# conf.set: Find all confounded effects In conf.design: Construction of factorial designs

## Description

Find minimal complete sets of confounded effects from a defining set for symmetric confounded factorial designs. Useful for checking if a low order interaction will be unintentionally confounded with blocks. As in the usual convention, only effects whose leading factor has an index of one are listed.

All factors must have the same (prime) number of levels.

## Usage

 `1` ```conf.set(G, p) ```

## Arguments

 `G` Matrix whose rows define the effects to be confounded with blocks, in the same way as for `conf.design`. `p` Number of levels for each factor. Must be a prime number.

## Details

The function constructs all linear functions of the rows of `G` (over GF(p)), and removes those rows whose leading non-zero component is not one.

## Value

A matrix like `G` with a minimal set of confounded with blocks defined in the rows.

## Side Effects

None

`conf.design`
 ``` 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 32``` ```### If A B^2 C and B C D are confounded with blocks, then so are A C^2 D ### and A B D^2. G <- rbind(c(A = 1, B = 2, C = 1, D = 0), c(A = 0, B = 1, C = 1, D = 1)) conf.set(G, 3) ### A B C D ### [1,] 1 2 1 0 ### [2,] 0 1 1 1 ### [3,] 1 0 2 1 ### [4,] 1 1 0 2 ### Only three-factor interactions are confounded, so the design is ### presumably useful. as.matrix(replications( ~ .^2, conf.design(G, 3))) ### [,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 ```