# Split-Plot Design: Simple Definition and Example

## What is a Split-Plot Design?

When some factors (independent variables) are difficult or impossible to change in your experiment, a completely randomized design isn’t possible. The result is a split-plot design, which has a mixture of hard to randomize (or hard-to-change) and easy-to-randomize (or easy-to-change) factors. The hard-to-change factors are implemented first, followed by the easier-to-change factors.

The “Plot” part of split-plot originally comes from a plot of land in agriculture. Split-plots were invented by Fisher (1935) and it has been suggested that all agricultural experiments are split-plot designs (Box et. al, 2005). Although these designs are commonly seen in industry, they can also be used across a wide variety of disciplines, including medicine. In fact, any experiment where one of your factors is difficult to change or randomize is a candidate for a split-plot design.

## Example

You want to study the effects of two irrigation methods (factor 1) and two different fertilizer types (factor 2) on four different fields (“whole plots”). However, you run into a practical problem with randomization. While a field can easily be split into two for the two different fertilizers, the field cannot easily be split into two for irrigation: One irrigation system normally covers a whole field and the systems are expensive to replace.

Step 1: Randomize the fixed or hard-to-change factor (in this example, that’s the irrigation method) among the four fields:

Step 2: Split the plots into two.

Step 3: Randomize the non-fixed or easy-to-change factor within each plot (in this example, that’s the fertilizer):

Compare the above image with one you might get from a complete randomization — where both the irrigation and fertilizer are randomly allocated between the 8 subplots:

Compared to completely randomized designs, split-plot designs have the following advantages:

• Cheaper to run. In the above example, implementing a new irrigation method for each subplot would be extremely expensive.
• More efficient statistically, with increased precision.

This type of design does have many disadvantages, including:

• Implementing the design can be difficult, and requires advanced knowledge of a specific discipline (e.g. agriculture, factory production, or epidemiology). These designs are difficult to create and to spot– many published papers contain split-slot designs that are incorrectly classified and analyzed (Jones & Nachtsheim, 2009).
• Software packages that assist with the design are hard to find, although SAS and JMP have options.

Next: Split-Block Design

References
Box, G. and Meyer, R. D. (1986). Box, G.; Hunter, W.; and Hunter, S. (2005). Statistics for
Experimenters: Design, Innovation, and Discovery, 2nd edition. New York, NY: Wiley-Interscience.“An Analysis for Unreplicated Fractional Factorials”. Technometrics 28, pp. 11–18.
Fisher, R. A. (1925). Statistical Methods for Research Workers. Edinburgh: Oliver and Boyd.
Jones, B. & Nachtsheim, C. (2009). “Split-Splot Designs: What, Why, and How.” Journal of Quality Technology ,October.