Create 2-Level Split-Plot Design

A split-plot design is a designed experiment that includes at least one hard-to-change factor that is difficult to completely randomize because of time or cost constraints. In a split-plot experiment, levels of the hard-to-change factor are held constant for several experimental runs, which are collectively treated as a whole plot. The easy-to-change factors are varied during these runs, each combination of which is considered a sub-plot within the whole plot. You should randomize the order in which you run both the whole plots and the sub-plots within whole plots.

Example of a split-plot design

A large-scale bakery is designing a new brownie recipe. They are experimenting with two levels of chocolate and sugar using two different baking temperatures. However, to save time they decide to bake more than one tray of brownies at the same time instead of baking each tray individually. The brownie example includes 2 whole plots replicated twice (total of 4 whole plots). Each whole plot contains 4 sub-plots. The whole plot is all the trays of brownies being baked at the temperature. The sub-plots are each individual tray of brownies.

Table 1. Whole Plot 1: Baked at temperature 1. The whole plot is all the trays of brownies being baked at the first temperature. The sub-plots are each individual tray of brownies.
Tray 1 (Chocolate 1, Sugar 1)	Tray 2 (Chocolate 1, Sugar 2)	Tray 3 (Chocolate 2, Sugar 1)	Tray 4 (Chocolate 2, Sugar 2)

Table 2. Whole Plot 2: Baked at temperature 1. This is a replicate of the first whole plot.
Tray 1 (Chocolate 1, Sugar 1)	Tray 2 (Chocolate 1, Sugar 2)	Tray 3 (Chocolate 2, Sugar 1)	Tray 4 (Chocolate 2, Sugar 2)

Table 3. Whole Plot 3: Baked at temperature 2. The whole plot is all the trays of brownies being baked at the second temperature. The sub-plots are each individual tray of brownies.
Tray 1 (Chocolate 1, Sugar 1)	Tray 2 (Chocolate 1, Sugar 2)	Tray 3 (Chocolate 2, Sugar 1)	Tray 4 (Chocolate 2, Sugar 2)

Table 4. Whole Plot 4: Baked at temperature 2. This is a replicate of the third whole plot.
Tray 1 (Chocolate 1, Sugar 1)	Tray 2 (Chocolate 1, Sugar 2)	Tray 3 (Chocolate 2, Sugar 1)	Tray 4 (Chocolate 2, Sugar 2)

Split-plot designs were originally used in agriculture where the whole plots referred to a large area of land and the sub-plots were smaller areas within each whole plot.

Perform the analysis

Complete the following steps to specify the design.

Enter the name of your response variable

The worksheet includes a column with this name where you enter the data from the experiment.

Table of factors

For a design with more than 2 factors, specify whether each factor is hard-to-change or easy-to-change.

Under Name, enter a descriptive name for each factor.

For any continuous factors, enter numbers. Enter the lower number for the study in the Low column. For example, to study the temperatures 30 and 40, enter 30 in the Low column and 40 in the High column.

For any categorical factors, enter labels for the levels. Labels can be numbers or text. If you have a text factor and the levels have no natural order, you can specify the levels in any order.

Replicates

Number of replicates of the hard-to-change factor: Select the number of times to replicate the base design. Replicates are multiple experimental runs with the same factor settings (levels). So that the statistical significance of the hard-to-change factor is possible to calculate, the value is at least 2. Usually, you consider the available resources and the purpose of your design when you select the number of replicates. You can add replicates of the hard-to-change factors after you store the design in the worksheet with Stat > DOE > Modify Design.
Number of replicates of the easy-to-change factor: Select how many times to repeat the runs with the same settings for the easy-to-change factors within each whole plot. For example, if the base design has 2 runs per whole plot and you select 2 subplot replicates, then each whole plot has 4 runs. Usually, you consider the available resources and the purpose of your design when you select the number of replicates.

Example

Researchers at a plastics manufacturer want to increase the strength of a plastic. The researchers identify additive percentage, agitation rate, and processing time as the possible factors that affect strength. The temperature at which the plastic bakes also affects strength. To run a completely randomized 4-factor design requires that the researchers bake each combination of the within-batch factor levels individually at one of the two temperature settings. Because the process takes too long, the researchers decide to use a split-plot design. The researchers plan to bake all 8 combinations of additive percent, agitation rate, and processing time at one temperature, and then bake all 8 combinations at the second temperature. They replicate this process so that they use each temperature setting twice.

Choose Stat > DOE > Quick Designs.
Select Select a Four-Factor Design.
Select Create an experiment with two or more continuous factors. Select OK.
Select Estimate main and interaction effects when some factors are hard to change. Select OK.
In the new dialog, in Enter the name of your response variable, enter Strength.

Complete the table with the following settings:

Changes	Name	Type	Low	High
Hard to change	Temperature	Continuous	350	550
Easy to change	Additive percentage	Continuous	2	5
Easy to change	Agitation rate	Continuous	100	200
Easy to change	Processing time	Continuous	10	40

In Number of replicates of the hard-to-change factor, select 2.
In Number of replicates of the easy-to-change factor, select None. Select OK.

The design summary table shows that the design has 32 base runs, which includes 8 runs per whole plot. The worksheet contains the 32 runs in run order. The runs for temperature within a replicate are together so that all the combinations of the randomized, easy-to-change factors are complete before the temperature changes.