Generates fractional factorial designs (M.F. Franklin & R.W. Payne).

### Options

`PRINT` = string token |
Controls whether or not to print a plan of the design (`design` ); if unset in an interactive run `AGFRACTION` will ask whether the design is to be printed, in a batch run the default is not to print the design |
---|---|

`ANALYSE` = string token |
Controls whether or not to analyse the design, and produce a skeleton analysis-of-variance table using `ANOVA` (`no` , yes); default is to ask if this is unset in an interactive run, and not to analyse if it is unset in a batch run |

`FACTORIAL` = scalar |
Limit on number of factors in treatments terms in the analysis of variance; default 2 |

`FILENAME` = text |
Name of the backing store file containing the design information; default uses the standard fractional design file |

### Parameters

`LEVELS` = scalars |
Number of levels of the treatment factors in each design |
---|---|

`FRACTION` = scalars |
Denominator of required fraction |

`NTREATMENTFACTORS` = scalars |
Number of treatment factors |

`NUNITS` = scalars |
Number of units per block |

`SEED` = scalars |
Seed to be used to randomize each design; a negative value implies no randomization |

`TREATMENTFACTORS` = pointers |
Specifies identifiers for the treatment factors |

`BLOCKS` = factors |
Identifier for the block factor |

`UNITS` = factors |
Identifier for the factor to index the units (or plots) within each block |

`STATEMENT` = texts |
Saves a command to recreate each design (useful if the design information has been specified in response to questions from `AGFRACTION` ) |

### Description

`AGFRACTION`

generates fractional factorial designs from stored keys & other information. It also sets the block and treatment formulae (using the `BLOCKSTRUCTURE`

and `TREATMENTSTRUCTURE`

directives) to allow the design to be analysed by `ANOVA`

.

The procedure relies upon a backing-store file that contains a repertoire of available designs, together with the information required to form them. There is a standard file, used by default, but the `FILENAME`

option allows you to specify another if you wish to form your own alternative file.

`AGFRACTION`

has two other options. The `PRINT`

option can be set to `design`

to print the plan of the design. By default, if you are running Genstat in batch, the plan is not printed. If you do not set `PRINT`

when running interactively, `AGFRACTION`

will ask whether or not you wish to print the design. Similarly the `ANALYSE`

option governs whether or not `AGFRACTION`

produces a skeleton analysis-of-variance table (containing just source of variation, degrees of freedom and efficiency factors). Again `AGFRACTION`

assumes that this is not required if `ANALYSE`

is unset in a batch run, and asks whether it is required if `ANALYSE`

is unset in an interactive run. The `FACTORIAL`

option sets a limit on the number of factors in the treatment terms in the analysis of variance; by default, this is two.

The information required to select the design and give identifiers to its factors can be defined using the parameters of `AGFRACTION`

. In an interactive run, `AGFRACTION`

will ask questions to obtain any necessary information that is not supplied in this way; when running in batch, if any of the required information has not been specified, `AGFRACTION`

will terminate with a warning message.

It is thus easiest to use `AGFRACTION`

interactively. Then all the information necessary to select and define the required design will be obtained by (clearly explained) questions. You need set the parameters only if you wish to anticipate some of the questions, or if you wish to use `AGFRACTION`

in batch. If, however, you wish to recreate the same design later, the `STATEMENT`

parameter allows you to save a Genstat text structure containing a command specifying the same information.

The number of levels of the treatment factors can be defined using the `LEVELS`

parameter. The `FRACTION`

parameter defines the denominator of the required fraction, and the `NTREATMENTFACTOR`

parameter specifies how many treatment factors the design is to contain. Thus, for example,

`AGFRACTION [PRINT=design] LEVELS=2; FRACTION=4; NTREATMENTF=6`

would print the plan of a quarter replicate of a 2^{6} design.

For some of the designs it is possible also to allow a blocking factor (and you will be given details of what is feasible if you are running `AGFRACTION`

interactively). The `NUNITS`

parameter can then be used to define the number of units per block.

The `SEED`

parameter allows you to specify a seed to be used to randomize the design. In batch the default seed is -1, to suppress randomization. If you do not set `SEED`

when running interactively `AGFRACTION`

will ask for a seed, and again a negative value suppresses any randomization.

The `TREATMENTFACTORS`

parameter can specify a pointer to supply identifiers for the treatment factors in the design. For example, if there are two factors you could define their identifiers to be `A`

and `B`

by forming the pointer `Tf`

(say) with the statement

`POINTER [VALUES=A,B] Tf`

and then setting `TREATMENTFACTORS=Tf`

. Alternatively, and more succinctly, you could put `TREATMENTFACTORS=!p(A,B)`

, where `!p(A,B)`

is an unnamed pointer containing the required two identifiers. The remaining parameters, `BLOCKS`

and `UNITS`

, allow you to specify identifiers for the block and unit-within-block factors. If the treatment, block or unit factors are not specified in a batch run, `AGFRACTION`

will use identifiers that are local within the procedure and thus lost at the end of the procedure. If you are running interactively, `AGFRACTION`

will ask you to provide identifiers, and these will remain available after `AGFRACTION`

has finished running.

Options: `PRINT`

, `ANALYSE`

, `FACTORIAL`

, `FILENAME`

.

Parameters: `LEVELS`

, `FRACTION`

, `NTREATMENTFACTORS`

, `NUNITS`

, `SEED`

, `TREATMENTFACTORS`

, `BLOCKS`

, `UNITS`

, `STATEMENT`

.

### Method

The `QUESTION`

procedure is used to obtain the details of the required design. The design is then generated using `GENERATE`

and the other standard Genstat directives for calculation and manipulation.

### See also

Procedures: `AGDESIGN`

, `AGFACTORIAL`

, `AGHIERARCHICAL`

.

Commands for: Design of experiments, Analysis of variance.

### Example

CAPTION 'AGFRACTION example',!t(\ 'This example prints the (unrandomized) plan',\ 'of a quarter replicate of a 2x2x2x2x2x2.'); STYLE=meta,plain AGFRACTION [PRINT=design; ANALYSE=no] LEVELS=2; FRACTION=4;\ NTREATMENTFACTORS=6; NUNITS=16; TREATMENTFACTORS=!p(A,B,C,D,E,F);\ SEED=-1 " To see the full repertoire of designs, you should run AGFRACTION interactively, without setting the parameters."