My previous post demonstrated some advantages of designed experiments using random blocks rather than the more traditional fixed blocks. My main point was that random blocks can allow for more cost-effective experiments because they require fewer runs for a given set of factors and model specification. There is another advantage
“The most commonly used class of experimental design in many industrial laboratories is the two-level factorial.” – Greenfield (1976). This bold statement was true in 1976, and I would not be surprised if were still true today. Certainly, two-level factorial designs are a standard feature in a first course in
It is fairly common that experiments run in a time sequence experience linear drift in the response over the course of the experiment. If you randomize the order of the runs, then the effect of this drift will not tend to bias the estimated factor effects, but it will increase
In my previous post, I talked about the fundamental quantities that affect the ability of a designed experiment to detect non-negligible effects of the factors. These are: 1) The size of the effect 2) The root mean squared error (RMSE) of the fitted model 3) The significance level of the
When I took my first course in linear models and design of experiments, my professor told the class that the most common question that he encountered in his statistical consulting was, “How many samples do I need [for my results to be statistically significant]?” This question comes out of a
Among other kinds of factors, the Custom Designer in JMP has a mechanism for adding factors with values that are not controllable but are known in advance of experimentation. I call these factors covariate factors, although in regression analysis covariates have a slightly different meaning. Can you provide a realistic
Among other kinds of factors, the Custom Designer in JMP has facilities for continuous factors and for categorical factors with an arbitrary number of levels. The designer assumes that continuous factors can take any value within the specified range from low to high. Sometimes, though, there are practical restrictions to
When one or more factors in an experiment are continuous, many investigators like to add several runs at the center of the design region. This practice accomplishes two things: 1) It allows for a test of overall curvature. 2) It provides replicated runs, which means that JMP can calculate an
Take a look at this matrix of symbols. ++++++++++++++++++++++++++++++++ +−+−+−+−+−+−+−+−+−+−+−+−+−+−+−+− ++−−++−−++−−++−−++−−++−−++−−++−− +−−++−−++−−++−−++−−++−−++−−++−−+ ++++−−−−++++−−−−++++−−−−++++−−−− +−+−−+−++−+−−+−++−+−−+−++−+−−+−+ ++−−−−++++−−−−++++−−−−++++−−−−++ +−−+−++−+−−+−++−+−−+−++−+−−+−++− ++++++++−−−−−−−−++++++++−−−−−−−− +−+−+−+−−+−+−+−++−+−+−+−−+−+−+−+ ++−−++−−−−++−−++++−−++−−−−++−−++ +−−++−−+−++−−++−+−−++−−+−++−−++− ++++−−−−−−−−++++++++−−−−−−−−++++ +−+−−+−+−+−++−+−+−+−−+−+−+−++−+− ++−−−−++−−++++−−++−−−−++−−++++−− +−−+−++−−++−+−−++−−+−++−−++−+−−+ ++++++++++++++++−−−−−−−−−−−−−−−− +−+−+−+−+−+−+−+−−+−+−+−+−+−+−+−+ ++−−++−−++−−++−−−−++−−++−−++−−++ +−−++−−++−−++−−+−++−−++−−++−−++− ++++−−−−++++−−−−−−−−++++−−−−++++ +−+−−+−++−+−−+−+−+−++−+−−+−++−+− ++−−−−++++−−−−++−−++++−−−−++++−− +−−+−++−+−−+−++−−++−+−−+−++−+−−+ ++++++++−−−−−−−−−−−−−−−−++++++++ +−+−+−+−−+−+−+−+−+−+−+−++−+−+−+− ++−−++−−−−++−−++−−++−−++++−−++−− +−−++−−+−++−−++−−++−−++−+−−++−−+ ++++−−−−−−−−++++−−−−++++++++−−−− +−+−−+−+−+−++−+−−+−++−+−+−+−−+−+ ++−−−−++−−++++−−−−++++−−++−−−−++ +−−+−++−−++−+−−+−++−+−−++−−+−++− Beautiful isn’t it? This matrix has several wonderful properties. Ignoring
Replication is one of the four basic principles of experiment design introduced by R. A. Fisher. The other three were the factorial principle, randomization and blocking. The value of replication is that it provides an estimate of the run-to-run variability in the response that is unaffected if the model is