[Jprogramming] Looking for graphical inspiration

[Devon McCormick]

Bill - here's one view of your data.  I swapped the middle two columns to
make
the axis labeling consistent, i.e.

   mm=. 0.2 0.1 0.2 0.1,0.7 0.6 0.7 0.6,0.8 0.6 0.8 0.6,:2.2 1.7 2.2 1.7

   mm=. |:mm
   mm=. |:(2 1{mm) 1 2}mm NB. flip middle columns so axes consistent

L L 0.2 0.2 0.1 0.1
L H 0.7 0.7 0.6 0.6
H L 0.8 0.8 0.6 0.6
H H 2.2 2.2 1.7 1.7
        L   L    H    H   Var 3
        L   H    L    H   Var 4

I would avoid moving around axes based on the particular values of data, as
you suggested, because this would give arbitrary and inconsistent pictures
of the
data across different experiments.

With the axes so moved, the ravel of the data could be labeled by base-2
values
of i. 16, e.g. #:i.16, but this linearizes it graphically, so is probably
not what you want.
However, the simplicity of labelling reflects the consistency of the axes.

Anyway, here's a view I came up with:
   mm=. 2 2 2 2$,mm NB. Conceptually, this is a 4-D array
   $<"2 mm
2 2
   <"2 mm
+-------+-------+
|0.2 0.2|0.7 0.7|
|0.1 0.1|0.6 0.6|
+-------+-------+
|0.8 0.8|2.2 2.2|
|0.6 0.6|1.7 1.7|
+-------+-------+
   ,.&>/,&.>/<"2 mm NB. Flatten it out
0.2 0.2 0.7 0.7
0.1 0.1 0.6 0.6
0.8 0.8 2.2 2.2
0.6 0.6 1.7 1.7
   viewmat ,.&>/,&.>/<"2 mm

Which has a nice symmetry though I don't know how helpful this is as far as
interpreting
your data.

Oleg's suggestion is a good example of extending plot but, in general, we
don't do a good
job of comparing relative areas which is what you get when you turn the
values into
diameters.

Regards,

Devon

On 4/5/07, Bill Harris <bill_harris at facilitatedsystems.com> wrote:
>
> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1
>
>
> I'm trying to communicate the results of a simple 4-factor factorial
> experiment.  I've set each of those factors to their miminum and maximum
> values, and I've got a list of 16 numbers representing the response at
> each of those 16 settings.
>
> I tried a surface or wire plot, but I couldn't figure out how to label
> the axes.  I tried a plot with i.16 on the abscissa, the responses at
> each of the 16 points on the ordinate, and a table to relate data point
> (abscissa) to experimental condition, but one person out of two who have
> seen it so far found that non-intuitive.
>
> If I try to sketch it here, it would become something like
>
>           V  V
>           a  a
>           r  r
>
>           1  2
>                  +---------------------+
>           L  L   |0.2   0.1   0.2   0.1|
>                  |                     |
>           L  H   |0.7   0.6   0.7   0.6|
>                  |                     |
>           H  L   |0.8   0.6   0.8   0.6|
>                  |                     |
>           H  H   |2.2   1.7   2.2   1.7|
>                  +---------------------+
>                   L     H     L     H     Var 3
>                   L     L     H     H     Var 4
>
>
> but with a graph in the middle.
>
> Has anyone seen a nice way to plot this?  It'd be nice if it worked well
> in J (or possibly Gnuplot) without a lot of manual placing of text on
> the graph.
>
> Part of me wonders if I'd be better off just to do a table of numbers.
> That might be pretty clear, especially if I swap the zeroth and first
> columns.  That would put the two highest variables at the center bottom
> and the next two at the outside bottom.  (Making such a table
> cylindrical makes that even clearer, but that may be a bit excessive.)
>
> Thoughts?
>
> Thanks,
>
> Bill
> - --
> Bill Harris                      http://facilitatedsystems.com/weblog/
> Facilitated Systems                              Everett, WA 98208 USA
> http://facilitatedsystems.com/                  phone: +1 425 337-5541
> -----BEGIN PGP SIGNATURE-----
> Version: GnuPG v1.4.3 (MingW32)
> Comment: For more information, see http://www.gnupg.org
>
> iD8DBQFGFXpI3J3HaQTDvd8RAkKcAJ41M7II96cKjgqjY5j0++hyEJK4wQCfchxt
> Ei7zaYmHBVhHJrLYHG9xH8Y=
> =UL2z
> -----END PGP SIGNATURE-----
>
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>



-- 
Devon McCormick, CFA
^me^ at acm.
org is my
preferred e-mail