Re: New plot capability: "bee swarm" plots

[Ethan A M. <sf...@us...>]

On Tuesday, 15 September, 2015 21:32:17 Tait wrote:
> >   http://www.jmp.com/support/help/images/students.gif
> > ...
> > I found those random jitter plots to be ugly so I never pursued it.
> > I find the beeswarm plots to be much nicer visually and they also
> > convey more information.  ...
> 
> Random jitter may not be very pretty, but within the bounds of what
> it's meant to do, it doesn't distort the data. 

But it does distort!  It gives the visual impression of a uniform scatter
at every y value, which hides the very feature that it is intended 
to convey.  What you want (or at least what I would want :-) is
to leave singleton points unperturbed but separate overlapped points
so you can see how many there are.  That is what the beeswarm plots
do, but not what random jitter does.

> In the limit of
> enough data points, a random jitter would also approach a 2-D
> boxplot or "violin" plot. 

That is not correct.  The distribution of points at each y value
will approach the randomization function, not the PDF envelope
of the data.  And not a standard box plot either.

Here is a direct comparison of the output using the swarm jitter
and a random (normal distribution) displacement about x.

  http://skuld.bmsc.washington.edu/~merritt/gnuplot/violin.html

The random jitter is better than I might have predicted,
but is strictly worse than a violin plot IMHO.  

A uniform random jitter would convey almost no information.
Note that a standard box plot is even worse.

> Pretty graphs are nice, but the plotting
> tool should not encourage them at the expense of accuracy.

Yeah, but in my experience random jitter is not a good way to convey
the desired information.  I played with it a fair amount a couple
of years ago as a possible gnuplot option for version 5 before giving up.

At that same time I tried to work out how to implement violin
plots, and failed to find a good solution.

For both of these reasons I was very pleased when Kevin Rattigan's
question made me aware of beeswarm plots.

	Ethan