Deltagraph Related News
Hearne staffer wins 2001 Best Technical Writer Award.
30 March, 2002
Hearne staffer wins 2001 Best Technical Writer Award.
Congratulations to all finalists and winners of the fifth annual Consensus IT Writers Awards announced and presented on Wednesday 7 March 2001 at the Merchant Court Hotel, Sydney.
Shaun Flint has managed technical support at Hearne for seven
years. The winning article, which was published in Charter, is
reproduced below.
Graph created with SigmaPlot 2000
Introduction
Graphs are now ubiquitous in modern society. Intuitively, we are
expected to know how to read them and build them. Essentially, they're
constructed by adapting a list of common components that - depending on
how skilfully they are used - will either help or hinder their message.
These components include axes, data points, legends, titles, error
bars, reference lines and others. Within each of these, there are many
variations open to the graph builder: for example, each axis can be
varied according to its scale, weight, position, tickmarks or labels.
What principles should artists apply in determining how to adapt these
elements to their own graphs? Their key concern should be to produce
graphs in which data points are clearly defined and not cluttered. The
data region should be similarly well defined - the standard technique
is to frame it with the rectangle formed by two pairs of axes. Under
the headings that follow, I have tried to summarize the essentials of
my own reading into what constitutes an effective graph. A number of
texts and articles were especially useful in compiling this article;
they're listed below.
Graph created with Systat 9
Simplicity
One key principle underlying an effective graph is simplicity. When
an eye scans the page, it registers everything - that attractive
background graphic, the odd scale on the X axis, the fancy gridlines,
the plot frame, the colors and (you hope) the thin black trace that is
the focus of the whole affair. By keeping your graphs clean and
uncluttered, you remove the ambient noise and allow the reader to
concentrate on your core message - your results.
Graph created with SigmaPlot 2000
Contrast
The eye does not perceive things in isolation, and for a graph to
have impact it helps to have a bold contrast that clearly
differentiates between groups within your results or clearly
differentiates your results from the graph's background. This is
because the process we use to translate the image on our retina into
objects that we can manipulate with our minds (in other words, the
process we use to recognize that a picture of a horse does, in fact,
correspond to a horse) depends largely on edge recognition. A crisp,
clean delineation at edges makes it easy for our subconscious edge
recognition algorithm, the ultimate outcome being a graph that stands
out and draws the reader's attention.
Graph created with Axum 6
How Many Lines
The short answer to this question is: no more than about six. When
we view a graph we mentally deconstruct it, extract the important
points and temporarily store them in short-term memory. As most people
discovered fairly early in life, our short-term memory is only good for
storing about eight to ten items at most. Given that short-term memory
is the first step to long-term remembering, it makes sense that we
don't overload this gateway.
Graph created with SigmaPlot 2000
Axis scales and coordinate systems
Don't feel constrained to a standard Cartesian coordinate system
with linear x,y axes - often, by careful consideration of the purpose
of your graph leads you find a much more appropriate choice. For
example, to illustrate the parametric function for a cylinder, use
cylindrical coordinates. To illustration logarithmic relationships use
a logarithmic scale. Logarithmic scales and other data transforms are
also useful in increasing the resolution of severely skewed data. Try
to arrange the axis scaling so that the data fills as much of the plot
region as possible. Furthermore, if your reader needs to compare data
from two different graphs, make the scales identical. When designing a
graph's axes, remember that sometimes it is useful for a reader to
reference the same data points using two different scales; for example,
where two different unit systems are generally accepted.
Graphs created with SigmaPlot 2000
Problems with perspective
It's a neat trick, the way you can turn a standard, two-dimensional
plot into a three-dimensional masterpiece just by adding some depth.
From the point of view of communicating information, however, tricks
like this can be counterproductive. Adding perspective adds numerous
confusing visual cues that make comparisons between traces difficult
and reading values from axes next to impossible. Compare the two graphs
shown with the purpose of analysing magnitudes and trends - the point
is made.
Graph created with Mathcad 2000
Illusions of 3D
Three-dimensional vision is subtler than just simply interpreting
binocular disparity (the slightly different pictures presented to each
eye). Close one eye - the world does not suddenly appear flat. In
truth, we also rely on a number of other visual cues to create the
impression of depth. Shading and the convergence of parallel lines are
important cues in creating the three-dimensional illusion of the
spheres in the graph, above. Their relative sizes form a powerful hint
that they lie at different distances from the observer. When these
sorts of cues are delivered out of context (especially those involving
angles) classic visual illusions are created that distort our judgement
of lengths and angles. Be aware that such errors in judgement may also
feature in graphs, where these cues can appear either intentionally or
unintentionally.
Graph created with SigmaPlot 2000
Figure-ground separation
The way a graph is framed can have just as much influence on our
interpretation as the data points themselves; this interaction between
data points and their background is known as figure-ground separation.
In this example, the same data are plotted in both graphs. The data on
the right, however, appear to cluster strongly in a circle whereas the
data on the left seem much more irregular. The key factor is the
greater degree of contrast between the data on the right and the
background; this contrast leads the mind to unconsciously integrate the
data points into an overall pattern, making them seem more correlated.
