[S] pie charts

Dave Krantz (dhk@paradox.psych.columbia.edu)
Fri, 13 Nov 1998 10:51:59 -0500 (EST)

I have to confess that I don't remember exactly what Bill Cleveland's
arguments were, re pie charts, but I will chime in with a few comments
anyway. I don't suppose that my Ph.D. in mathematical psychology
will be rescinded, any more than Charlie Roosen's in statistics.

Robert Garrett's example is a good one, because it rests on two
advantages of circles over bars. The center of a circle is much
more perceptually salient than that of a bar (and very much more
than the centroid of a group of bars), so circle centers are a good
code for conveying location. Moreover, with circles, one can let
radii convey absolute magnitudes while angular arcs convey relative
proportions; it is not clear that anything one could do with bars
would be as effective in this respect. These two advantages
seem to be more important than the disadvantages of pie charts,
for the application that Garrett described.

There are many advantages to systematic psychophysical study of
graphical devices, of the sort that Cleveland and others have
undertaken; but it is also important to recognize that when it
comes to human perception, we can (and do) test many things just
by looking at them. There is some danger in this, because we
may look at graphs with various conventions in mind that we know
well and our readers know less well or not at all; but keeping
this danger in mind, it is still possible to run quick perceptual
experiments to find out a lot about what works in particular cases.
One should be careful about extrapolating laboratory results,
obtained with particular tasks, beyond the range of conditions
in which they were tested. Jim Hodges' suggestion that bar charts
are (always?) superior to pie charts perceptually seems too strong.

Apart from Garrett's example, which is perhaps atypical, the
relative merits of pie and bar charts may depend on several
factors such as (a) whether chromatic color, rather than gray
scale or pattern is used; (b) whether the key mental operations
for the inference task involve comparisons of proportions within
a group or comparisons of corresponding proportions between groups;
and (c) the importance of providing salient estimates of sampling error
(which is much harder in pie charts).

While I do not usually like pie charts, and in particularly tend
to agree with all of Peter Bouman's points, it is still true that
many clients really like pie charts, and it behooves us to
think hard about why this is so; it can be a good clue to the
mental operations that they are performing on the graphic input.

Dave Krantz

----partial summary of previous contributions follows----

Bill Venables, Nov 12, 1998:

> I received the following...
> N> I have been recently converted to being an S-Plus user,
> N> and as an avid fan of pie diagrams I was gravley concerned
> N> to find some hostility from you aimed towards them in your
> N> set of notes.
> The answer is yes, I do rather look down upon pie diagrams as an
> ineffective device and something that can be easily bettered, but
> also as something so typical of the abuses of statistics that
> Disraeli so justifiably ridiculed. Nevertheless I am curious to
> know what other people think about them. Am I alone in this?
> Irrespective of my opinion of their value I do support their
> inclusion in S-PLUS, though. After all managers, advertising
> executives, lawyers, politicians and their kind have as much
> right to use S-PLUS as any of us... :-)

Charlie Roosen, Nov 12, 1998:

> Note that I'm not at all speaking for MathSoft...
> I like pie charts!
> In particular, I like pie charts for showing the proportions allocated
> to different groups. For example, displaying how my meagre 401K
> (retirement) account is allocated between different mutual funds.
> Now my understanding is that it's too late to take back my
> Statistics degree, even if I go around spouting such heresy...

Peter Bouman <pbouman@sachs.com> Nov 13 1998:

> In general, Cleveland documents that the "visual tasks" involved in
> decoding the information presented in pie chart format are more
> difficult and less accurate than those involved in reading, say, a dot
> chart. For example, the eye just isn't as good at comparing
> information encoded in angles (pie charts) as in distances along a common
> scale (dot charts).
> Many of us also work in areas where data points have associated
> uncertainties and confidence intervals, which dot charts (e.g.) can present,
> but pie charts can't.
> More generally, why use a presentation format which demonstrably distorts
> or hides subtle data differences, and has to be supplemented, by
> Roosen's own admission, by numbers next to the pie slices? This seems to
> violate the spirit of good graphical presentation of data, which
> should invite the eye to make valid data comparisons on its own.
> I suppose I write this only because I have seen so many poor graphical
> presentations of data which often acted to obscure the very point
> they were trying to make-inexcusable because there are so many good authors
> in the field (Cleveland, Tufte, Tukey, et. al.) who have publicized good
> practices.

Robert Garrett, Nov 13 1998:

> I agree that Pie Diagrams have their problems, but I would like to
> give one example where they did help visualization of a complex
> spatial data set.
> Heavy minerals were separated from glacial tills in the Canadian
> Prairies and semi-quantitatively analysed. As a result the data set
> consisted of a spatial location, the total weight of heavy minerals
> separated, mg/kg, and the weights, mg, of the individual types of heavy
> minerals for some 816 sites. An initial investigation showed that six
> of the heavy mineral types provided useful information for identifying
> the regions which were the sources of the glacial tills, but that
> absolute weight of heavy minerals was important. The solution to
> visualizing this data set was to plot pies at their spatial locations
> on a map where the diameter of the pie was proportional to the sum of
> the six heavy mineral weights, and the pie was divided and coloured in
> proportion to the contributions of the six heavy minerals. This
> provided a visualization where the seven important variates were
> displayed in a form that allowed recognition of individual glacial
> tills with characteristic heavy mineral assemblages in the Canadian
> Prairie region, and provided geologists with information they could use
> to ascertain the source areas of the tills.

Jim Hodges Nov 13 1998:

> Thanks to Robert Garrett for sending the example, but for my money it'd
> still be better to make a bunch of little bar charts than a bunch of
> little pie charts. If the bar charts were all on the same scale, you
> could still convey both kinds of information and it would, per Cleveland,
> be perceptually superior.

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