conf.design-package {conf.design}

Confounded Factorial Block Design

Description

Construct confounded designs with specific contrasts confounded with blocks. The package only directly handles the p^k case, that is, all treatment factors having the same (prime) number of levels. Some simple facilities are provided for combining component designs into larger ones, thus providing some facilities for generating interesting designs for the more general case. Some fractional replication is also possible with the tools proveded.

Details

Package:	conf.design
Type:	Package
Version:	2.0.0
Date:	2013-02-23
License:	GPL-2

The key functions are conf.design, rjoin and direct.sum. The help information for these functions contain some fairly detailed examples.

Some ancillary functions may be of independent interest, for example primes for generating prime numbers and factorize, which has an experimental design application, but a default method can be used to factorize (not too large) integers into prime factors.

Author(s)

Bill Venables

Maintainer: Bill Venables <[e-mail]>

References

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

See Also

The CRAN task view on Design of Experiments

Examples

### Generate a half replicate of a 2^3 x 3^2 experiment.  The factors
### are to be A, B, C, D, E.  The fractional relation is to be I = ABC
### and the DE effect is to be confounded with blocks.

### First construct the 2^3 design, confounded in two blocks:
d1 <- conf.design(c(A = 1, B = 1, C = 1), p=2)

### Next the 3^2 design, with DE confounded in blocks:
d2 <- conf.design(c(D = 1, E = 1), p=3)

### Now extract the principal block from the 2^3 design and form the direct
### sum withthe 3^2 design
dsn <- direct.sum(subset(d1, Blocks == "0"), d2)
head(dsn)
###    Blocks A B C Blocksa D E
###  1      0 0 0 0       0 0 0
###  2      0 0 0 0       0 2 1
###  3      0 0 0 0       0 1 2
###  4      0 0 0 0       1 1 0
###  5      0 0 0 0       1 0 1
###  6      0 0 0 0       1 2 2
###
### Combine the two "Blocks" factors into a single block factor:
dsn <- within(dsn, {
  Blocks <- join(Blocks, Blocksa)
  Blocksa <- NULL
})
### Now to do some checks.
as.matrix(replications( ~ .^2, dsn))

### Blocks     12
### A          18
### B          18
### C          18
### D          12
### E          12
### Blocks:A    6
### Blocks:B    6
### Blocks:C    6
### Blocks:D    4
### Blocks:E    4
### A:B         9
### A:C         9
### A:D         6
### A:E         6
### B:C         9
### B:D         6
### B:E         6
### C:D         6
### C:E         6
### D:E         4

### We can check the confounding by analysing some dummy data:

dsn$y <- rnorm(nrow(dsn))
dummyAov <- aov(y ~ A*B*C*D*E + Error(Blocks), data=dsn)
summary(dummyAov)

###  Error: Blocks
###      Df Sum Sq Mean Sq
###  D:E  2  8.915   4.458
###
###  Error: Within
###        Df Sum Sq Mean Sq
###  A      1  2.077   2.077
###  B      1  1.111   1.111
###  C      1  3.311   3.311
###  D      2  1.929   0.964
###  E      2  0.848   0.424
###  A:D    2  3.421   1.711
###  B:D    2  3.231   1.615
###  C:D    2  2.484   1.242
###  A:E    2  0.214   0.107
###  B:E    2  0.006   0.003
###  C:E    2  0.349   0.174
###  D:E    2  1.442   0.721
###  A:D:E  4  2.560   0.640
###  B:D:E  4  4.454   1.114
###  C:D:E  4  7.942   1.986

### Two of the D:E degrees of freedom are confounded with Blocks, as desired.