Duh, duh, exhibits ignored, personal defensive stance taken, while my aim
was quite the opposite (I thought it was obvious, but apparently ...).
Anyway, my point was and is that notched boxplots *ARE* used in "real
display of information", "heat of the battle" or whatever one calls that --
at least every now and then.
To add to the ignored exhibits (deliberately as diverse as I could find -- I
thought it was obvious that wide as my interest and experience may be,
neither am I an entomologist or anthropologist, but apparently ...), they
are not exceedingly rare in medical articles.
Related to that, I remember MedCalc (
www.medcalc.be, a
clinician-not-statistician oriented package) being praised in a software
review in a medical journal for producing them. And Minitab produces them
also, which has a reputation of "canning" only the actually used methods
rather than as many as possible in comparison to some other stats packages.
Anyway, precisely the attention of Excel experts (Pope, Cotter, Peltier; be
the attitude positive or negative) or even my own rant in an Excel forum
might make them less "obscure" for the "general public".
Now, if that does eventually happen, a further point worth mentioning is the
problem with what the whole point of the notches is, i.e., visually
assessing whether medians are [statistically significantly] different.
Namely, just like with error bars representing confidence interval for mean,
once you compare more than two samples, you run into the problem of multiple
comparisons ...
A publicly available reference from statistics education (BTW, full of
notched boxplots
) mentioning this is
http://www.amstat.org/publications/jse/v9n2/garrett.html
(Note that the main point is comparing variability rather then centre, so
the variable being plotted in Fig. 2 is absolute deviation from the median;
the key quote is "Groups for which the boxplot notch intervals do not
overlap are likely different in variability. (Here we encounter once again
the multiple comparison issue.)"
So, to summarise, if the aim is inference, perhaps the notches should be
appropriately <shortened> to compensate for multiple comparisons, i.e.,
prevent inflated type I error ('false alarms' in layman terms). Sort of like
the basic idea of Analysis of Means (ANOM) as a graphical alternative to
ANOVA.
Anyway, this is an Excel forum, not a statistical one (though, fortunately,
with precisely those experts I mentioned above, and some others, "under the
surface" actually making it mainly quite statistically sound). So, please,
Dr. Peltier, Mr. Cotter and others, take this just as praise and inspiration
for your knowledge and talents and good will to take notched boxplots into
account, and perhaps also ANOM.
To push thins further, both are, IMHO, among the many candidates for an
ambitious projects of a publicly available Excel "charting" add-in (perhaps
we should buzz-call it InfoVis add-in) ... Especially with Excel 2007 still
leaving so many thing to be desried in this department ...
-- I know that you, Dr. Peltier, have already done *A LOT* of great work in
this direction, but I'm just abusing this oportunity to ask you (and
others -- Mr. Cinquegrani comes to my mind first, and also Mr. O'Day) to
think how much time and funding this would take. -- Namely, for a while I've
been baldly thinking of an applied scientific project (with EU funding,
which can be seriously substantial; you <do most of the work>, I <take care
of the scientific references and pompous justification to actually get the
project>), and even Microsoft support is not unrealistic ... -- If you think
it's an uterly silly idea, or that the last thing you need is my advice and
co-operation, please, let me know, and likewise if you think it's not so
silly. It might even happen at some point after you will have finished and
successfully marketed your commercial add-in for a while -- the project and
funding could perhaps just make the add-in more comprehensive and compensate
for making it public domain.
Anyway, enough of digressions. Please, take the things I write utterly
benevolently -- like they are *ALWAYS* meant.
Cordial regrads,
Gaj
Jon Peltier said:
Gaj -
I'm not an entomologist, nor have I read much on the anthropology of
monkeys. I've worked in scientific research as a metallurgist (for my
doctorate and a dozen years of employment following that), and as an
engineer in manufacturing. Maybe not the widest mathematical background, and
I'm not degreed in statistics (though I've taken a graduate level course or
three). I've encountered thousands of box and whisker charts and their
variants, but I've never seen a notched box chart used in the heat of
battle.
