By Linfield C. Brown, Paul Mac Berthouex
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Extra info for Press-Statistics for Environmental Engineers
This becomes important if the smoothing function is used to predict future values, but it is not necessary if we just want to clarify the general underlying pattern of variation. An alternate to the moving average smoothers is the nonparametric median smooth (Tukey, 1977). A median-of-3 smooth is constructed by plotting the middle value of three consecutive observations. It can be constructed without computations and it is entirely resistant to occasional extreme values. The computational simplicity is an insignificant advantage, however, because the moving averages are so easy to compute.
The graph in the left-hand panel copies a style of graph 1 that appears often in print. The plot conveys little information and distorts part of what it does display. The T on top of the column shows the upper standard error of the mean. The lower standard-error-bar is hidden by the column. Because the data are plotted on a log scale, the lower bar (hidden) is not symmetrical. A small table would convey the essential information more clearly and in less space. Plots of Residuals Graphing residuals is an important method that has applications in all areas of data analysis and model building.
If the averages are calculated from different numbers of values, the confidence intervals would be different multiples of the standard error bars (according to the appropriate degrees of freedom of the t-distribution). Cleveland (1994) suggests two-tiered error bars. The inner error bars would show the 50% confidence interval, a middle range analogous to the box of a box plot. The outer of the two-tiered error bars would reflect the 95% confidence interval. Plotting data on a log scale or transforming data by taking logarithms is often a useful procedure (see Chapters 4 and 7), but this is usually done when the process creates symmetry.