Helps to select and generate effective experimental designs (R.W. Payne, M.F. Franklin & A.E. Ainsley).

### Option

`STATEMENT` = text |
Saves a command to recreate the design |
---|

### No parameters

### Description

`DESIGN`

is a procedure which can be used interactively to form experimental designs of various types. The process involves answering questions, posed by Genstat, first to select the particular type of design, then to give details such as names of factors, numbers of treatments, and so on. A range of subsidiary procedures may be called, depending on the type of design selected. If you wish to avoid some of the question-and-answer process, the subsidiary procedures can also be called directly. They all have options and parameters which provide an alternative way of supplying the information otherwise obtained by the various questions and, provided you supply all the required information, they can also be used in batch. The `STATEMENT`

option of `DESIGN`

allows you to save a Genstat text structure containing a command to use the relevant subsidiary procedure, and setting all the options and parameters required to recreate the design.

There are 18 types of design.

Orthogonal hierarchical designs – designs such as randomized blocks, split-plots, split-split-plots, &c.

Complete factorial designs (with interactions confounded with blocks) – these are available for treatments that all have the same number of levels *k*, where *k* is a prime number or a power of a prime number. The design, constructed by procedure `AGFRACTION`

, will be a minimum-aberration design. (To explain this, we first define the resolution of a design as the largest integer *r* such that no interaction term with *r* factors is confounded with blocks. The aberration of the design is the number of interaction terms with *r*+1 factors that are confounded. A minimum aberration design is defined as a design with the smallest aberration out of the designs with the highest available resolution. So, essentially this selects the best design by minimizing the number of interactions with the minimum number of factors that are confounded.)

Fractional factorial designs (with blocking if required) – these are formed by `AGFACTORIAL`

by taking one block of a minimum-aberration factorial design. If required, the resulting fractional factorial can be further dividing into its own blocks.

Factorial designs from a repertoire (with blocking) – these have several treatment factors and a single blocking factor (giving strata for blocks and plots within blocks). The blocks are too small to contain a complete replicate of the treatment combinations and so various interaction are confounded with blocks. (See procedure `AGDESIGN`

.)

Fractional factorial designs from a repertoire (with blocking) – again there are several treatment factors but the design does not contain every treatment combination and so some interactions are aliased; there can also be a blocking factor and some interactions will then be confounded with blocks. (See procedure `AGDESIGN`

.)

Lattice designs – designs for a single treatment factor with number of levels that is the square of some integer *k*. The design has replicates, each containing *k* blocks of *k* plots, and different treatment contrasts can be confounded with blocks in each replicate. (See procedure `AGSQLATTICE`

.)

Lattice squares – these are similar to lattices except that the blocking structure with the replicates has rows crossed with columns; again different treatment contrasts can be confounded with the rows and columns in each replicate. (See procedure `AGSQLATTICE`

.)

Latin squares – designs are available for any number of treatments (subject to workspace limitations) also, where feasible, more than one orthogonal treatment factor can be generated to form Graeco-Latin squares etc. (see procedure `AGLATIN`

).

Latin squares balanced for carry-over effects – these are relevant when the same plots or subjects are treated during several successive time periods, and there is interest both in the direct effect of a treatment during the period in which it is applied and its carry-over (or “residual”) effect during later periods (see procedure `AGCROSSOVERLATIN`

).

Semi-Latin squares – *n* × *n* Latin squares whose individual plots are split into *k* sub-plots to cater for a treatment factor with *n* × *k* levels; three types are available Trojan squares, interleaving Latin squares and inflated Latin squares (see procedure `AGSEMILATIN`

).

Complete and quasi-complete Latin squares – Latin squares designed to guard against interference between plots; a complete Latin square is a Latin square in which each ordered pair of treatments appears exactly once within the rows of the square, and exactly once within the columns; a quasi-complete Latin has similar properties, but here each unordered pair occurs exactly twice within the rows, and exactly twice within the columns (see procedure `AGQLATIN`

).

Alpha designs – these again have a single treatment factor but there is no constraint on the number of levels; the blocking structure has replicates and blocks within replicates. Further details are given in the description of the procedure `AFALPHA`

or by (Patterson & Williams 1976).

