Calculates main and interaction effects using Yate's algorithm.
ef = scidoe_yates(y) ef = scidoe_yates(y,sort_eff) [ef,id] = scidoe_yates(...)
a n-by-1 vector of doubles, containing the calculated response from a two-level complete factorial design in standard order
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.
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.
a (n-1)-by-k matrix of doubles, the identification matrix of main and interaction effects.
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
"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