Graph created with Surfer 7
Colour scales
We're all familiar with the standard linear representation of the
colour spectrum, ranging from deep red on the left to vivid blues and
purples on the right. Unfortunately, our brain doesn't work like that -
our internal representation of the same visible spectrum is probably
closer to a horseshoe than a line, with the result that colours on
opposite ends of the spectrum seem 'closer' to each other than to those
mid-spectrum. This can lead us into trouble when we use the colour
spectrum to represent a linear variable, because although your graphing
software might create a perfect linear colour scale in the mind's eye
this is subtly transformed into complex nonlinear relationship. The
workaround? Use carefully selected segments of the colour spectrum for
your colour scales, if you use them at all.
Graph created in Deltagraph 4.0
Pitfalls of the power law
You may be tempted to use attributes such as area, volume or
shading to represent information in your graphs - a word of warning.
The way in which the human brain interprets these properties is not
entirely accurate. For example suppose you were using the area of a
circle to represent a variable, such as harvest yields. Imagine that
one of these circles was twice the area of another, signifying that the
yield had doubled. Instead of recognising this correctly, the reader is
likely to underestimate the change and perceive ratio of areas as only
about 1.6. Stanley Stevens, in 1953, researched this phenomenon and
deduced a power law relationship between the perceived magnitude and
the actual magnitude of a stimulus such as area. The exponent n varies
depending on the particular stimulus; for area, it can vary from
0.6-0.9. To represent data in graphs you obviously want to pick a
stimulus with an n as close to 1 as possible; a good example of this is
position measured against a common scale (the standard method of
plotting xy data).
Graph created with Mathcad 2000
Cleveland's list
In his book, The Elements of Graphing Data (1985), W.S. Cleveland
identified an approximate ordering of the ways of graphing a
quantitative variable. This ranking was developed according to the
ability of the method to accurately represent actual values with as
little distortion in the interpretation as possible (see Pitfalls of
the Power Law). From most accurate to least accurate, Cleveland's
hierarchy is as follows:
Graphs created with Axum 6
Humble Pies
It's not the purpose of this article to place a blanket ban on pie
charts but you must at the very least consider your alternatives
carefully before using them, given the following facts: 1. Any data
represented by a Pie Chart can be represented using the standard x,y
coordinate system. 2. Pie Charts rely on angle judgements to
communicate quantity. 3. Angle judgements are deceptive and difficult
(on Cleveland's list, angles judgements are rated as much less reliable
than judgements of position on a common or nonaligned scales and
length). By way of a simple demonstration, try to rank the slices in
the example Pie chart in order of size. Then compare your results with
the chart on the left.
Graph created with S-Plus
Effective complexity
There are a number of ways to simplify the presentation of complex,
multidimensional data, thus increasing its impact. Instead of resorting
to three dimensional plots -creating problems of depth and perspective
as a consequence - consider using a Trellis graphic (see inset) to plot
the extra dimensions as conditioning variables. This method creates a
number of different 'snapshots' of your data that are then presented as
panels of a trellis. The corresponding range of the conditioning
variable is shown in the strip chart above each panel. A scatterplot
matrix is another alternative that can be used to reduce
multidimensional data in two dimensions.
Graph created in Deltagraph 4.0
Audience is important
It may sound obvious, but graphs destined for a slide presentation
and an academic journal should look different. Consider carefully such
factors as the length of time your audience will spend viewing your
graph and the level of familiarity your audience has with your subject.
These factors should ultimately determine the design of the finished
graph.
Graph created with Systat 9
Out of the ordinary
Over the years a number of creative ways of qualitatively
representing a large number of variables has been developed. Chernoff
Faces rely on the special ability of the human brain to distinguish
between human faces. Each aspect of the cartoon faces - for example,
the angle of the eyebrows or curve of the mouth - in the illustration
is controlled by a different variable. The overall effect is to allow
qualitative comparison of different cases - those with similar
expressions have similar underlying characteristics. Of course,
different facial features have a varying impact on our assessment -
experiments have demonstrated that when volunteers scan a picture of a
face, their eyes movements overwhelmingly concentrate on the eyes and
nose.
Graph created with Mathematica 4
Graphics as art
Of course, so far I have arguably omitted an often neglected
function of graphs - to inspire. By presenting a visually appealing
image graphs can become works of art in their own right, with no
purpose other than to enthuse the reader to become more deeply involved
in their subject. When you create a graph in this manner, designed to
motivate rather than communicate a result, the principles presented
here cease to be binding. Only time and imagination then bound your
graph's potential. The example only touches the surface of what's
possible - for one perspective of graphs as art, point your web browser
to www.graphica.com
Bibliography
Three books have been useful in compiling this list, and I
recommend any of them - but especially the first two - to anyone
interested in honing their skills in graph construction further.
Cleveland, W S (1985) The elements of graphing data Monterey, California: Wadsworth Advanced Books.
Wilkinson, L (1998) Cognitive Science and Graphic Design in Systat 8.0 Graphics (1998) Chicago: SPSS, Inc.
Kandel, E R, Schwartz, J H and Jessel, T M (1991) Principles of
Neural Science 3rd Edition, East Norwalk, Conneticut: Appleton and
Lange.
Attribution
Shaun Flint is a technical specialist at Hearne Scientific
Software, a role that involves working with a wide range of leading
graphing, statistical and mathematical software. In 1998 he completed a
BSc (Melb), with a major emphasis in the health sciences.