# DOE: Handling Hard-to-Change Factors with Split-Plot Designs in Minitab

Split-plot designs are experimental designs that include at least one hard-to-change factor that is difficult to completely randomize due to time or cost constraints. By making the creation of split-plot experiment designs simple, Minitab makes the benefits of this powerful statistical technique accessible to everyone.

Consider the case of a baking company that wants to use design of experiments (DOE) to simultaneously study three factors to optimize the formula for its chocolate cake. Two of these factors are easy to change:  the amount of flour and the amount of sugar in the mix. But another factor, oven temperature, isn’t so easy to change. Changing this factor is difficult because the enormous ovens the company uses take several hours to attain a stable temperature. An experiment that includes a hard-to-change factor, such as the bakery’s oven temperature, calls for a special type of DOE called a split-plot design.

Creating a split-plot experiment in Minitab is easy—just choose the 2-level split-plot option under Stat > DOE > Factorial > Create Factorial Design to create a design with up to 3 hard-to-change factors.

After creating the design, running the experiment, and recording the measurements in Minitab, analyze the design as you would any other experiment in Minitab, with Stat > DOE > Factorial > Analyze Factorial Design.

## Why not randomize all factors in a designed experiment?

In an ideal world, we would randomize all factors in any experiment.  But randomizing all factors is simply not always practical.  Changing a variable for full randomization may be too costly, or take too much time, or may not be feasible.  Faced with these challenges, people use split-plot designs because they save time and money while collecting the same amount of data.

Consider the example of the bakery. With three variables (temperature, flour, and sugar), each with two levels (a low and a high setting), eight combinations of factors are possible. And if the bakery wants to do two replications of the experiment to get better estimates, then 16 cakes need to be baked in total.  The oven can fit four cakes at a time, but randomizing the temperature setting will restrict baking to as few as one cake at a time.  If each cake needs to bake for an hour, the experiment could take up to 16 hours, plus the time required for the oven to change temperature.

A completely randomized factorial
design requires oven temperature to

But what if we don’t randomize the temperature?  If we instead use a split-plot design, the flour and sugar amounts can still be varied for each cake with minimal adjustments to the hard-to-change oven temperature.

Using a split-plot design, multiple
cakes can be baked at the same time,
minimizing changes to oven temperature.

## Why use a split-plot design?

In a split-plot experiment, you hold levels of the hard-to-change factor constant for several experimental runs, which are collectively treated as a whole plot. You vary the easy-to-change factors over these runs, each combination of which makes a subplot within the whole plot.

Using a split plot design, the bakery can fix the oven temperature at 325 degrees F, and bake four cakes that use the four possible combinations of flour and sugar simultaneously. Then the bakery changes the oven to 375, and bakes four cakes using all four cake mix combinations again. Two replications of this experiment would take only four hours, plus the time to change the oven temperature—a tremendous savings in time and energy.

To evaluate the hard-to-change factor, think of each whole plot of the easy-to-change factor as a set of repeated measures for the given level of your hard-to-change factor. The average of these repeated measures produces one observation for the hard-to-change factor.  The hard-to-change factor is randomized across the whole plots, where each whole plot represents one experimental unit, or one opportunity to collect data at the given level of the hard-to-change factor.

So why is it called a “split-plot” design?  Split-plot designs were originally used in agriculture. The term “whole plot” referred to a large area of land, and subplots were smaller areas within each whole plot.

## Split-plot designs in practice

You can turn to split-plot designs when randomizing a variable would make an experiment cost too much, take too much time, or cause too much difficulty. Temperature is a common hard-to-change variable because heating and cooling often require significant time and expense. Other common hard-to-change variables include pressure settings and machinery that requires disassembly or recalibration to change settings.

Use split-plot designs to answer such questions as:

• Which hard-to-change factors have large effects on the response?
• Which easy-to-change factors have large effects on the response?
• Which interactions between hard-to-change and easy-to-change factors have large effects on the response?

For example, a split-plot design could be used to investigate:

• How humidity (hard-to-change) affects crop yield.
• How the amount of sugar (easy-to-change) affects taste test scores.
• How the interaction between temperature (hard-to-change) and processing time (easy-to-change) affects tensile strength.

## Minitab Makes Split-Plot Designs Easy

If you’re not already using the power of Minitab to get the maximum value from your data, download a free, fully-functional 30-day trial of Minitab Statistical Software today.

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