# Design of experiment in R

## Contents

When I started writing my companion textbook for Montgomery’s *Design and Analysis of Experiments*, there was not so much dedicated package available on CRAN.

Now, I realize that there are a lot of very handy packages on CRAN. Most of them were released in 2010 and are listed in the correspoding Task View, ExperimentalDesign.

In the White Book (*Statistical Models in S*, Chambers & Hastie, 1992), section 5.2.3 pp. 169-175 is dedicated to full- and fractional factorial designs, with `fac.design`

and `oa.design`

. However, those two functions are not available in R, and we only have `expand.grid`

(see Venables & Ripley, MASS 4th ed., pp. 167-169) which is not very useful for the purpose of generating fractional designs.

Let’s consider a 2^{5-2} design, with the following generator: D=±AB and E=±AC. The corresponding design matrix can be easily found using the BHH2 package, which provides R functions and datasets from Box, Hunter and Hunter’s book, *Statistics for Experimenters II* (Wiley, 2005):

```
library(BHH2)
d52 <- ffDesMatrix(5, gen=list(c(4,1,2), c(5,1,3)))
```

Or we can use

```
library(FrF2)
FrF2(8,5)
```

Note that the FrF2 package has an Rcmdr plugin that facilitates its use.

In both cases, we get

```
A B C D E
1 -1 1 -1 -1 1
2 -1 -1 -1 1 1
3 -1 -1 1 1 -1
4 1 1 -1 1 -1
5 -1 1 1 -1 -1
6 1 -1 1 -1 1
7 1 -1 -1 -1 -1
8 1 1 1 1 1
```

Now, we want to find the aliases that this structure defines. We already know that for this kind of 2^{5-2} design, every main effect is aliased with at least one first order interaction. Let’s check it:

```
> design.info(FrF2(8,5))$aliased
$legend
[1] "A=A" "B=B" "C=C" "D=D" "E=E"
$main
[1] "A=BD=CE" "B=AD" "C=AE" "D=AB" "E=AC"
$fi2
[1] "BC=DE" "BE=CD"
```

There’s lot more to see in this package, including plot of main effects in 2^{k} designs, Daniel’s plot, “cube plot”, alias structure for standard `lm`

object, or construction of split-plot designs.