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` |
---|

### Parameters

`TREATMENTS` = factors |
Specifies the treatment factor of the original design |
---|---|

`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