design.digest(levels, factor.names=<<see below>>,
          replic=1, row.names=<<see below>>,
          fraction=<<see below>>, n.cp=<<see below>>,
          cp.values=<<see below>>, cp.place=<<see below>>,
          block.size=<<see below>>, n.blocks=<<see below>>,
          block.gen=<<see below>>)

levels:

a legal design name or a vector of the number of levels for the factors in the design. Legal design names are of the form "ff0516" where the first two characters specify the design type (e.g., ff=fractional factorial, if=irregular fractional factorial, mf=mixed-level fractional factorial, pb=Plackett-Burman design), the next two digits are the number of experimental factors, the last two digits are the number of runs.

factor.names:

object that names the factors. This may be a vector of character strings which are the names of the factors. It may also be a list, in which case the names attribute of the list is the names of the factors, and the components of the list (which need not be of mode character) label the levels of the corresponding factor. If factor names are not given, they default to A, B, etc. If levels are not given, they default to - and + for two-level designs and to -, 0, and + for three-level designs.

replic:

the number of times the complete design should be replicated.

row.names:

names to use for the rows of the design. The default is 1:nrows, where nrows is the number of observations in the design.

fraction:

definition for the fraction desired in a fractional factorial design. This may either be a numerical fraction (e.g, ) or a formula giving the defining contrasts. Fractional factorials are provided for 2-level factors and for some designs with one factor at three levels (e.g., "mf0412"). The default is a complete fraction (1), i.e., a full factorial design is created

n.cp:

number of center points to add. If the design is blocked, this is the number of center points per block. Default is 0.

cp.values:

vector of level names for the center points, which must equal in length to the number of factors. (See factor.names above). The default is 0 for each factor if no factor levels are given, otherwise it is "cp".

cp.place:

a character string for where center points should be placed; namely, "first", "last", "ends", "spaced", "random". If the design is blocked the placement occurs within each block. When "ends" is used, half of the center points are placed at the beginning and half at the end. When "spaced" is used, center points are evenly divided between the beginning, middle, and end of the design (block). The value of n.cp is adjusted if not divisible by 2 or 3, respectively. The default is "last".

block.size:

the number of runs in each block.

n.blocks:

the number of blocks.

block.gen:

a model formula giving one or more defining contrasts (e.g., ). to be used to generate blocks. If either block.size or n.blocks is given, then design.digest looks up block.gen in a table of blocking patterns as given by Box, Hunter and Hunter (1978).

design.name:

the design name from the original data (e.g., "ff0516");

fraction:

either a numerical fraction (e.g., 1/4) or a model formula giving the defining contrasts (e.g., A:B:D + B:C:E) for this fraction;

fract.part:

the fractional number of runs (e.g., 1/4);

resolution:

the resolution of the design (e.g., resolution V if all main effects and two-factor interactions are independent of each other);

confounding.patern:

the pattern which describes dependencies among main effects and two-factor interactions for design which are less than resolution V.

If a design has been blocked, then the fac.design object also has the attributes giving the number of runs in each block, block.size; the number of blocks, n.blocks; and the defining contrast used to generated the blocks, block.gen. If standard blocking was used (i.e., block.gen was not supplied), then the attribute conf.tfi is T if blocks are confounded with at least one two-factor interactions, otherwise it is false. A factor Blocks is added to the beginning of the data frame.

If the design includes center points, then the attribute n.cp gives the total number of center points if the design is not blocked, and the number of center points per block if the design is blocked. A factor named Quad is added to the end of the data frame that differentiates between center points and design points. This factor is not ordinarily printed, see print.fac.design.

The complete list of legal design names is:

"ff0308" "ff0408" "ff0508" "ff0608" "ff0708" "ff0416" "ff0516" "ff0616" "ff0716" "ff0816" "ff0916" "ff1016" "ff1116" "ff0532" "ff0632" "ff0732" "ff0832" "ff0932" "ff1032" "ff1132" "ff0664" "ff0764" "ff0864" "ff0964" "ff1064" "ff1164" "mf0312" "mf0412" "mf0512" "mf0424" "mf0524" "if0412" "if0512" "if0612" "if0624" "pb0712" "pb0812" "pb0912" "pb1012" "pb1112" "pb0724" "pb0824" "pb0924" "pb1024" "pb1124"

These designs are described in the Design Digest appendix to the S+DOX Users' Manual.

The twelve-run Plackett-Burman designs always have eleven factors, i.e. "pb0712" is generated with seven regular factors plus four dummy factors that can be used in the analysis to detect possible two-factor interactions.

The mixed-level fraction designs have one factor at three levels and are non-orthogonal unless they are full factorials. The irregular fractions, are also non-orthogonal.

design.digest chooses defining contrasts for factors so that all effects have the same standard error, specifically, t(x)*(x)=diag(n). Designs are returned in reverse Yates order. If center points are added or the design is blocked, additional factors Quad and Block are added to the data frame, as described above.

To randomize a design use the function randomize.design (a randomized design can restored to standard order by sort.design). To print out a copy of the design worksheet use the function worksheet. Center points can be added to a design with the function addcp. To convert a dataframe into an object of class fac.design, use the function as.fac.design. To convert a factor to a numeric vector use the function fac2num. To change the factor names use the function factor.names. To change the row names use the function row.names.

Haaland, P. D. (1989). Experimental Design in Biotechnology. New York: Marcel Dekker.

# a 1/2 fraction of a 2^5 design
buffer.design <- design.digest("ff0516", c("pH", "chelex", "azide",
                               "gent", "thimer"))
summary(buffer.design)
buffer.rate <-c(6.90, 9.81, 8.78, 7.92, 8.42, 7.04, 7.21, 9.96, 2.34,
                1.22, 1.29, 1.73, 1.55, 1.68, 1.81, 1.36 )
buffer.df <- cbind(buffer.design, rate = buffer.rate)

# a 1/2 fraction of a 2^5 design in two blocks
design.digest("ff0408", n.blocks = 2)

# a 2^3 design with 3 center points
a.fnames <- list(wash=c(1,3), pH=c(7,9), time=c(5,10),
                 buffer=c("Tris","Tween"))
design.digest("ff0408", a.fnames, n.cp=3,
              cp.values = c("2","8","7.5","BSA"))

# various options for blocking and center points
design.digest("ff0416", n.blocks=2, n.cp=2, cp.place="ends")
design.digest("ff0416", n.blocks=4, n.cp=1)
design.digest("ff0416", n.blocks=2, n.cp=3, cp.place="spaced")

# Placket-Burman design
design.digest("pb1112")