Why You Need to Know About Split-Plot Designs

Bradley Jones, Director of R&D for JMP, and Christopher Nachtsheim, Professor in the Carlson School of Management at the University of Minnesota, collaborated on a paper that was published this month in the Journal of Quality Technology. Both authors have published widely on the subject of design of experiments and are recognized as experts in the field.

Their new paper is titled “Split-Plot Designs: What, Why and How,” and in this interview with Brad, I asked him those same questions contained in the paper title. Subscribers to the Journal of Quality Technology can read the full article via the ASQ Web site.

Arati: What is a split-plot design?

Brad: A split-plot experiment is a statistically designed study where the experimental runs are grouped so that certain variables do not change their settings within a group. The experimenter only changes these variables or factors between groups of runs. Holding these factors constant for an entire group of runs means that the run order for these experiment is not completely random. Statisticians often recommend the use of completely randomized designs rather than split-plot designs.

Arati: Why are split-plot designs important for practicing statisticians to know about?

Brad: Though complete randomization avoids certain problems in the analysis and interpretation of results from experiments, it often requires substantial extra effort. In many processes, certain factors are hard to change from one processing run to the next. To change some factors is as easy as turning a dial or flipping a switch. Changing others can require making time-consuming and expensive alterations to the system. It makes sense to structure your experimental runs to take this practical constraint into account. That is, you would like to do several runs in a row only changing factors that are easy to manipulate before stopping the system to make a big change. Slavish insistence on complete randomization has sometimes resulted in operational people sorting a randomized design for logistical convenience without informing the principal investigator. This sorting makes the design a split-plot design but generally a poorly constructed one. Worse yet, the principal investigator, being unaware of the sorting, analyzes the data as though the run order was random. Since the appropriate analysis of a completely randomized design is different from that of a split-plot design, the consequence of the run-sorting subterfuge can invalidate the results and make for poor decisions.

Arati: Tell me about one or two of the recent developments in designing and analyzing split-plot experiments.

Brad: In the last decade, the design and analysis of split-plot experiments has been a hot topic in research literature. For my money, the most exciting developments have been the methods for design and analysis of optimal split-plot experiments. It is not really the optimality of the designs that makes this approach exciting, though optimal designs certainly have desirable properties. The real value of these methods it that they allow for much more flexible problem specification and thus much wider applicability.

Arati: What was your purpose in writing this article with Professor Nachtsheim?

Brad: A couple of years ago I had a conversation with two past editors of the Journal of Quality Technology. They noted the resurgence of interest in split-plot designs. They also were concerned that the mathematical complexity of some of the publications were leaving most practitioners behind. There was the fact that different researchers often recommend slightly different approaches. This can confuse practitioners who do not have the background to discriminate between competing methods. Professor Nachtsheim and I wrote the article to cover all the major research lines pursued in the last decade or so and to present even-handedly their strong and weak points. I included Professor Nachtsheim in the project because I have been an advocate for one approach, and I thought it would be more objective to include an author who had no strong prior convictions.

Arati: Who is the audience for this article, and how do you hope they will use the information in it?

Brad: We wrote the article for two audiences. For the statistician who is unfamiliar with the recent trend in this area, our article provides a reference list and a guide to the main lines of research. The more important audience, however, is the community of practitioners. We wanted to provide information to empower this community to use these new methods profitably.