- Jon
-------
Jon Peltier, Microsoft Excel MVP
Tutorials and Custom Solutions
Peltier Technical Services, Inc. -
http://PeltierTech.com
_______
Gaj Vidmar said:
Duh, every now and then even proved experts (even with a degree in
statistics) say something that leaves me deeply perplexed.
Less than five minutes of googling reveals these five fine examples:
- Exhibit 1 (electronics / mobile phone manufacturing, 1996)
http://ieeexplore.ieee.org/iel3/4031/12221/00561268.pdf?arnumber=561268
- Exhibit 2 (experimental / cognitive psychology, 1996)
http://faculty.washington.edu/jmiyamot/jmfiles/yamagishi asymmetries in strgth of pref.pdf
- Exhibit 3 (physical anthropology / monkeys, 2002)
http://www.hopkinsmedicine.org/FAE/CBR2002AJPA.pdf
- Exhibit 4 (entomology / PhD thesis on honeybee parasites, 1994)
[I mean, I've published in truly numerous fields of medicine, psychology,
statistics, computer science, nuclear physics, physiotherapy, management,
phylosophy and more and what not, but is this topic exotic or what?!]
http://doc.rero.ch/lm.php?url=1000,40,4,20050504083404-FL/2_these_RickliM.pdf
- Exhibit 5 (a physicist teaching maths presenting grade distribution at
an
exam, 2006/7)
[trust me from plenty of experience with such people that being a
physicist
and/or teaching mathematics otherwise tends to preclude knowledge and
understanding of statistics]
http://www.maths.qmul.ac.uk/~ob/MAS205_0607/moddocs/stats.pdf
[if URLs are broken across lines, please put them together in your
browser]
Note that I've selected only freely downloadable publications, while from
an
academic institution with subscription to various online services from
major
scientific publishers there are literaly dozens more readily available
examples!
Of course, your definition of "real display of information" might exclude
any kind of scientific or even technical publication, thus meaning only
"business" stuff and the general press. (Though I sincerly hope that it is
not what you meant.) In that case, my objection should be disregarded.
Regards,
Gaj Vidmar, PhD
Univ. of Ljubljana, Fac. of Medicine, Inst. of Biomedical Informatics
Jon Peltier said:
Del -
Your chart allows plenty of different quantities to be shown, but I suspect
it may become cluttered, and at least for now, it's unfamiliar, and
forces a
lot of back and forth between the chart and the legend. Don't knock a
"familiar idiom".
The box plot is pretty much self-explanatory especially since it is
familiar, and the difference between the box itself and the whiskers is
immediately recognizable (compared to your multiple error bars colored
different shades of gray, which is slower to be interpreted). If you
could
make whiskers of various line lengths, that might help.
I agree that the notched box plot must be rather obscure, as I've never seen
it used in any real display of information.
- Jon
-------
Jon Peltier, Microsoft Excel MVP
Tutorials and Custom Solutions
Peltier Technical Services, Inc. -
http://PeltierTech.com
_______
The technique describes how to use an xy-scatter to construct the
boxes.
You need to add a few more xy pairs in order to reduce the width of
the Median line and form the notches.
While I have as much reverence for the late John Tukey as the next
person, I don't see that boxes and whiskers as such are necessary these
days, except that they're a familiar idiom that the graph viewer will
usually recognise.
And even that isn't true for notched boxes, which I don't think many
people have seen. Certainly most couldn't interpret without them a
guide; I never even knew until reading that article just now what the
notches were supposed to represent-- I thought they were just meant to
enphasise the median in some way.
If we abandon the need to copy Tukey's shapes, doing this stuff in
Excel
immediately gets a lot easier. Here's my idea of a boxless "box" and
whisker distribution chart, with circled outliers and an error range
around the median, all just using the standard Excel symbol shapes.
http://i146.photobucket.com/albums/r264/del_c/
infographics/not_boxplot.gif
It would be simple to substitute circles, diamonds, or half-ticks, and
alter the thickness or colour of the Excel error bars, to suit your
preferences, and I think the point comes across even though they're not
the traditional boxes.
--
Del Cotter
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