Statistics for Environmental Engineers

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FIGURE 3.14 Several versions of plots that show how banning DDT helped the recovery of the bald eagle population in northwestern Ontario.

middle row are clear. The version on the right is cleaner and clearer (the box frame is not needed). The white lines through the bars serve as the vertical scale. The two graphs in the bottom row are better yet. The bars become dots with a line added to emphasize the trend. The version on the right smoothes the trend with a curve and adds a note to show when DDT was banned.

Most data sets, like this simple one, can be plotted in a variety of ways. The viewer will appreciate the effort required to explore variations and present one that is clear, precise, and efficient in the presentation of the essential information.

Should We Always Plot the Data?

According to Farquhar and Farquhar (1891), two 19th century economists, “Getting information from a table is like extracting sunlight from a cucumber.” A virtually perfect rule of statistics is “Plot the data.” There are times, however, when a plot is unnecessary. Figure 3.15 is an example. This is a simplified reproduction (shading removed) of a published graph that showed five values.

pH = 5 COD = 2300 mg/L BOD = 1500 mg/L TSS = 875 mg/L TDS = 5700 mg/L

FIGURE 3.15 This unnecessary graph, which shows just five values, should be replaced by a table.

These five values say it all, and better than the graph. Do not use an axe to hack your way through an open door. Aside from being unnecessary, this chart has three major faults. It confuses units—pH is not measured in mg/L. Three-dimensional effects make it more difficult to read the numerical values. Using a log scale makes the values seem nearly the same when they are much different. The 875 mg/L TSS and the 1500 mg/L COD have bars that are nearly the same height.

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