such as Table 8.2 effectively reduces the
number of dimensions from two to one. This presentation makes it more
difficult for the reader to discern the subgroup information that the analysis
emphasizes. While this organization matches the input to most statistical
packages for correct analysis, it is not the best presentation for humans
to discern the groups.
Keep in mind that tables are simply text-based graphics. All of the rules
presented for graphical displays apply equally to textual displays.
The proper organization of the table in two dimensions clarifies the subgroup
analysis. Tables may be augmented with decorative elements just as
we augment graphics. Effective additions to the table are judged on their
ability to focus attention on the science; otherwise these additions serve as
distracters. Specific additions to tables include horizontal and vertical lines
to differentiate subgroups, and font/color changes to distinguish headings
from data entries.
Fat Surfactant
1 2 3
1 5.57 6.20 5.90
2 6.80 6.20 6.00
3 6.50 7.20 8.30
Specifying a y axis that starts at zero obscures the differences of the
results and violates Rule 3 seen previously. If we focus on the actual values
of the subgroups, we can more readily see the differences.
TWO RULES FOR TEXT ELEMENTS IN GRAPHICS
If a picture were worth a thousand words, then the graphics we produce
would considerably shorten our written reports. While attributing "a thousand
words" for each graphic is an exaggeration, it remains true that the
graphic is often much more efficient at communicating numeric information
than equivalent prose. This efficiency is in terms of the amount of
CHAPTER 8 GRAPHICS 121
Fat Surfactant Volume
1 1 5.57
1 2 6.20
1 3 5.90
2 1 6.80
2 2 6.20
2 3 6.00
3 1 6.50
3 2 7.20
3 3 8.30
TABLE 8.2 Volume of a Mixture Based on the Included
Fat and Surfactant Typesa
a
Problem: The two categorical variables are equally of
interest, but the table uses only one direction for
displaying the values of the categories. This demonstrates
that table generation is similar to graphics generation, and
we should apply the same graphical rules honoring
dimensions to tables.
TABLE 8.3 Volume of a Mixture Based on the Included
Fat and Surfactant Typesa
a
The two categorical variables are equally of interest.
With two categorical variables, the correct approach is to
allow one to vary over rows and the other to vary over
columns. This presentation is much better than the
presentation of Table 8.2 and probably easier to interpret
than any graphical representation.
information successfully communicated and not necessarily any space
savings.
If the graphic is a summary of numeric information, then the caption is a
summary of the graphic. This textual element should be considered part of
the graphic design and should be carefully constructed rather than placed as
an afterthought. Readers, for their own use, often copy graphics and tables
that appear in articles and reports. Failure on the part of the graphic
designer to completely document the graphic in the caption can result in
gross misrepresentation in these cases. It is not the presenter who copied
the graph who suffers, but the original author who generated the graphic.
Tufte [1983] advises that graphics "should be closely integrated with the
statistical and verbal descriptions of the data set" and that the caption of the
graphic clearly provides the best avenue for ensuring this integration.
Rule 9: Captions for your graphical presentations must be complete.
Do not skimp on your descriptions.
The most effective method for writing a caption is to show the graphic to
a third party. Allow them to question the meaning and information presented.
Finally, take your explanations and write them all down as a series of
simple sentences for the caption. Readers rarely, if ever, complain that the
caption is too long. If they do complain that the caption is too long, it is a
clear indication that the graphic design is poor. Were the graphic more
effective, the associated caption would be of a reasonable length.
Depending on the purpose of your report, editors may challenge the
duplication of information within the caption and within the text. While
we may not win every skirmish with those that want to abbreviate our
reports, we are reminded that it is common for others to reproduce only
tables and graphics from our reports for other purposes. Detailed captions
help alleviate misrepresentations and other out-of-context references we
certainly want to avoid, so we endeavor to win as many of these battles
with editors as possible.
Other text elements that are important in graphical design are the axes
labels, title, and symbols that can be replaced by textual identifiers. Recognizing
that the plot region of the graph presents numerical data, the axis
must declare associated units of measure. If the axis is transformed (log or
otherwise), the associated label must present this information as well. The
title should be short and serves as the title for the graphic and associated
caption. By itself, the title usually does not contain enough information to
fully interpret the graphic in isolation.
When symbols are used to denote points from the data that can be
identified by meaningful labels, there are a few choices to consider for
improving the information content of the graphic. First, we can replace all
122 PART II HYPOTHESIS TESTING AND ESTIMATION
symbols with associated labels if such replacement results in a readable
(nonoverlapping) presentation. If our focus highlights a few key points, we
can substitute labels for only those values.
When replacing (or decorating) symbols with labels results in an overlapping
indecipherable display, a legend is an effective tool provided that
there are not too many legend entries. Producing a graphical legend with
100 entries is not an effective design. It is an easy task to design these elements
when we stop to consider the purpose of the graphic. It is wise to
consider two separate graphics when the amount of information overwhelms
our ability to document elements in legends and the caption.
Too many line styles or plotting points can be visually confusing and
prevent inference on the part of the reader. You are better off splitting the
single graphic into multiple presentations when there are too many subgroups.
