Dear Joe,
I believe that what you're referring to is Stevens's Law in psychophysics,
which states that the perceived strength of a stimulus is proportional to
some power of the physical stimulus, with the power varying by type of
stimulus and by person. The average power for judgment of lengths is close
to 1, while for areas it's something like 0.8, making length judgments
superior in general to area judgments. This theory (and the aesthetic
objections to pie charts) notwithstanding, I believe that the several
experiments that have compared pie charts to bar charts have produced
conflicting and inconclusive evidence.
That said, I think that this is not relevant to comparisons between coxcomb
plots and pie charts, since both entail area judgments (although pie charts
also encode quantity in angles and arc lengths).
Regards,
John
At 10:07 AM 1/9/2004 -0600, you wrote:
Although Fox is technically correct, I believe there are _psychological_
results indicating that while our comparative perception of lines is
directly proportional to the quantities indicated, our perception of areas
is not proportional to the quantities. I've not been able to find the
reference though, so this remains a factoid.
Joe
-----Original Message-----
From: John Fox [<mailto:jfox@mcmaster.ca>mailto:jfox@mcmaster.ca]
Sent: Friday, January 09, 2004 8:28 AM
To: Naomi B. Robbins
Cc: 's-news'; Mike Friendly
Subject: Re: [S] Nightingale roses
Dear Naomi,
At 07:47 AM 1/9/2004 -0500, Naomi B. Robbins wrote:
>Apologies. I should have been more specific. There is a chapter on
roses in
>Wainer's "Visual Revelations." Florence Nightingale introduced these
plots
>in 1858. Other names for them are coxcomb plots, radial area plots,
>Nightingale's pies, and wedges plots. Harris in "Information Graphics"
calls
>them sector graphs. While a pie chart has fixed radius and varies the
angles,
>these plots have fixed angles and vary the radius: the radius varies
with the
>square root of the data. Nightingale's example can be seen at the following
>sites:
>
><http://www.florence-nightingale.co.uk/small.htm>http://www.florence-nigh
tingale.co.uk/small.htm
>
>http://www.math.yorku.ca/SCS/Gallery/historical.html
>
>It's clear from the latter that they can be drawn with SAS, but I don't
have
>or know how to use SAS.
Michael Friendly's four-fold plots (which are coxcomb-like plots for 2 x 2
contingency tables -- Wainer discusses a similar display) are implemented
in R, both in the base package and in the vcd (visualizing categorical
data) package. You might be able to adapt this code to your needs.
>While we're on the subject, I'd also be interested in your comments on
them.
>Clearly they are of historical interest. They lack some of the
weaknesses of
>pies, such as comparing angles.
Actually, the areas of pie segments, as well as the angles and arc lengths,
are proportional to the quantity plotted, so this isn't an argument for
coxcombs.
> Since the same category is always in the same
>position, it is easier to compare multiple roses than pies.
This is a better point, I think.
I hope that this helps,
John
-----------------------------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario, Canada L8S 4M4
email: jfox@mcmaster.ca
phone: 905-525-9140x23604
web: www.socsci.mcmaster.ca/jfox
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John Fox
Department of Sociology
McMaster University
Hamilton, Ontario, Canada L8S 4M4
email: jfox@mcmaster.ca
phone: 905-525-9140x23604
web: www.socsci.mcmaster.ca/jfox
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