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 16 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 16 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
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
factorialdesign requires oven temperature tobe adjusted
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,
multiplecakes can be baked at the same time,minimizing changes to oven
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.
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:
For example, a split-plot design could be used to investigate:
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