# Statistics for Environmental Engineers

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Randomization also helps to eliminate the corrupting effect of serially correlated errors (i.e., process or instrument drift), nuisance correlations due to lurking variables, and inconsistent data (i.e., different operators, samplers, instruments).

Figure 22.1 shows some possibilities for arranging the observations in an experiment to fit a straight line. Both replication and randomization (run order) can be used to improve the experiment.

Must we randomize? In some experiments, a great deal of expense and inconvenience must be tolerated in order to randomize; in other experiments, it is impossible. Here is some good advice from Box (1990).

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No replication No randomization

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Randomization without replication

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Replication with Randomization • 5 • 3 • 1

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FIGURE 22.1 The experimental designs for fitting a straight line improve from left to right as replication and randomization are used. Numbers indicate order of observation.

1.    In those cases where randomization only slightly complicates the experiment, always randomize.

2.    In those cases where randomization would make the experiment impossible or extremely difficult to do, but you can make an honest judgment about existence of nuisance factors, run the experiment without randomization. Keep in mind that wishful thinking is not the same as good judgment.

3.    If you believe the process is so unstable that without randomization the results would be useless and misleading, and randomization will make the experiment impossible or extremely difficult to do, then do not run the experiment. Work instead on stabilizing the process or getting the information some other way.

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