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scidoe_yates

Calculates main and interaction effects using Yate's algorithm.

Calling Sequence

ef = scidoe_yates(y)
ef = scidoe_yates(y,sort_eff)
[ef,id] = scidoe_yates(...)

Parameters

y :

a n-by-1 vector of doubles, containing the calculated response from a two-level complete factorial design in standard order

sort_eff :

a 1-by-1 matrix of booleans, set to true to sort the effects (default sort_eff=%f). If sort_eff is true, sorts the id matrix and the corresponding ef vector, so that main effects are first, followed by two-factor and three-factor interactions.

ef :

a n-by-1 vector of doubles, containing average response, main effects and interaction effects. ef(1) is the average response and ef(2:$) contain the main effects and interaction effects corresponding to the vector id.

id :

a (n-1)-by-k matrix of doubles, the identification matrix of main and interaction effects.

Description

Calculates main and interaction effects using Yates algorithm.

Let us analyse the output of the first example below:

For i=1,2,...,n-1, the entry ef(i+1) is the effect of the parameters in id(i,:).

ef(1) is the average response of the experiment.

The effect ef(2) = 23 is associated with id(1,:) = [1 0 0], which shows what is the effect of the parameter X1 (while X2 and X3 remain fixed).

The effect ef(6) = 10 is associated with id(5,:) = [1 3 0], which shows the effect when X1 and X3 interact (while X2 remains fixed).

The effect ef(8) = 0.5 is associated with id(7,:) = [1 2 3], which shows the effect when X1, x2 and X3 interact.

This function is adapted from the WAFO toolbox : http://www.maths.lth.se/matstat/wafo/documentation/wafodoc/wafo/wstats/yates.html

Examples

// Calculate main and interaction effects
D = scidoe_ff2n(3); // complete 2^3 design in standard order.
y = [60 72 54 68 52 83 45 80]'; // Responses to design D.
[ef,id] = scidoe_yates(y)
// Another example
D = scidoe_ff2n(3)
y = [28 36 22 31 25 33 19 26]'
[ef,id] = scidoe_yates(y)

// See the sort_eff option in action
[ef,id] = scidoe_yates(y,%t)

Bibliography

"Statistics for experimenters Design,Innovation and Discovery", Second Edition, George E.P Box, J. Stuart Hunter, William Hunter, Wiley Series, 2005. 177-183, 191.

http://www.itl.nist.gov/div898/handbook/eda/section3/eda35i.htm

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