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st: Scales dropping from your eyes (was broken axes)
Let me repeat, at a risk of becoming repetitive, that design decisions
should not be based on a whim, a vague personal preference, "what looks
prettier", or "what fills the space" *unless you have consciously decided
that the choice is trivial and irrelevant to the message.* Decisions are
made for positive reasons (it enhances the message) or because of
constraints (the Editor demands). The comments about transformed scales
in the current discussion do not appear to be backed with reasoning.
The ability of the audience to interpret the graph is also a vital
consideration, but do not assume that a more professional audience will be
able to correctly deconstruct a more complex graph, unless it is a layout
with which they are familiar (ie, a local standard).
One reason to use a transformed scale is to clarify a relationship. If
effects act on a variable in a multiplicative manner, the resulting plot
will generally be a curve. Plotting the transformed data (ie on a
transformed scale) may make the relationship a straight line. The
question of whether to label the transformed axis with the original or
transformed units is separate. One example Nick gave was to plot SARS
cases, or any epidemic where 1 carrier may infect N new cases. You
might choose to emphasize to the general public the potential rapid
growth, so plot on a natural scale, or attempt to model the spread for a
medical audience, so use a log scale and estimate the slope.
Another reason is to expand the detail in part of the scale. The problem
of displaying several categories when one is huge compared to all others
has been mentioned. Transforming to a log scale is one approach, but so
is making a nested display: one display of dominant versus the rest,
linked to a subdisplay of categories within "the rest". Plotting
percentages near 0 or 100 on a log scale makes it easier to see the rate
of change. A example I use comes from a US DOH report showing the varying
success of anti-smoking campaigns by age and educational groups.
Thirdly, the choice of units for measurements is itself a pragmatic
decision. We report temperature on a "linear" scale, but linear in what?
(I don't know, I've forgotten the physics). But acidity is always
reported on a log scale (pH), which gardeners seem to accept.
Earthquakes are reported on a log scale (Richter) related to energy, as is
loudness of sound (dB). Many plots, however, do not rely upon basic
measurements but display functions of them (eg, ratios).
Try "findit transint" to download a zip file of Stata hlp files for a
discussion on using transformations.
What is "right" for a graphic depends upon what you are trying to say, and
many problems arise because the creator of the graph clicked and accepted,
and did not design. You may have come across programs that "generate
jargon": from a list of words they assemble sentences that are grammatical
English, may sound impressive, but have no reason to be sensible or
If I'm not careful, I might use "axis of evil" as an example.
R. Allan Reese Email: firstname.lastname@example.org
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