Produce a Fractional Factorial Design
DESCRIPTION:
Produces a fractional factorial design.
USAGE: 
fractionate(design, fraction)
REQUIRED ARGUMENTS:
design:
a design object; that is, a data frame containing factors.
fraction:
the fraction desired. This is either a numeric fraction (e.g., 1/2, 1/4), or a formula containing the terms to be used as defining contrasts.
VALUE:
a new design object, containing the rows of the original design specified by fraction. The function only works for 2^k designs. Defining fractions for factors with three or more levels is more complicated, and we have not attempted to do so. The design has an attribute "fraction" containing the defining contrast(s).
DETAILS:
If the fraction argument is numeric, fractionate will choose a fraction according to a set of defining contrasts representing an attempt to allow estimation of as many low-order effects as possible. (The fractions are in the object dimdc.list if you want to look at them.)

If a formula is supplied for fraction, its terms should generally be simple high-order interactions - that is, factor names linked by : (colon). Each such term defines one interaction (combination of factors). The design will be divided in half according to whether the corresponding contrast variable has value +1 or -1. The term can appear in the formula with sign either "+" or "-", and the positive or negative half will be chosen accordingly. Notice that negative and positive terms do not cancel in this use of formulas.

SEE ALSO:
fac.design , factor.names .
EXAMPLES: 
# a 1/4 replicate from the full 2^5 design in full.design
# specifying the -1 fraction for the first contrast
davies.design <- fractionate(full.design,
    fraction = ~ -A:C:D + A:B:E)