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scidoe_fracfact

Fractional Factorial Design

Calling Sequence

H = scidoe_fracfact(gen)

Parameters

gen :

a 1-by-n matrix of strings, consisting of lowercase ,uppercase letters or operators "-" and "+", indicating the factors of the experiment

H :

a m-by-n matrix of doubles, the fractional factorial design. m is 2^k, where k is the number of letters in gen, and n is the total number of entries in "gen"

Description

The function computes a fractional factorial design. Fractional factorial designs are used instead of full factorial designs, because they need fewer runs.

In "gen" we define the main factors of the experiment and the factors whose levels are the products of the main factors. For example, if 

gen = "a b ab"
then "a" and "b" are the main factors, while the 3rd factor is the product of the first two. If we input uppecase letters in gen, we get the same result. We can also use the operators "+" and "-" in gen.

For example, if 

gen = "a b -ab"
then the 3rd factor is the opposite of the product of "a" and "b".

The output matrix includes a two level full factorial design, built by the main factors of gen, and the products of the main factors. The columns of H follow the sequence of "gen". For example, if 

gen = "a b ab c"
then columns H(:,1), H(:,2) and H(4,:) include the two level full factorial design and H(:,3) includes the products of the main factors.

Examples

// Fractional factorial design, where the 3rd factors
// is the product of the first two
H = scidoe_fracfact("a b ab")
// The same with uppercase letters
H = scidoe_fracfact("A B AB")
// Use of operators
H = scidoe_fracfact("a b -ab c +abc")

Bibliography

http://www.itl.nist.gov/div898/handbook/pri/section3/pri3342.htm

http://www.mathworks.com/help/toolbox/stats/fracfact.html

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