# des.MOLS: Construction of Designs Based on Mutually Orthogonal Latin... In crossdes: Construction of Crossover Designs

## Description

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.

## Usage

 1 des.MOLS(trt, k = trt)

## Arguments

 trt A prime power less than 100. The number of treatments (products) to be tested. k An integer <= trt. Number of periods for each subject.

## Details

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.

## Value

A matrix with trt(trt-1) rows and k columns representing the experimental design.

Oliver Sailer

## 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.

## Examples

 1 2 des.MOLS(7,7) des.MOLS(8,5)

### Example output

[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,]    1    2    3    4    5    6    7
[2,]    2    3    4    5    6    7    1
[3,]    3    4    5    6    7    1    2
[4,]    4    5    6    7    1    2    3
[5,]    5    6    7    1    2    3    4
[6,]    6    7    1    2    3    4    5
[7,]    7    1    2    3    4    5    6
[8,]    1    3    5    7    2    4    6
[9,]    2    4    6    1    3    5    7
[10,]    3    5    7    2    4    6    1
[11,]    4    6    1    3    5    7    2
[12,]    5    7    2    4    6    1    3
[13,]    6    1    3    5    7    2    4
[14,]    7    2    4    6    1    3    5
[15,]    1    4    7    3    6    2    5
[16,]    2    5    1    4    7    3    6
[17,]    3    6    2    5    1    4    7
[18,]    4    7    3    6    2    5    1
[19,]    5    1    4    7    3    6    2
[20,]    6    2    5    1    4    7    3
[21,]    7    3    6    2    5    1    4
[22,]    1    5    2    6    3    7    4
[23,]    2    6    3    7    4    1    5
[24,]    3    7    4    1    5    2    6
[25,]    4    1    5    2    6    3    7
[26,]    5    2    6    3    7    4    1
[27,]    6    3    7    4    1    5    2
[28,]    7    4    1    5    2    6    3
[29,]    1    6    4    2    7    5    3
[30,]    2    7    5    3    1    6    4
[31,]    3    1    6    4    2    7    5
[32,]    4    2    7    5    3    1    6
[33,]    5    3    1    6    4    2    7
[34,]    6    4    2    7    5    3    1
[35,]    7    5    3    1    6    4    2
[36,]    1    7    6    5    4    3    2
[37,]    2    1    7    6    5    4    3
[38,]    3    2    1    7    6    5    4
[39,]    4    3    2    1    7    6    5
[40,]    5    4    3    2    1    7    6
[41,]    6    5    4    3    2    1    7
[42,]    7    6    5    4    3    2    1
[,1] [,2] [,3] [,4] [,5]
[1,]    1    2    3    4    5
[2,]    2    1    4    3    6
[3,]    3    4    1    2    7
[4,]    4    3    2    1    8
[5,]    5    6    7    8    1
[6,]    6    5    8    7    2
[7,]    7    8    5    6    3
[8,]    8    7    6    5    4
[9,]    1    3    5    7    4
[10,]    2    4    6    8    3
[11,]    3    1    7    5    2
[12,]    4    2    8    6    1
[13,]    5    7    1    3    8
[14,]    6    8    2    4    7
[15,]    7    5    3    1    6
[16,]    8    6    4    2    5
[17,]    1    4    7    6    8
[18,]    2    3    8    5    7
[19,]    3    2    5    8    6
[20,]    4    1    6    7    5
[21,]    5    8    3    2    4
[22,]    6    7    4    1    3
[23,]    7    6    1    4    2
[24,]    8    5    2    3    1
[25,]    1    5    4    8    7
[26,]    2    6    3    7    8
[27,]    3    7    2    6    5
[28,]    4    8    1    5    6
[29,]    5    1    8    4    3
[30,]    6    2    7    3    4
[31,]    7    3    6    2    1
[32,]    8    4    5    1    2
[33,]    1    6    2    5    3
[34,]    2    5    1    6    4
[35,]    3    8    4    7    1
[36,]    4    7    3    8    2
[37,]    5    2    6    1    7
[38,]    6    1    5    2    8
[39,]    7    4    8    3    5
[40,]    8    3    7    4    6
[41,]    1    7    8    2    6
[42,]    2    8    7    1    5
[43,]    3    5    6    4    8
[44,]    4    6    5    3    7
[45,]    5    3    4    6    2
[46,]    6    4    3    5    1
[47,]    7    1    2    8    4
[48,]    8    2    1    7    3
[49,]    1    8    6    3    2
[50,]    2    7    5    4    1
[51,]    3    6    8    1    4
[52,]    4    5    7    2    3
[53,]    5    4    2    7    6
[54,]    6    3    1    8    5
[55,]    7    2    4    5    8
[56,]    8    1    3    6    7

crossdes documentation built on May 30, 2017, 4:14 a.m.