# aliquote

## < a quantity that can be divided into another a whole number of time />

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 corresponding Task View, ExperimentalDesign.

In the so-called 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 and Ripley, MASS 4th ed., pp. 167-169) which is not very useful for the purpose of generating fractional designs.

Let’s consider a 25-2 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 could 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 25-2 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 2k designs, Daniel’s plot, “cube plot”, alias structure for standard lm object, or construction of split-plot designs.