See Jain, Chapters 16-23
Motivation for experimental design
- Minimize number of experiments
- Maximize useful information
- Note: categorical factors assumed throughout, and mostly
we assume a linear model.
Families of experimental designs
- ``Simple design:'' base case plus vary one factor at a time.
- Full factorial design: all combinations of factor/levels, 1 or more
- Fractional factorial design: subset of full factorial, carefully
factorial design (chap. 17)
- Simple case of full factorial design: each of k factors has only
- Model (for k=2)
and similarly for .
- unknowns (effects) and experiments. So
a direct method (with tabular tricks) yields values for
the effects and for allocation of variation (via sums-of-squares
factorial design with replication (chap. 18)
- Idea: replicate experiments to yield error estimates and rigorous
confidence intervals (t-tests) and ANOVA (F-tests).
- Model (for k=2)
- Tabular tricks still work, with sample means replacing single
- Given variance estimates, can compute confidence intervals for
effects and for predicted future responses.
- And F-tests can be used to determine if a significant amount of
variation is attributable to a particular factor.
Important visual tests to verify assumptions
- Are errors independent? Plot residuals vs. or
residuals vs. experiment number.
- Are errors distributed normally? Normal quantile-quantile plot.
fractional factorial designs (chap. 19)
- Idea: reduce cost of full design by only doing
experiments, carefully chosen to give information
about 1st order effects at expense of 2nd, 3rd, 4th, ...
One-factor designs (chap. 20)
- Another simple case of full factorial design -- this time
only have 1 factor, but > 2 levels.
Two-factor full factorial designs (chps. 21, 22)
General full factorial designs (chap. 23)
C. J. Ribbens,