Generates cyclic designs from standard generators (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 `AGCYCLIC` will ask whether the design is to be printed, in a batch run the default is not to print the design |
---|---|

`METHOD` = string token |
Type of design – ordinary cyclic, cyclic change-over or cyclic superimposed (`cyclic` , `changeover` , `superimposed` ); if unset in an interactive run `AGCYCLIC` will ask about the type of design, in a batch the default is assumed to be `cyclic` |

### Parameters

`LEVELS` = scalars |
Number of treatments |
---|---|

`NBLOCKS` = scalars |
Number of blocks |

`NUNITS` = scalars |
Number of units per block, or number of periods in a cyclic change-over design |

`SEED` = scalars |
Seed for randomization; a negative value implies no randomization |

`TREATMENTS` = factors |
Identifier for the treatment factor |

`SUPERIMPOSED` = factors |
Identifier for the second treatment factor in a cyclic superimposed design |

`BLOCKS` = factors |
Identifier for the factor to index the blocks |

`UNITS` = factors |
Identifier for the factor to index the units within each block, or the periods of a cyclic change-over design |

`INITIALBLOCKS` = variates or pointers |
To save one (variate) or more (pointer to variates) initial blocks |

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

### Description

Cyclic designs provide an effective way of assessing treatments using a block design where the blocks are each too small to hold all the treatments. In its simplest form, the cyclic method of generation starts with an initial block containing some subset of the treatments. This subset is represented by integers in the range 0…*m*-1 where *m* is the number of treatment levels. The second and subsequent blocks are then generated by successive addition modulo *m* of one to the numbers in the subset. Some designs have more than one initial block, and the increment need not be one. Further details of the method are given in the description of procedure `AFCYCLIC`

.

The efficiency of the design depends very much on the choice of initial blocks. Procedure `AGCYCLIC`

selects appropriate initial blocks from a repertoire obtained mainly from the program `DSIGNX`

(Franklin & Mann 1986), and including designs from Davis & Hall (1969), Hall & Williams (1973) and John, Wolock & David (1972). It then calls `AFCYCLIC`

to generate the design.

`AGCYCLIC`

is easiest to use interactively. It then asks questions to determine the necessary information to form the design. In particular, it will tell you which block sizes are available for your chosen number of treatments. The options and parameters allow you to anticipate questions, or to define all the necessary information if you want to use `AGCYCLIC`

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 first question, which can be anticipated by setting the `METHOD`

option, determines the type of cyclic design. In addition to the standard cyclic designs, `AGCYCLIC`

can also generate the cyclic change-over designs of Davis & Hall (1969) and the cyclic superimposed designs of Hall & Williams (1973). The change-over designs are used for trials in which subjects are given different treatments in different time periods; these thus have a crossed block structure `subjects*periods`

. The extension in the cyclic superimposed design is that there are two treatment factors (each with the same number of levels); the design is intended to estimate their main effects but not their interaction.

The `PRINT`

option controls whether `AGCYCLIC`

prints a 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, `AGCYCLIC`

will ask whether or not you wish to print the design, after it has been generated.

The number of treatments can be defined using the `LEVELS`

parameter. Similarly, the `NBLOCKS`

and `NUNITS`

parameters define the number of blocks and the number of units per block (or the number of periods in a cyclic change-over design). 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 `AGCYCLIC`

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

Parameters `TREATMENTS`

, `SUPERIMPOSED`

, `BLOCKS`

and `UNITS`

, allow you to specify identifiers for the treatment, the superimposed treatment (for a cyclic superimposed design), the block and unit-within-block factors. If these are not specified in a batch run, `AGCYCLIC`

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

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

has finished running.

Finally, the `INITIALBLOCKS`

parameter allows you to save the initial blocks, in a variate if there is only one, or in a pointer (to a list of variates) if there are several.

Options: `PRINT`

`METHOD`

.

Parameters: `LEVELS`

, `NBLOCKS`

, `NUNITS`

, `SEED`

, `TREATMENTS`

, `SUPERIMPOSED`

, `BLOCKS`

, `UNITS`

, `INITIALBLOCKS`

, `STATEMENT`

.

### Method

The `QUESTION`

procedure is used to obtain the necessary details of the design. The initial blocks are then recovered from a backing-store file and procedure `AFCYCLIC`

is called to generate the design.

### References

Davis, A.W. & Hall, W.B. (1969). Cyclic change-over designs. *Biometrika*, 56, 283-293.

Franklin, M.F. & Mann, A.D. (1986). *DSIGNX a Program for the Construction of Randomized Experimental Plans*. Scottish Agricultural Statistics Service, Edinburgh (revised edition).

Hall, W.B. & Williams, E.R. (1973). Cyclic superimposed designs. *Biometrika*, 60, 47-53.

John, J.A., Wolock, F.W. & David, H.A. (1972). *Cyclic Designs*. National Bureau of Standards, Applied Mathematics Series 62.

### See also

Commands for: Design of experiments, REML analysis of linear mixed models.

### Example

CAPTION 'AGCYCLIC example',!t(\ 'This example prints the (unrandomized) plan of',\ 'a design for 20 treatments in blocks of size 3.'); STYLE=meta,plain AGCYCLIC [PRINT=design; METHOD=cyclic] LEVELS=20; NBLOCKS=20; NUNITS=3;\ SEED=-1; TREATMENTS=treat; BLOCKS=block; UNITS=plot " To obtain details of the full set of possibilities, you should run AGCYCLIC interactively, without setting the LEVELS or NUNITS parameters."