Page 34 - Statistics for Environmental Engineers

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3

Plotting Data

KEY WORDS box plot, box-and-whisker plot, chartjunk, digidot plot, error bars, matrix scatterplot,
percentile plot, residual plots, scatterplot, seasonal subseries plot, time series plot.

“The most effective statistical techniques for analyzing environmental data are graphical methods. They
are useful in the initial stage for checking the quality of the data, highlighting interesting features of the
data, and generally suggesting what statistical analyses should be done. Interesting enough, graphical
methods are useful again after intermediate quantitative analyses have been completed, and again in the
final stage for providing complete and readily understood summaries of the main findings of investiga-
tions (Hunter, 1988).”
The first step in data analysis should be to plot the data. Graphing data should be an interactive experimental
process (Chatfield, 1988, 1991; Tukey, 1977). Do not expect your first graph to reveal all interesting aspects
of the data. Make a variety of graphs to view the data in different ways. Doing this may:

1. reveal the answer so clearly that little more analysis is needed
2. point out properties of the data that would invalidate a particular statistical analysis
3. reveal that the sample contains unusual observations
4. save time in subsequent analyses
5. suggest an answer that you had not expected
6. keep you from doing something foolish

The time spent making some different plots almost always rewards the effort. Many top-notch statisti-
cians like to plot data by hand, believing that the physical work of the hand stimulates the mind’s eye.
Whether you adopt this work method or use one of the many available computer programs, the goal is
to free your imagination by trying a variety of graphical forms. Keep in mind that some computer
programs offer a restricted set of plots and thus could limit rather than expand the imagination.

Make the Original Data Record a Plot
Because the best way to display data is in a plot, it makes little sense to make the primary data record
a table of values. Instead, plot the data directly on a digidot plot, which is Hunter’s (1988) innovative
combination of a time-sequence plot with a stem-and-leaf plot (Tukey, 1977) and is extremely useful
for a modest-sized collection of data.
The graph is illustrated in Figure 3.1 for a time series of 36 hourly observations (time, in hours, is
measured from left to right).

30 27 41 38 44 29 43 21 15
33 33 28 49 16 22 17 17 23
27 32 47 71 46 42 34 34 34
44 27 32 28 25 36 22 29 24

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