AGNATURALBLOCK procedure

Forms 1- and 2-dimensional designs with blocks of natural size (P.D. Johnstone & D.B. Baird).


Options

PRINT = string
Controls printed output (design, search); default desi

DESIGNTYPE = string
Type of design to create (block, rowcolumn); default rowc

NSIMULATIONS = scalar
Number of randomizations to search to find the best design; default 1000

SEED = scalar
Seed for the randomization; default 0 defines the seed automatically from the computer clock

FIRSTPLOT = string
Defines the starting location for allocating plots to the row-by-column grid (lowleft, lowright, upleft, upright); default uple

FILLMETHOD = string
Defines the order in which the plots are filled (colserpentine, colbycol, rowserpentine, rowbyrow); default rows


Parameters

LEVELS = scalars or variates
Defines the levels of the treatment factor for each design

NROWS = scalars
Number of rows in the smallest rectangle containing the layout of each design; not required if the ROWS parameter is set to a factor with values

NCOLUMNS = scalars
Number of columns in the smallest rectangle containing the layout of each design; not required if the COLUMNS parameter is set to a factor with values

NUNITS = scalar
Number of plots that will be assigned a treatment in each design; not required if the either the ROWS or COLUMNS parameter is set to a factor with values

TREATMENTS = factors
Saves the treatment allocation for each design

ROWS = factors
Defines or saves the row locations of the plots to receive treatments in each design

COLUMNS = factors
Defines or saves the column locations of the plots to receive treatments in each design

PLAN = matrices
Saves the treatment layout in each design


Description

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 FACTOR directive.

   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 ROWS and 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 NROWS and NCOLUMNS parameters. If the ROWS or 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 NROWS or 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 ROWS or COLUMNS, or else NROWS × NCOLUMNS, if ROWS or COLUMNS are not specified. Thus, you only need to specify NUNITS if you are not using the full grid of NROWS × NCOLUMNS values, or you wish to limit the units used in ROWS and COLUMNS.

   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 ROWS and COLUMNS parameters. Alternatively, you can specifying the size of the grid with the NROWS and NCOLUMNS parameters, in which case the LAYOUT option is used to allocate units to the grid. Again, if the ROWS or 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 FIRSTPLOT and FILLMETHOD options control how the plots are allocated to to the row and column locations when these are not defined by ROWS and COLUMNS factors. The FIRSTPLOT option defines the starting location as follows:

    lowleft
left-hand plot at the bottom of the grid;

    lowright
right-hand plot at the bottom of the grid;

    upleft
left-hand plot at the top of the grid (default);

    upright
right-hand plot at the top of the grid.

The FILLMETHOD option defines the order in which the plots are then filled:

    colserpentine
column-by-column in a serpentine way e.g. top-to-bottom, and then bottom to top;

    colbycol
column-by-column taking the same direction for every column;

    rowserpentine
in a serpentine way e.g. left-to-right, and then right-to-left (default);

    rowbyrow
row-by-row taking the same direction for every row.

   The NSIMULATIONS option defines the number of random designs to be searched, and the SEED option specifies the starting seed for the randomization process. 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 PRINT option, with settings:

    design
to print the best design;

    search
to print the current best design during the search.

 

Options: PRINT, DESIGN, NSIMULATIONS, SEED, FIRSTPLOT, FILLMETHOD.

Parameters: LEVELS, NROWS, NCOLUMNS, NUNITS, TREATMENTS, ROWS, COLUMNS, BLOCKS, PLAN.


Method

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.


Action with RESTRICT

If any of the factors is restricted, only the part of the design not excluded by the restriction will be generated.


References

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.