Analyze Factorial Design

Two-Level Factorial Designs
Alias Structure - Confounding

  

In fractional designs, some of the effects are confounded with each other. That is, you cannot estimate all the effects separately. For example, if Factor A is confounded with the three-way interaction BCD, then the estimated effect for A also includes any effect that is caused by the BCD interaction. Effects that are confounded are said to be aliased. The alias structure describes the confounding that occurs in a design.

In some cases, effects are partially confounded. For example, in Plackett-Burman designs and when a covariate is in the model. The terms that are partially confounded, and how much the terms are partially confounded, depends on the terms that are in the model.

The Alias Structure table lists the factors and their names to clarify the abbreviations in the aliases.

Example Output

Aliases

 

I - 5.42 ABC + 28.92 ABD - 9.04 ACD - 10.85 BCD + 45.19 ABCD

A + 0.15 ABC - 0.77 ABD + 0.24 ACD + 0.29 BCD - 1.21 ABCD

B - 0.03 ABC + 0.19 ABD - 0.06 ACD - 0.07 BCD + 0.29 ABCD

C - 0.01 ABC + 0.03 ABD - 0.01 ACD - 0.01 BCD + 0.05 ABCD

D - 0.05 ABC + 0.25 ABD - 0.08 ACD - 0.09 BCD + 0.39 ABCD

AB + 0.04 ABC - 0.24 ABD + 0.07 ACD + 0.09 BCD - 0.37 ABCD

AC + 0.06 ABC - 0.32 ABD + 0.10 ACD + 0.12 BCD - 0.50 ABCD

AD - 0.09 ABC + 0.47 ABD - 0.15 ACD - 0.18 BCD + 0.74 ABCD

BC + 0.09 ABC - 0.47 ABD + 0.15 ACD + 0.18 BCD - 0.74 ABCD

BD + 0.02 ABC - 0.08 ABD + 0.03 ACD + 0.03 BCD - 0.13 ABCD

CD - 0.01 ABC + 0.07 ABD - 0.02 ACD - 0.03 BCD + 0.11 ABCD

Interpretation

For the insulation experiment, the design is a full factorial design. But partial confounding is present because the temperature when the manufacturer records the measurements is a covariate. When the measurement temperature is included in the model, all the effects are partially confounded to some degree. The confounded effects could represent the combined effect of different linearly dependent terms.

Larger coeffecients for partially confounded terms are of most concern. For example, the main effect for material is partially confounded with  the three-way interaction between material, injection pressure, and cooling temperature (ABD). If this three-way interaction exists, then the difference between materials could be different from the prediction of the model.

For the insulation data, if the measurement temperature is not in the model, the partial confounding is not present.