Forms the complement of an incomplete block design (W. van den Berg).
Option
PRINT = string token |
Controls whether or not to print a plan of the design (design); default desi |
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Parameters
TREATMENTS = factors |
Specifies the treatment factor of the original design |
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REPLICATES = factors |
Specifies the replicate factor of the original design when this is a resolvable design |
BLOCKS = factors |
Specifies the block factor of the original design |
NEWTREATMENTS = factors |
Saves the treatment factor of the complement design |
NEWREPLICATES = factors |
Saves the replicate factor of the complement design when this is a resolvable design |
NEWBLOCKS = factors |
Saves the block factor of the complement design |
NEWUNITS = factors |
Saves the treatment factor of the complement design |
SEED = scalars |
Seed for the random-numbers to randomize the design; default 0 |
Description
An incomplete-block design is a design that is set out in blocks that do not each contain a plot with every treatment. Examples within Genstat include balanced-incomplete-block designs (see procedure AGBIB), cyclic designs (see AFCYCLIC and AGCYCLIC), and alpha designs (see AFALPHA and AGALPHA). The complement design is formed by taking each block of the incomplete-block design and replacing its treatments by those not in the block.
This extends Genstat’s repertoire of designs. For example AGCYCLIC provides a cyclic design for 7 treatments levels, 7 blocks and 3 units per block, but not one with 7 treatments levels, 7 blocks and 4 units per block. However, the second design is the complement of the first design, and can thus be constructed using FCOMPLEMENT. One useful feature is that, if the original design is balanced, the complement design will also be balanced.
The block and treatment factors of the original design are specified by the TREATMENTS and BLOCKS parameters. The corresponding factors of the complement design can be saved with the NEWBLOCKS and NEWTREATMENTS parameters. If the original design is a resolvable design (i.e. one where the blocks can be grouped together into replicates), you can use the REPLICATES parameters to supply the replicate factor for the original design, and the NEWREPLICATES parameter to save the replicate factor for the complement design.
The SEED parameter allows you to specify a seed for the random numbers that are used by the RANDOMIZE directive, inside FCOMPLEMENT, to randomize the design. The default of zero continues the existing sequence of random numbers if RANDOMIZE has already been used in the current Genstat job. If RANDOMIZE has not yet been used, Genstat picks a seed at random. Note that you can set SEED=-1 if you want to avoid any randomization.
By default a plan of the complement design is printed, but you can set option PRINT=* to suppress this.
Option: PRINT.
Parameters: TREATMENTS, REPLICATES, BLOCKS, NEWTREATMENTS, NEWREPLICATES, NEWBLOCKS, SEED.
Method
From a variate containing all the treatment levels, a subset is made for each block, discarding the levels present in the original design. These are then appended together to form the full design.
See also
Procedures: AFALPHA, AFCYCLIC, AGALPHA, AGBIB, AGCYCLIC.
Commands for: Design of experiments.
Example
CAPTION 'FCOMPLEMENT example'; STYLE=meta
AGCYCLIC [PRINT=design; METHOD=cyclic] 7; NBLOCKS=7; NUNITS=3;\
TREATMENTS=Treat; BLOCKS=Block; UNITS=Unit; SEED=-1
FCOMPLEMENT Treat; BLOCK=Block; SEED=-1