Interpret the key results for Create 2-Level Split-Plot Design

Complete the following steps to examine the properties of the design. Key outputs include the design summary and the alias structure.

Step 1: Examine the design properties

Use the summary of the design to examine key design properties. Most properties of the design match selections that you made for the base design. Whole-plot replicates and subplot replicates increase the number of runs in the design.

Design Summary Factors: 4 Whole plots: 4 Hard-to-change: 1 Runs per whole plot: 8 Runs: 32 Whole-plot replicates: 2 Blocks: 1 Subplot replicates: 1
Key output: Design summary

In these results, 16 runs form a full factorial design among the 4 factors in the design. Two whole-plot replicates doubles the number of runs in the design to 32 runs.

Step 2: Examine the alias structure

The alias structure describes the confounding pattern that occurs in a design. Terms that are confounded are also said to be aliased.

Aliasing, also known as confounding, occurs in fractional factorial designs because the design does not include all of the combinations of factor levels. For example, if factor A is confounded with the 3-way interaction BCD, then the estimated effect for A is the sum of the effect of A and the effect of BCD. You cannot determine whether a significant effect is because of A, because of BCD, or because of a combination of both. When you analyze the design in Minitab, you can include confounded terms in the model. Minitab removes the terms that are listed later in the terms list. However, certain terms are always fit first. For example, if you include blocks in the model, Minitab retains the block terms and removes any terms that are aliased with blocks.

You can use the alias structure to verify that important terms are not aliased with each other. If the alias structure is unacceptable, consider taking one of the following actions:
  • Create the design again, but enter the factors into Minitab in a different order.
  • Use a larger fraction of the design.

To see how to determine the alias structure, go to All statistics for Create 2-Level Split-Plot Design and click "Defining relation".

Key Results: Alias structure

Use the alias structure to verify that important terms are not aliased with each other. For example, researchers at an agricultural station want to learn about controlling the growth of a weed without the use of an herbicide. The researchers design an experiment to study the effect of these 5 factors:
  • A: Type of habitat
  • B: Introduction of competing plants
  • C: Use of molluscicide
  • D: Fencing
  • E: Use of insecticide
Because the researchers have limited space and creating a particular habitat is time-consuming, the researchers design a split-plot fractional factorial experiment so that the habitat is held constant while the other factors vary. The researchers agree that the interaction between fencing (D) and the introduction of competing plants (E) is likely to be important.

The alias table shows that the interaction between factors D and E is aliased with whole plots (A). Because DE is aliased with A, the researchers cannot separate the interaction between fencing and the introduction of competing plants from the effect of habitat. Using the alias table, the engineer sees that the following 2-way interactions are not aliased with whole plots, 2-way interactions, or 3-way interactions: AD, BD, CD. By changing the order that the researchers enter the factors in Minitab, the engineer can create a design where the interaction between fencing and the introduction of competing plants is independent of any effects, except for a 4-way interaction. The engineer recreates the design and changes the order of use of insecticide and introduction of competing plants so that the interaction between fencing and introduction of competing plants is BD, not DE.

Fractional Factorial Split-Plot Design

Design Summary Factors: 5 Whole plots: 4 Resolution: IV Hard-to-change: 1 Runs per whole plot: 4 Fraction: 1/2 Runs: 16 Whole-plot replicates: 1 Blocks: 1 Subplot replicates: 1

Design Generators: E = ABC

Hard-to-change factors: A

Whole Plot Generators: A, DE

Whole plots are confounded with the following terms: DE, ADE, BCD, ABCD

Alias Structure I + ABCE A + BCE B + ACE C + ABE D + ABCDE E + ABC AB + CE AC + BE AD + BCDE AE + BC BD + ACDE CD + ABDE ABD + CDE ACD + BDE
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