pg_0045
5.
Process Improvement
5.3.
Choosing an experimental design
5.3.3.
How do you select an experimental design.
5.3.3.1.
Completely randomized designs
These designs
are for studying
the effects of
one primary
factor without
the need to take
other nuisance
factors into
account
Here we consider completely randomized designs that have one
primary factor. The experiment compares the values of a response
variable based on the different levels of that primary factor.
For completely randomized designs, the levels of the primary factor
are randomly assigned to the experimental units. By
randomization
,
we mean that the run sequence of the
experimental units
is
determined randomly. For example, if there are 3 levels of the
primary factor with each level to be run 2 times, then there are 6
factorial possible run sequences (or 6! ways to order the
experimental trials). Because of the replication, the number of unique
orderings is 90 (since 90 = 6!/(2!*2!*2!)). An example of an
unrandomized design would be to always run 2 replications for the
first level, then 2 for the second level, and finally 2 for the third
level. To randomize the runs, one way would be to put 6 slips of
paper in a box with 2 having level 1, 2 having level 2, and 2 having
level 3. Before each run, one of the slips would be drawn blindly
from the box and the level selected would be used for the next run of
the experiment.
Randomization
typically
performed by
computer
software
In practice, the randomization is typically performed by a computer
program (in Dataplot, see the Generate Random Run Sequence menu
under the main DEX menu). However, the randomization can also be
generated from random number tables or by some physical
mechanism (e.g., drawing the slips of paper).
Three key
numbers
All completely randomized designs with one primary factor are
defined by 3 numbers:
k = number of factors (= 1 for these designs)
L = number of levels
n = number of replications
and the total sample size (number of runs) is N = k x L x n.
5.3.3.1. Completely randomized designs
http://www.itl.nist.gov/div898/handbook/pri/section3/pri331.htm (1 of 3) [5/7/2002 4:01:46 PM]
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