Lucas, James M.; Ju, Huey L. (1992, ASQC) Du Pont Company, Wilmington, DE 19808 and University of Delaware, Newark, DE 19711
When there is an inherent split-plot error structure, a completely randomized experiment will not give the proper error estimate for testing some of the effects.
In the scheme described in this paper, the second-error term is created by changes in the levels of some of the variables. This situation will often occur when there are hard-to-change and easy-to-change variables in the same experiment. A new value of the second error term is introduced when any of the hard-to-change variables are changed. Although this paper examines experiments with two error terms, extensions to cases with multiple error terms is also possible.
It is useful to completely restrict randomization of the hard-to-change factor when there is only one in the experiment. Randomization is carried out over the easily-changed factors, which is more precise for all effects except the main effects of the hard-to-change factor. The significance of the hard-to-change factor cannot be tested; testing versus the residual will overestimate the result of the hard-to-change factor.
Chemical and process industries,Experiments,Problem solving,Statistics