HANDLING ATTENTION POINTS◆ 185Other techniques for data reduction
The only way to grasp a mathematical concept is
to see it in a multitude of different contexts, think
through dozens of specific examples, and find at
least two or three metaphors to power intuitive
speculations.
Greg Evans^6To present data well you have to really understand them. And
to do that, you have to look hard at them for a long time, and
ask an array of well-thought-out questions about what they
show. Yet modern PCs and software give all of us the ability to
crunch far more numbers than perhaps we have fully analysed,
and then to inflict them on our readers in an undigested way.
Data reduction means simplifying the numbers we are working
with. The field of exploratory data analysis offers many power-
ful techniques for doing this, and has an interesting literature
which I will only briefly touch on here.^7 Properly exploring and
reducing data is an essential principle for making progress in
understanding any set of numbers that you have to analyse, let
alone conveying that information accurately to readers. The
key principles of data reduction are:
◆Look hard at your primary data. Do not rely on analysis
packages to give you an intuitive picture of what you are
dealing with or to tell you what questions to ask. Analysis
packages can only work well for you if you already know
what shape of data you have. This is easy enough in
coursework where you are replicating someone else’s prior
analysis, but often very difficult for brand-new information
that you have just generated by research.
◆Always put your data in a numerical progression (easily
done in any spreadsheet). Chart them wherever possible,
and then look hard at the results. Never engage in more
complex forms of multivariable analysis, such as
correlations or regression analysis, without understanding
the visual shape of the primary data you are handling.
◆When trying to see patterns in your data remove as much of
the ‘clutter’ as possible. For instance, try looking at a version