crossdes (version 1.1-2)

williams: Construction of Williams Designs

Description

The function constructs williams designs. Williams designs are row-column designs. They are used if each of the treatments in the study is given to each of the subjects. If the number of treatments to be tested is even, the design is a latin square, otherwise it consists of two latin squares.

Usage

williams(trt)

Arguments

trt

An integer > 1, giving the number of treatments in the design.

Value

A matrix representing the experimental design.

Details

The resulting design is a (generalized) latin square that is also balanced for first order carryover effects. Carryover balance is achieved with very few subjects. In the experimental design the treatments are numbered 1,…,\(trt\). The entry \((i,j)\) of the design corresponds to the treatment the \(i\)-th subject gets in the \(j\)-th period.

References

Wakeling, I.N. and MacFie, H.J.H. (1995): Designing consumer trials balanced for first and higher orders of carry-over effect when only a subset of k samples from t may be tested. Food Quality and Preference 6, 299-308.

Williams, E. J. (1949): Experimental designs balanced for the estimation of residual effects of treatments. Australian Journal of Scientific Research, Ser. A 2, 149-168.

See Also

get.plan

Examples

# NOT RUN {
williams(3)
williams(10)
# }