An ad hoc rule of thumb is to limit the number of colors or
symbols to less than eight.
Rule 10: Keep line styles, colors, and symbols to a minimum.
MULTIDIMENSIONAL DISPLAYS
Representing several distinct measures for a collection of points is problematic
in both text and graphics. The construction of tables for this
display is difficult due to the necessity of effectively communicating the
array of subtabular information. The same is true in graphical displays, but
the distinction of the various quantities is somewhat easier.
CHOOSING EFFECTIVE DISPLAY ELEMENTS
As Cleveland and McGill (1988) emphasize, graphics involve both encoding
of information by the graphic designer and decoding of the information
by the reader. Various psychological properties affect the decoding of
the information in terms of the reader's graphical perception. For example,
when two or more elements are presented, the reader will also envision
byproducts such as implied texture and shading. These byproducts can be
distracting and even misleading.
Graphical displays represent a choice on the part of the designer in terms
of the quantitative information that is highlighted. These decisions are
based on the desire to assist the analyst and reader in discerning performance
and properties of the data and associated models fitted to the data.
While many of the decisions in graphical construction simply follow convention,
the designer is still free to choose geometric shapes to represent
points, color or style for lines, and shading or textures to represent areas.
The referenced authors included a helpful study in which various graphical
styles were presented to readers. The ability to discern the underlying inforCHAPTER
8 GRAPHICS 123
Rank Graphical Elementb
1 Positions along a common scale
2 Positions along identical, nonaligned scales
3 Lengths
4 Angles
4­10 Slopes
6 Areas
7 Volumes
8 Densities
9 Color saturations
10 Color hues
mation was measured for each style, and an ordered list of effective elementary
design choices was inferred. The ordered list for illustrating numeric
information is presented in Table 8.4. The goal of the list is to allow the
reader to effectively differentiate among several values.
CHOOSING GRAPHICAL DISPLAYS
When relying completely on the ability of software to produce scientific
displays, many authors are limited by their mastery of the software. Most
software packages will allow users to either (a) specify in advance the
desired properties of the graph or (b) edit the graph to change individual
items in the graph. Our ability to follow the guidelines outlined in this
chapter is directly related to the time we spend learning to use the more
advanced graphics features of software.
SUMMARY
* Examine the data and results to determine the number of dimensions
in the information to be illustrated. Limit your graphic to
that many dimensions.
* Limit the axes to exactly (or closely) match the range of data in
the presentation.
* Do not connect points in a scatterplot unless there is an underlying
interpolation that makes scientific sense.
124 PART II HYPOTHESIS TESTING AND ESTIMATION
TABLE 8.4 Rank-Ordered List of Elementary Design
Choices for Conveying Numeric Informationa
a
Slopes are given a wide range of ranks since they can be
very poor choices when the aspect ratio of the plot does
not allow distinction of slopes. Areas and volumes
introduce false dimensions to the display that prevent
readers from effective interpretation of the underlying
information.
b
Graphical elements are ordered from most (1) to least
(10) effective.
ˇ Recognize that readers of your reports will copy tables and figures
for their own use. Ensure that you are not misquoted by completely
describing your graphics and tables in the associated
legends. Do not skimp on these descriptions or you force readers
to scan the entire document for needed explanations.
* If readers are to accurately compare two different graphics for
values (instead of shapes or predominant placement of outcomes),
use the same axis ranges on the two plots.
* Use pie charts only when there are a small number of categories
and the sum of the categorical values has scientific meaning.
* Tables are text-based graphics. Therefore, the rules governing
organization and scientific presentation of graphics should be
honored for the tables that we present. Headings should be differentiated
from data entries by font weight or color change. Refrain
from introducing multiple fonts in the tables and instead use one
font where differences are denoted in weight (boldness), style
(slanted), and size.
* Numeric entries in tables should be in the same number of significant
digits. Furthermore, they should be right justified so that
they line up and allow easy interpretation while scanning columns
of numbers.
* Many of the charts could benefit from the addition of grid lines.
Bar charts especially can benefit from horizontal grid lines from
the y-axis labels. This is especially true of wider displays, but grid
lines should be drawn in a lighter shade than the lines used to
draw the major features of the graphic.
* Criticize your graphics and tables after production by isolating
them with their associated caption. Determine if the salient information
is obvious by asking a colleague to interpret the display. If
we are serious about producing efficient communicative graphics,
we must take the time ensure that our graphics are interpretable.
TO LEARN MORE
Wilkinson (1999) presents a formal grammar for describing graphics, but
more importantly (for our purposes), the author lists graphical element
hierarchies from best to worst. Cleveland (1985) focuses on the elements
of common illustrations where he explores the effectiveness of each
element in communicating numeric information. A classic text is Tukey
(1977), where the author lists both graphical and text-based graphical
summaries of data. More recently, Tufte (1983, 1990) organized much of
the previous work and combined that work with modern developments.
For specific illustrations, subject-specific texts can be consulted for particular
displays in context; for example, Hardin and Hilbe (2003, pp.
143­167) illustrate the use of graphics for assessing model accuracy.
CHAPTER 8 GRAPHICS 125