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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.

UPDATE on 4 May 2010: This article won the prestigious Brumbaugh Award from ASQ. You can download a PDF of the article from the JMP Web site.

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Phil Stojan wrote:

Who are these practitioners?

If you refer to the people like who actually utilise statistics as a tool which aids clarification for detecting pattern, maybe it would be beneficial to consult with multidisciplinary practitioners-Applied Science may have valid and obvious reasons why methods are altered or revised.


Phil Stojan wrote:

I stumbled across this page (and by chance-have some familiarity with split plot sample comparisons between individuals from natural populations in the field, so I'll add something).

From a Field Ecologist's perspective, I find your comments relating to "Split-plot" designs somewhat perplexing and feel it necessary to point out a couple of real world facts:

1. Confusion underlying the complex "mathematistry" necessary to attain an optimal design questions whether investigators/anyone else should actually bother proceeding in terms of sampling effort required (as an analogy).

2. If one can actually create such an optimal split-plot design-either the pattern is so obvious, it probably doesn't require the use of a test statistic to reject the Ho, or you're just being cheap-risking a Type 2 error (at the end of the runs because:

"....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."

Of course we would-if for no other reason it would save time!

You've blindly assumed however that the order in which treatments are applied (ie testing for factor effects) does not introduce bias to the analysis-which at this point you cannot even argue since by failure to randomise, you aren't really entitled to make inferences.

What would Fisher and Gossett think?

I don't mean to cause a fuss-and I may not be quite right given I haven't read the article, but maybe instead I can shed some light on how undergraduate students apply it to Manipulative Field BIology experiments:

Split-plot designs have been well understood in Manipulative studies of Biology since RA Fisher worked where I do.

The inferences made regarding treatment effects of this design suffer spatial and temporal pseudoreplication and thus only relate to where the plots are placed: a common comparison in Ecology is when a vegetation patch is split and sujtected to some kind of manipulation-the other half constituting its control.

The effect of water addition compared to control for example.

Most often, Biology is concerned with the magnitude of the effect size which a treatment produces, and avoiding Type 2 errors. a priori setting of alpha is arbritary and means little if you maximise the effect size and have ample Statistical power.

I cannot understand why you would employ a split-plot design with the intention of optimising it: they're already about as close as you could position them?

FInally, sequence of treatments often return interactions (meaning in Nature, sequence of events is important)-it sounds as though the treatment replications you are referring to are very precise and somehow do not introduce bias in the absence of randomisation.

We refer to this Gremlin as Demonic intrusion in Ecology.

Please let me know.



Bradley Jones Wins ASQ Brumbaugh Award - JMP Blog wrote:

[...] They co-wrote an article titled â Split-Plot Designs: What, Why, and Howâ that was published in the Journal of Quality Technology in October 2009. The Brumbaugh Award was founded in 1949 and is presented for the paper, published in the previous year, that the committee decides has made the largest single contribution to the development of industrial application of quality control. In a previous blog post about this article, Bradley explained why you need to know about split-plot designs. [...]


Article on Split-Plot Designs Is Honored Again - JMP Blog wrote:

[...] may also want to check out a previous blog post about this article in which Jones explains why you need to know about split-plot designs. tags: Design of Experiments [...]