GraecoLatin: Graeco-Latin squares

In blocksdesign: Nested and Crossed Block Designs for Factorial and Unstructured Treatment Sets

Description

Constructs mutually orthogonal Graeco-Latin squares for the following N:

i) any odd valued N

ii) any prime-power N = p**q where p and q can be chosen from

prime p	maximum q
2	13
3	8
5	6
7	5
11	4
13 17 19 23	3
29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97	2
Any prime >97	1

iii) any even valued N <= 30 except for 6 or 2

Usage

GraecoLatin(N)

Arguments

N	any suitable integer N

Details

Plans are given for pairs of MOLS classified by rows and columns. The output is a single data frame of size p**q x (r+2) for the required set of MOLS with a column for the rows classification, a column for the columns classification and a column for each treatment set from the required set of MOLS.

Also see the function MOLS which will generate complete sets of MOLS for prime-power design sizes.

Value

Data frame of factor levels for rows, columns and treatment sets

References

Street, A. P. & Street, D. J. (1987). Combinatorics of Experimental Design, Chapters 6 and 7. Clarendon Press, Oxford.

See Also

MOLS

Examples

X=GraecoLatin(8) 
table(X[,3],X[,4])
X=GraecoLatin(9) 
table(X[,3],X[,4])
X=GraecoLatin(32)
table(X[,3],X[,4])
 

Example output

   
    1 2 3 4 5 6 7 8
  1 1 1 1 1 1 1 1 1
  2 1 1 1 1 1 1 1 1
  3 1 1 1 1 1 1 1 1
  4 1 1 1 1 1 1 1 1
  5 1 1 1 1 1 1 1 1
  6 1 1 1 1 1 1 1 1
  7 1 1 1 1 1 1 1 1
  8 1 1 1 1 1 1 1 1
   
    1 2 3 4 5 6 7 8 9
  1 1 1 1 1 1 1 1 1 1
  2 1 1 1 1 1 1 1 1 1
  3 1 1 1 1 1 1 1 1 1
  4 1 1 1 1 1 1 1 1 1
  5 1 1 1 1 1 1 1 1 1
  6 1 1 1 1 1 1 1 1 1
  7 1 1 1 1 1 1 1 1 1
  8 1 1 1 1 1 1 1 1 1
  9 1 1 1 1 1 1 1 1 1
    
     1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
  1  1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  2  1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  3  1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  4  1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  5  1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  6  1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  7  1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  8  1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  9  1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  10 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  11 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  12 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  13 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  14 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  15 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  16 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  17 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  18 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  19 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  20 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  21 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  22 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  23 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  24 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  25 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  26 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  27 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  28 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  29 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  30 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  31 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  32 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
    
     29 30 31 32
  1   1  1  1  1
  2   1  1  1  1
  3   1  1  1  1
  4   1  1  1  1
  5   1  1  1  1
  6   1  1  1  1
  7   1  1  1  1
  8   1  1  1  1
  9   1  1  1  1
  10  1  1  1  1
  11  1  1  1  1
  12  1  1  1  1
  13  1  1  1  1
  14  1  1  1  1
  15  1  1  1  1
  16  1  1  1  1
  17  1  1  1  1
  18  1  1  1  1
  19  1  1  1  1
  20  1  1  1  1
  21  1  1  1  1
  22  1  1  1  1
  23  1  1  1  1
  24  1  1  1  1
  25  1  1  1  1
  26  1  1  1  1
  27  1  1  1  1
  28  1  1  1  1
  29  1  1  1  1
  30  1  1  1  1
  31  1  1  1  1
  32  1  1  1  1

blocksdesign documentation built on April 8, 2021, 1:07 a.m.