WT: Williams Transformation
In LHD: Latin Hypercube Designs (LHDs)

Description Usage Arguments Value References Examples

WT returns a matrix after implementing the Williams transformation

1	WT(X, baseline = 1)

`X`	A matrix object. In general, `X` stands for the design matrix, e.g. an LHD or a GLP design.
`baseline`	A integer, which defines the minimum value for each column of the matrix. The default is set to be 1.

If all inputs are logical, then the output will be a matrix whose sizes are the same as input matrix.

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

#create a toy LHD with 5 rows and 3 columns
toy=rLHD(n=5,k=3);toy
toy2=toy-1;toy2  #make elements of "toy" become 0,1,2,3,4

#Implementing Williams transformation on both toy and toy2:
#The result shows that "WT" function is able to detect the
#elements of input matrix and make adjustments.
WT(toy)
WT(toy2)

#Change the baseline
WT(toy,baseline=5)
WT(toy,baseline=10)