| Details of the FACTEX Procedure |
Resolution
The resolution of a design indicates which effects can be estimated free
of other effects.
The resolution of a design is generally defined as the smallest
order*
of the
interactions that are confounded with zero. Since having an effect of
order n+m confounded with zero is equivalent to having an effect of
order n confounded with an effect of order m, the resolution
can be interpreted as follows:
- If r is odd, then effects of order e=(r-1)/2 or less can be
estimated free of each other. However, at least some of the
effects of order e are confounded with interactions of order
e+1. A design of odd resolution is appropriate when effects
of interest are those of order e or less, while those of
order e+1 or higher are all negligible.
- If r is even, then effects of order e=(r-2)/2 or less can be
estimated free of each other and are also free of interactions
of order e+1. A design of even resolution is appropriate
when effects of order e or less are of interest, effects of
order e+1 are not negligible, and effects of
order e+2 or higher are negligible. If the
design uses blocking, interactions of order e+1 or higher may
be confounded with blocks.
In particular, for resolution 5 designs, all main effects and two-factor
interactions can be estimated free of each other. For resolution 4 designs,
all main effects can be estimated free of each other and free of two-factor
interactions, but some two-factor interactions are confounded with each
other and/or with blocks. For resolution 3 designs, all main effects can be
estimated free of each other, but some of them are confounded with
two-factor interactions.
In general, higher resolutions require larger designs. Resolution 3
designs are popular because they handle relatively many factors in a
minimal number of runs. However, they offer no protection against
interactions. If resources allow, you should use a resolution 5 design
so that all main effects and two-factor interactions will be independently
estimable. If a resolution 5 design is too large, you should use a design
of resolution 4, which ensures estimability of main effects free of any
two-factor interactions. In this case, if data from the initial design
reveal significant effects associated with confounded two-factor
interactions, further experiments can be run to distinguish between
effects that are confounded with each other in the design. See
Example 15.2 for an
example.
Note that most references on fractional factorial designs use Roman
numerals to denote resolution of a design -III, IV, V, and so on. A
common notation for an orthogonally confounded design of resolution r
for k q-level factors in qk-p runs is
-
qk-pr
For example, 25-1V denotes a design
for five two-level factors
in 16 runs that allows estimation of all main effects and two-factor
interactions.
This chapter uses Arabic numerals for resolution since these are specified
with the RESOLUTION= option in the MODEL statement.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.