Cyclic designs – these are designs with a single blocking factor which defines blocks that are too small to contain every treatment. Usually there is a single treatment factor, but you can also generate the cyclic superimposed designs of Hall & Williams (1973) in which there are two treatment factors and the treatment structure fits only the main effects. An alternative refinement (Davis & Hall 1969) has a crossed blocking structure generally taken to represent `subjects*time`

. Details of the cyclic process by which the treatment levels are generated can be found in the description of the procedure `AFCYCLIC`

.

Balanced-incomplete-block designs – designs where the experimental units are grouped into blocks such that every pair of treatments occurs in an equal number of blocks. All comparisons between treatments are thus made with equal accuracy, so the design is balanced and, in particular, can be analysed by `ANOVA`

. Further details are given in the description of procedure `AGBIB`

.

Neighbour-balanced designs – designs that allow an adjustments to be made for the effect that a treatment may have on adjacent plots. Further details are given in the description of procedure `AGNEIGHBOUR`

.

Central composite designs – used to study multi-dimensional response surfaces; see procedure `AGCENTRALCOMPOSITE`

.

Box-Behnken designs – used to study multi-dimensional response surfaces; see procedure `AGBOXBEHNKEN`

.

Plackett Burman (main effect) designs – for estimating main effects of factors with two levels, using a minimum number of experimental units (Plackett & Burman 1946). Further details are given in the description of procedure `AGMAINEFFECT`

.

Loop designs – for use e.g. in time-course microarray experiments; see procedure `AGLOOP`

.

Reference-level designs – for use e.g. in two-colour microarray experiments; see procedure `AGREFERENCE`

.

You will be asked to provide a seed to be used to randomize the design and then given the opportunity to print a plan. If the design can be analysed by `ANOVA`

, the procedures will define appropriate block and treatment formulae and then ask if you want to see the skeleton analysis-of-variance table (containing just source of variation, degrees of freedom and efficiency factors). Whether or not you choose to print any of this information, at the end of the whole process all the block and treatment factors necessary to define the design will be available – and they will have the identifiers that you have supplied in response to the various questions asked by the procedures.

Option: `STATEMENT`

.

Parameters: none.

### Method

The `QUESTION`

procedure is used to find out what design is required. `DESIGN`

then calls either `AGHIERARCHICAL`

(for an orthogonal hierarchical design), `AGFACTORIAL`

(for minimum-aberration complete or fractional factorial designs), `AGDESIGN`

(for a factorial design), `AGFRACTION`

(for a fractional factorial design), `AGLATIN`

(for mutually orthogonal Latin squares), `AGCROSSOVERLATIN`

(for Latin squares balanced for carry-over effects), `AGSEMILATIN`

(for a semi-Latin square), `AGQLATIN`

(for complete and quasi-complete Latin squares), `AGSQLATTICE`

(for a square lattice or lattice square design), `AGALPHA`

(for an alpha design), `AGCYCLIC`

(for a cyclic design), `AGNEIGHBOUR`

(for a neighbour-balanced design), `AGCENTRALCOMPOSITE`

(for a central composite design), `AGBOXBEHNKEN`

(for a Box-Behnken design), `AGMAINEFFECT`

(for a Plackett Burman main effect design), `AGLOOP`

(for a loop design) or `AGREFERENCE`

(for a reference-level design). The designs are generated using `GENERATE`

and the other standard Genstat directives for calculation and manipulation. Some of the information needed to specify the designs is stored in backing-store files, and much of this was adapted from the standard designs of the program DSIGNX (Franklin & Mann 1986).

### 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.

Patterson, H.D. & Williams E.R. (1976). A new class of resolvable incomplete block designs. *Biometrika*, 63, 83-92.

Plackett, R.L. & Burman, J.P. (1946). The design of optimum factorial experiments. *Biometrika*, 33, 305-325 & 328-332.

### See also

Commands for: Design of experiments.

### Example

CAPTION\ 'DESIGN can only be run interactively - & is used simply by typing DESIGN.'