# conf.design: Construct symmetric confounded factorial designs. In conf.design: Construction of factorial designs

## Description

Construct designs with specified treatment contrasts confounded with blocks. All treatment factors must have the sampe (prime) number of levels.

## Usage

 `1` ```conf.design(G, p, block.name = "Blocks", treatment.names = NULL) ```

## Arguments

 `G` Matrix whose rows define the contrasts to be confounded. The number of columns of `G` defines the number of factors. `p` The common number of levels for each factor. Must be a prime number. `block.name` Name to be given to the factor defining the blocks of the design. `treatment.names` Name to be given to the treatment factors of the design. If `NULL` and if `G` has a `dimnames` attribute, then `dimnames[[2]]` is the default, otherwise T1, T2, ...

## Details

For example in a `3^4` experiment with `AB^2C` and `BCD` confounded with blocks (together with their generalized interactions), the matrix `G` could be given by

```rbind(c(A = 1, B = 2, C = 1, D = 0), c(A = 0, B = 1, C = 1, D = 1))```

For this example, `p = 3`

Having column names for the `G` matrix implicitly supplies the treatment factor names.

For a single replicate of treatments, blocks are calculated using the confounded contrasts in the standard textbook way. The method is related to that of Collings (1989).

## Value

A design with a `Blocks` factor defining the blocks and treatment factors defining the way treatments are allocated to each plot. (Not in randomised order!)

None.

## References

Collings, B. J. (1989) Quick confounding. Technometrics, v31, pp107-110.

`conf.set`, `direct.sum`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31``` ```### ### Generate a 3^4 factorial with A B^2 C and B C D confounded with blocks. ### d34 <- conf.design(rbind(c(A = 1, B = 2, C = 1, D = 0), c(A = 0, B = 1, C = 1, D = 1)), p = 3) head(d34) ### Blocks A B C D ### 1 00 0 0 0 0 ### 2 00 1 2 1 0 ### 3 00 2 1 2 0 ### 4 00 2 2 0 1 ### 5 00 0 1 1 1 ### 6 00 1 0 2 1 as.matrix(replications(~ .^2, d34)) ### [,1] ### Blocks 9 ### A 27 ### B 27 ### C 27 ### D 27 ### Blocks:A 3 ### Blocks:B 3 ### Blocks:C 3 ### Blocks:D 3 ### A:B 9 ### A:C 9 ### A:D 9 ### B:C 9 ### B:D 9 ### C:D 9 ```