Understanding lm-based analysis of fractional factorial experiments
On Mar 6, 2013, at 4:46 AM, Kjetil Kjernsmo <kjekje at ifi.uio.no> wrote:
All, I have just returned to R after a decade of absence, and it is good to see that R has become such a great success! I'm trying to bring Design of Experiments into some aspects of software performance evaluation, and to teach myself that, I picked up "Experiments: Planning, Analysis and Optimization" by Wu and Hamada. I try to reproduce an analysis in the book using lm, but have to conclude I don't understand what lm does in this context, even though I end up at the desired result. I'm currently using R 2.15.2 on a recent Fedora system, but I get the same result on Debian Wheezy and Debian Squeeze. I think the discussion below can be followed without having the book at hand though. I'm working with tables 5.2 and 5.5 in the above mentioned book. Table 5.2 contains data from the "Leaf spring experiment". The dataset is also in this zip file: ftp://ftp.wiley.com/public/sci_tech_med/experiments-planning/data%20sets.zip I've learned from the book that the effects can be found using a linear model and double the coefficients. So, I do
leaf <- read.table("/ifi/bifrost/a03/kjekje/fag/experimental-planning/book-datasets/LeafSpring table 5.2.dat", col.names=c("B", "C", "D", "E", "Q", paste("r", 1:3, sep=""), "yavg", "ssq", "lnssq"))
leaf.lm <- lm(yavg ~ B * C * D * E * Q, data=leaf)
leaf.lm
I'll ignore the rest of your question, in the hope that this will answer them sufficiently. You probably want a simple linear model, specified in R using "+" instead of "*".
leaf.lm <- lm(yavg ~ B + C + D + E + Q, data=leaf) leaf.lm
Call:
lm(formula = yavg ~ B + C + D + E + Q, data = leaf)
Coefficients:
(Intercept) B+ C+ D+ E+ Q+
7.50084 0.22125 0.17625 0.02875 0.10375 -0.25960
Does this give you the numbers you expect?
Peter
Kjetil -- Kjetil Kjernsmo PhD Research Fellow, University of Oslo, Norway Semantic Web / SPARQL Query Federation kjekje at ifi.uio.no http://www.kjetil.kjernsmo.net/
______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.