williams.BIB {crossdes}

Construction of Carryover Balanced Designs Based on Balanced Incomplete Block Designs

Description

Patterson (1951) combined balanced incomplete block designs (BIBDs) with Williams designs to get carryover balanced generalized Youden designs.

Usage

williams.BIB(d)

Arguments

d

A matrix representing a BIBD. Rows represent blocks (subjects).

Details

For each row of the design, a Williams design is constructed using the treatments of that row. The rows of the resulting designs are then combined. 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.

Value

A matrix representing the experimental design.

Warning

The resultig design is only balanced properly if the input design actually is a BIBD. This is NOT checked automatically. You have to do this by yourself, e.g. by applying isGYD to your design.

Note

BIBDs may be generated using find.BIB.

Author(s)

Oliver Sailer

References

Patterson, H.D. (1951): Change-over trials. Journal of the Royal Statistical Society B 13, 256-271.

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.

See Also

get.plan, isGYD, find.BIB, williams

Examples

d <- matrix( rep(1:3,each=2), ncol=2)
# # check for balance
# isGYD(d)
williams.BIB(d)