# fracfact

Fractional factorial design

## Syntax

```X = fracfact(gen) [X,conf] = fracfact(gen) [X,conf] = fracfact(gen,Name,Value) ```

## Description

`X = fracfact(gen)` creates the two-level fractional factorial design defined by the generator `gen`.

```[X,conf] = fracfact(gen)``` returns a cell array of character vectors containing the confounding pattern for the design.

```[X,conf] = fracfact(gen,Name,Value)``` creates a fractional factorial designs with additional options specified by one or more `Name,Value` pair arguments.

## Input Arguments

 `gen` Either a string array or cell array of character vectors where each element contains one “word,” or a character array or string scalar consisting of “words” separated by spaces. “Words” consist of case-sensitive letters or groups of letters, where `'a'` represents value `1`, `'b'` represents value `2`, ..., `'A'` represents value `27`, ..., `'Z'` represents value `52`. Each word defines how the corresponding factor’s levels are defined as products of generators from a `2^K` full-factorial design. `K` is the number of letters of the alphabet in `gen`.

### Name-Value Arguments

Specify optional pairs of arguments as `Name1=Value1,...,NameN=ValueN`, where `Name` is the argument name and `Value` is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose `Name` in quotes.

 `FactorNames` String array or cell array specifying the name for each factor. Default: `{'X1','X2',...}` `MaxInt` Positive integer setting the maximum level of interaction to include in the confounding output. Default: `2`

## Output Arguments

 `X` The two-level fractional factorial design. `X` is a matrix of size `N`-by-`P`, where `N` = `2^K`, where `K` is the number of letters of the alphabet in `gen`.`P` is the number of words in `gen`. Because `X` is a two-level design, the components of `X` are `±1`. For the meaning of `X`, see Fractional Factorial Designs. `conf` Cell array of character vectors containing the confounding pattern for the design.

## Examples

Generate a fractional factorial design for four variables, where the fourth variable is the product of the first three:

```x = fracfact('a b c abc') x = -1 -1 -1 -1 -1 -1 1 1 -1 1 -1 1 -1 1 1 -1 1 -1 -1 1 1 -1 1 -1 1 1 -1 -1 1 1 1 1```

Find generators for a six-factor design that uses four factors and achieves resolution IV using `fracfactgen`. Use the result to specify the design:

```generators = fracfactgen('a b c d e f',4, ... % 4 factors 4) % resolution 4 generators = 'a' 'b' 'c' 'd' 'bcd' 'acd' x = fracfact(generators) x = -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 -1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 -1 1 -1 1 1 1 1 -1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1 -1 1 1 1 -1 -1 1 1 1 1 -1 1 -1 -1 1 1 1 -1 -1 -1 1 1 1 1 1 1```

## References

 Box, G. E. P., W. G. Hunter, and J. S. Hunter. Statistics for Experimenters. Hoboken, NJ: Wiley-Interscience, 1978.

## Version History

Introduced before R2006a