What the Heck is a Split-Plot Design, and Why Would I Want It?

In previous posts on design of experiments, or DOE, we’ve covered:

Next on the list are split-plot experiments.

Split-plot designs are extremely popular in design of experiments because they cover a common case in the real world: when you have a factor that you want to study but can’t change as often as your other factors.

If you have an agricultural mind, as many scientists did back when they were inventing the name of this method, you’ll appreciate the language about "splitting a plot." Suppose that you wanted to study a fertilizer. You're going to use design of experiments to study 2 fertilizers and 4 seed varieties to see which combination provides the best crop yield. Using traditional design of experiments methods, you would randomly assign each fertilizer and seed combination to a different plot of land, eight plots in all.

But there's a problem. Whether you do it through crop dusting or using one of the fancy new water-soluble fertilizers, you can apply fertilizer only to a large area. You don't have enough land to get eight separate plots.

 Fertilizer 1   Seed 4 Fertilizer 2   Seed 2

One possible solution is to test different combinations across different seasons, but then you’d need 4 seasons to finish your experiment!

Fertilizer 2

 S1 S3 S2 S4

Fertilizer 1

 S3 S4 S1 S2

The solution offered by split-plot experiments is to apply the fertilizers to the large areas, then split the plots of land, using the smaller plots for different seeds. With a split-plot experiment, you not only need to set up the experiment differently, you also need to do different math to analyze the experimental data correctly. Fortunately, we can leave both the setup and the math in the hands of Minitab Statistical Software.

Of course, Minitab reminds us that these experiments are for any “hard-to-change” factors because they come up in so many different contexts. Several articles on our Web site offer more examples about the utility of split-plot designs. DOE: Handling Hard-to-Change Factors with Split-Plot Designs in Minitab describes how much longer a cake-baking experiment would take if you reset the oven temperature between every cake instead of baking several different recipes at the same time. How to Analyze a Split-Plot Experiment takes you through studying the water resistance of treated wood when some machines are designed to treat large pieces and others small pieces of wood. And check out How to Recognize a Split-Plot Experiment for two more examples, dealing with a printing press and manufacturing plastic parts.

Remember that design of experiments is all about learning as much as possible from the smallest amount of data. But sometimes you also need to collect that data as quickly as possible. So the next time you need to conduct an experiment and are faced with a hard-to-change factor, consider using a split-plot design. These experiments can greatly speed up data collection that would otherwise take a prohibitively long time, or even be impossible!

© The photograph of the cornfield is copyrighted by Pete Chapman and licensed for reuse under this Creative Commons Licence.