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Its addition may have been coincidental with a change in some other factor. The way to avoid a false
conclusion about X is to do a comparative experiment. Run parallel trials, one with X added and one with
X not added. All other things being equal, a change in output can be attributed to the presence of X. Paired
t-tests (Chapter 17) and factorial experiments (Chapter 27) are good examples of comparative experiments.
Likewise, if we passively observe a process and we see that the air temperature drops and output
quality decreases, we are not entitled to conclude that we can cause the output to improve if we raise
the temperature. Passive observation or the equivalent, dredging through historical records, is less reliable
than direct comparison. If we want to know what happens to the process when we change something,
we must observe the process when the factor is actively being changed (Box, 1966; Joiner, 1981).
Unfortunately, there are situations when we need to understand a system that cannot be manipulated
at will. Except in rare cases (TVA, 1962), we cannot control the flow and temperature in a river. Nevertheless,
a fundamental principle is that we should, whenever possible, do designed and controlled experiments.
By this we mean that we would like to be able to establish specified experimental conditions (temperature,
amount of X added, flow rate, etc.). Furthermore, we would like to be able to run the several combinations
of factors in an order that we decide and control.

Replication
Replication provides an internal estimate of random experimental error. The influence of error in the
effect of a factor is estimated by calculating the standard error. All other things being equal, the standard
error will decrease as the number of observations and replicates increases. This means that the precision
of a comparison (e.g., difference in two means) can be increased by increasing the number of experimental
runs. Increased precision leads to a greater likelihood of correctly detecting small differences between
treatments. It is sometimes better to increase the number of runs by replicating observations instead of
adding observations at new settings.
Genuine repeat runs are needed to estimate the random experimental error. “Repeats” means that the
settings of the x’s are the same in two or more runs. “Genuine repeats” means that the runs with identical
settings of the x’s capture all the variation that affects each measurement (Chapter 9). Such replication
will enable us to estimate the standard error against which differences among treatments are judged. If
the difference is large relative to the standard error, confidence increases that the observed difference
did not arise merely by chance.

Randomization
To assure validity of the estimate of experimental error, we rely on the principle of randomization. It
leads to an unbiased estimate of variance as well as an unbiased estimate of treatment differences.
Unbiased means free of systemic influences from otherwise uncontrolled variation.
Suppose that an industrial experiment will compare two slightly different manufacturing processes, A
and B, on the same machinery, in which A is always used in the morning and B is always used in the
afternoon. No matter how many manufacturing lots are processed, there is no way to separate the difference
between the machinery or the operators from morning or afternoon operation. A good experiment does not
assume that such systematic changes are absent. When they affect the experimental results, the bias cannot
be removed by statistical manipulation of the data. Random assignment of treatments to experimental units
will prevent systematic error from biasing the conclusions.
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 tole-
rated in order to randomize; in other experiments, it is impossible. Here is some good advice from
Box (1990).
© 2002 By CRC Press LLC