The grammar of graphics (L. Wilkinson)

October 30, 2009

(This article was first published on Vincent Zoonekynd's Blog , and kindly contributed to R-bloggers)


Though this book is supposed to be a description of the
graphics infrastructure a statistical system could
provide, you can and should also see it as a (huge,
colourful) book of statistical plot examples.

The author suggests to describe a statistical plot in
several consecutive steps: data, transformation, scale,
coordinates, elements, guides, display. The “data” part
performs the actual statistical computations — it has to be
part of the graphics pipeline if you want to be able to
interactively control those computations, say, with a slider
widget. The transformation, scale and coordinate steps,
which I personnally view as a single step, is where most of
the imagination of the plot designer operates: you can
naively plot the data in cartesian coordinates, but you can
also transform it in endless ways, some of which will shed
light on your data (more examples below). The elements are
what is actually plotted (points, lignes, but also
shapes). The guides are the axes, legends and other elements
that help read the plot — for instance, you may have more
than two axes, or plot a priori meaningful lines (say, the
first bissectrix), or complement the title with a picture (a
“thumbnail”). The last step, the display, actually produces
the picture, but should also provide interactivity
(brushing, drill down, zooming, linking, and changes in the
various parameters used in the previous steps).

In the course of the book, the author introduces many
notions linked to actual statistical practice but too
often rejected as being IT problems, such as data mining,
KDD (Knowledge Discovery in Databases); OLAP, ROLAP,
MOLAP, data cube, drill-down, drill-up; data streams;
object-oriented design; design patterns (dynamic plots
are a straightforward example of the “observer pattern”);
eXtreme Programming (XP); Geographical Information
Systems (GIS); XML; perception (e.g., you will learn that
people do not judge quantities and relationships in the
same way after a glance and after lengthy considerations),
etc. — but they are only superficially touched upon,
just enough to wet your apetite.

If you only remember a couple of the topics developped in
the book, these should be: the use of non-cartesian coordinates and,
more generally, data transformations;
scagnostics; data patterns, i.e., the meaningful reordering of
variables and/or observations.

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