### Experimental Design

#### 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.

#### Terminology

- Response
- Factors
- Levels
- Replication
- Design

#### Families of experimental designs

- ``Simple design:'' base case plus vary one factor at a time.
Bad idea.
- Full factorial design: all combinations of factor/levels, 1 or more
replication.
- Fractional factorial design: subset of full factorial, carefully
chosen.

#### factorial design (chap. 17)

- Simple case of full factorial design: each of
*k* factors has only
two levels.
- Model (for
*k*=2)

where

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
arguments).

#### 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
experiment values.

- 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)

CS 5014,
C. J. Ribbens,
10/17/2001