Construction of Designs Based on Mutually Orthogonal Latin Squares
The function constructs row-column designs based on complete sets of mutually orthogonal latin squares. Each subject may get each tratment at most once. The design is a generalized Youden design that is also balanced for carryover effects.
des.MOLS(trt, k = trt)
A prime power less than 100. The number of treatments (products) to be tested.
An integer <= trt. Number of periods for each subject.
A complete set of mutually orthogonal latin squares is constructed using Galois Fields. The rows of the designs represent the treatment orders for the subjects. If an incomplete design with k columns is needed, only the first k columns of the designs are considered. 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.
A matrix with trt(trt-1) rows and k columns representing the experimental design.
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.