Forms 1- and 2-dimensional designs with blocks of natural size (P.D. Johnstone & D.B. Baird).
|Controls printed output (
||Type of design to create (
||Number of randomizations to search to find the best design; default 1000|
||Seed for the randomization; default 0|
||Defines the starting location for allocating plots to the row-by-column grid (
||Defines the order in which the plots are filled (
||Defines the levels of the treatment factor for each design|
||Number of rows in the smallest rectangle containing the layout of each design; not required if the
||Number of columns in the smallest rectangle containing the layout of each design; not required if the
||Number of plots that will be assigned a treatment in each design; not required if the either the
||Saves the treatment allocation for each design|
||Defines or saves the row locations of the plots to receive treatments in each design|
||Defines or saves the column locations of the plots to receive treatments in each design|
||Defines or saves the allocation of the plots to blocks|
||Saves the treatment layout in each design|
This procedure uses random generation for obtaining block and row-column designs and selects the best of those designs using a criterion similar in effect to the M,S-optimality criterion of Shah (1960). The method used does not have any restrictions on the layout of plots in the array, which can be incomplete, or on the number of treatments or replicates per treatments, which may be unequal, as have some other design generators.
The number of treatments is specified by the
LEVELS parameter, either as a scalar (defining the number explicitly) or by a variate (defining a number for each level), as in the
DESIGNTYPE option specifies whether to form a row-column or a block design. With a row-column design (
DESIGNTYPE=rowcolumn), the layout of the plots can be defined in two factors supplied by the
COLUMNS parameters. Alternatively, if all plots are present, then just the number of rows and columns in the row-column array can be specified by the
NCOLUMNS parameters. If the
COLUMNS option is set to a factors whose values have not been defined, the factor values will be set up to define a regular grid of plots. The numbers of rows and columns must then defined by the corresponding
NCOLUMNS option. The
NUNITS parameter defines the number of plots in the design. If this is not specified, the number of plots to allocate treatments is taken from either the number of values in
COLUMNS, or else
COLUMNS are not specified. Thus, you only need to specify
NUNITS if you are not using the full grid of
NCOLUMNS values, or you wish to limit the units used in
For one-way block design (
DESIGNTYPE=block) with unequal block sizes, the
BLOCKS parameter must be set to a factor giving the block number for each plot. The block design can allocated to a two dimensional layout by specifying the position of each unit in two factors supplied by the
COLUMNS parameters. Alternatively, you can specifying the size of the grid with the
NCOLUMNS parameters, in which case the
LAYOUT option is used to allocate units to the grid. Again, if the
COLUMNS option is set to a factors whose values have not been defined, the factor values will be set up to define a regular grid of plots. With a block design, if
NUNITS is unset, the number of plots is taken from the number of values of the
BLOCKS factor. The
FILLMETHOD options control how the plots are allocated to to the row and column locations when these are not defined by
COLUMNS factors. The
FIRSTPLOT option defines the starting location as follows:
||left-hand plot at the bottom of the grid;|
||right-hand plot at the bottom of the grid;|
||left-hand plot at the top of the grid (default);|
||right-hand plot at the top of the grid.|
FILLMETHOD option defines the order in which the plots are then filled:
||column-by-column in a serpentine way e.g. top-to-bottom, and then bottom to top;|
||column-by-column taking the same direction for every column;|
||in a serpentine way e.g. left-to-right, and then right-to-left (default);|
||row-by-row taking the same direction for every row.|
NSIMULATIONS option defines the number of random designs to be searched. The
SEED option specifies the starting seed for the randomization process; the default of zero continues an existing sequence of random numbers if any have already been used in this Genstat job, or initializes the seed automatically. The resulting optimal treatment allocation can be saved, either in a factor specified by the
TREATMENTS parameter, or by setting the
PLAN parameter to a matrix to save the two-dimensional layout of the treatments.
Printed output is controlled by the
||to print the best design;|
||to print the current best design during the search.|
For a row-column design the treatments are allocated in random order down the columns, while for a block design they are allocated one replicate at a time. A number of designs (specified by the
NSIMULATIONS option) are generated. The design is chosen that minimizes both the range and the average of the standard errors of differences for all pairwise comparisons between elements of the generalized least squares estimates of treatment effects.
If any of the factors is restricted, only the part of the design not excluded by the restriction will be generated.
Johnstone, P.D. (2003). Random generation and selection of one- and two-dimensional designs for experiments on blocks of natural size. Journal of Agricultural, Biological and Environmental Statistics, 8, 67-74.
Shah, K.R. (1960). Optimality criteria for incomplete block designs. Annals of Mathematical Statistics, 22, 235-247.
Commands for: Design of experiments.
CAPTION 'AGNATURALBLOCK example',!t(\ 'Generate a design for 8 treatments in an incomplete',\ '16 row by 11 column array.'); STYLE=meta,plain FACTOR [LEVELS=16; VALUES=1,3,4...9,11,12...14,16,\ 1,2...5,7,8...16,1,2...11,13,14...15,1,2...15,\ 1,2...15,1,2...11,1,2...7,9,10...14,1,2...7,9,\ 10...14,1,2...3,5,6,8,9...13,1,3,4...13,1,2...8,\ 10,11...13] Row1 FACTOR [LEVELS=11; VALUES=13(1),15(2),14(3),15(4,5),11(6),\ 13(7,8),11(9),12(10,11)] Col1 AGNATURALBLOCK [PRINT=search; DESIGNTYPE=rowcolumn; SEED=234567]\ LEVELS=8; TREATMENT=Trt1; ROWS=Row1; COLUMNS=Col1 PRINT Row1,Col1,Trt1; FIELDWIDTH=5; DECIMALS=0 CAPTION !t('Generate a design for 5 treatments with blocks of',\ 'size 3, 6 and 4, and allocate the treatments to a 3 x 5',\ 'layout, starting in the top left corner, running across',\ 'rows in a serpentine manner (i.e. at the end of the first',\ 'row, drop directly down to the plot in the row below and',\ 'work back to the start of the row, etc.') FACTOR [LEVELS=4; VALUES=3(1),6(2),2(3),4(4)] Block AGNATURALBLOCK [PRINT=design; DESIGNTYPE=block; SEED=7856;\ FIRSTPLOT=lowright; FILLMETHOD=rowserpentine] LEVELS=5;\ TREATMENT=Trt2; BLOCK=Block; NROWS=3; NCOLUMNS=5 PRINT Block,Trt2; FIELDWIDTH=5; DECIMALS=0 CAPTION 'Generate a design for 13 treatments in a 8 row by 6 column array.' AGNATURALBLOCK [NSIMULATIONS=500] LEVELS=13; NROWS=8; NCOLUMNS=6;\ TREATMENT=Trt3