[R] Tables with Graphical Representations

[(Ted Harding)]

On 02-Sep-06 Anupam Tyagi wrote:
> First Graphic in the initial posting: I think this graphic need
> to be scaled in a manner so it can be interpreted correctly while
> going across rows, columns, and non-contguous cells, or the correct
> interpretation and way to read this provided. For example, in the
> last row one has to read the numbers to get the correct information
> out. It will be good to have documentation that explains how to
> read/interpret this graph, otherwise fixed length boxes are
> visually confusing. Anupam.

You are perhaps asking too much from this kind of graphic.

All graphical displays have both merits and limitations. The design
of the display (if it has been thought out) will be chosen so as to
exhibit what the writer wants the reader to see "immediately", along
with "deeper" detail which can be perceived by taking a longer and
closer look but without demanding too dispersed an attention which
can confuse and overload the reader.

In this particular case, one can very quickely see that some 4 cancers
(Prostate-Melanomas) have quite good survival rates over all 4 5-year
periods. For the next four (Breast-Urinary), though survival is good
for the first 5-year period, it can be seen that it is more variable
for subsequent periods. The next 8 (Cervix-Ovary) have a broadly
similar initial survival rate (50%-75%) with subsequent survival
very variable between different cancers. Then there is a somwhat
suddent jump to the final group of eight (Leukemia-Pancreas) where
initial survival (and therefore longer-term survival) is low.

I think the above summary is all that can be directly derived from
the graphical information, and it may be what the designer wanted
to convey, Or, at least, I hope so -- for, if the deigner wanted
to convey something different then the design has failed.

For instance, one important question is what are the chances of
survival over period 5-10 years, given that one has survived the
first 5 years. One can only get a very approximate and qualitative
idea of this from the graphic (see for instance the above comparison
between cancers 1-4 and cancers 5-8). So this design is bad for
conveying information about this question. A design appropriate for
this would show similar Red/Grey boxes, but now the proportion of
Red would be the probability of survival through the current 5-year
period, conditional on having survived to the beginning of it.

But then it would be difficult to interpret the graphic relative
to the question "what is the survival rate to 5 years, to 10 years,
... ?"

Of course one could combine the two kinds of graphic in the one
display -- a top row of boxes for each cancer as now, and a second
row giving conditional survival rates. But then the eye has trouble
comparing different cancers for one of these two, since there is
visual distraction from the other (a case of requiring dispersed
attention). This could be alleviated by off-setting the second row
to the right of the first row, so that as well as running horizontally
along each row the eye can also run down vertically along the column
for the particular type of survival (unconditional or conditional).
But then the table would become much wider, so there would be problems
about how best to fit it on the page (maybe in landscape).

And so it goes on ...

As to your point about not being able to perceive the numerical
variations in (say) the last row, you have to think about the
technology here. When I view that web page on my screen, I see
boxes about 1cm wide (a little less in fact). A computer screen
has about 5 pixels/mm, so 50 pixels/cm. But the percentages in
the last row: 4.0%, 3.0%, 2.7%, 2.7%, vary over a range 1.3%.
Now a percentage difference of less than 2% simply cannot be
perceived when 1 pixel is at least 2% of the width of the box.
You might argue that this would be helped by having wider boxes,
but they would have to be much wider (by a factor of say 10)
before you could make detailed sense of the last row.

Which goes to show that the main message which can be perceived
in this graphic is in the rather coarse comparisons which can
be made between cancers (and periods) where the rates differ by
fairly substantial amounts -- say at least 10%.

For anything else, you have to look at the numbers anyway. The
merit of this particular design is that you can look at the
boxes without being seriously distracted by the numbers, or look
at the numbers without being seriously distracted by the boxes,
yet both are present at the same time.

In summary: design of a graphic display is literally an art.
What one display can reveal, another will conceal.

Best wishes,
Ted.

--------------------------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
Fax-to-email: +44 (0)870 094 0861
Date: 02-Sep-06                                       Time: 10:29:20
------------------------------ XFMail ------------------------------