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L1592_frame_C22 Page 188 Tuesday, December 18, 2001 2:43 PM

No replication Randomization Replication with
No randomization without replication Randomization
• • • 5
• 6
y • 5 y • • 4 y • 3 • 1
1
• 4 • 3
• 3 • 6 • 4 • 6
• 2 • 2 • 2
1 5
x x x
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.

Blocking

The paired t-test (Chapter 17) introduced the concept of blocking. Blocking is a means of reducing
experimental error. The basic idea is to partition the total set of experimental units into subsets (blocks)
that are as homogeneous as possible. In this way the effects of nuisance factors that contribute systematic
variation to the difference can be eliminated. This will lead to a more sensitive analysis because, loosely
speaking, the experimental error will be evaluated in each block and then pooled over the entire
experiment.
Figure 22.2 illustrates blocking in three situations. In (a), three treatments are to be compared but they
cannot be observed simultaneously. Running A, followed by B, followed by C would introduce possible
bias due to changes over time. Doing the experiment in three blocks, each containing treatment A, B,
and C, in random order, eliminates this possibility. In (b), four treatments are to be compared using four
cars. Because the cars will not be identical, the preferred design is to treat each car as a block and
balance the four treatments among the four blocks, with randomization. Part (c) shows a field study area
with contour lines to indicate variations in soil type (or concentration). Assigning treatment A to only
the top of the field would bias the results with respect to treatments B and C. The better design is to
create three blocks, each containing treatment A, B, and C, with random assignments.

Attributes of a Good Experimental Design
A good design is simple. A simple experimental design leads to simple methods of data analysis. The
simplest designs provide estimates of the main differences between treatments with calculations that
amount to little more than simple averaging. Table 22.2 lists some additional attributes of a good experi-
mental design.
If an experiment is done by unskilled people, it may be difficult to guarantee adherence to a complicated
schedule of changes in experimental conditions. If an industrial experiment is performed under production
conditions, it is important to disturb production as little as possible.
In scientific work, especially in the preliminary stages of an investigation, it may be important to
retain flexibility. The initial part of the experiment may suggest a much more promising line of inves-
tigation, so that it would be a bad thing if a large experiment has to be completed before any worthwhile
results are obtained. Start with a simple design that can be augmented as additional information becomes
available.
© 2002 By CRC Press LLC