Regarding the 2^k-p fractional factorial designs (n= 4, 8, 16, 32, etc) & Plackett-Burman designs that are not a power of 2 (eg, n= 12, 20, 24, etc).
a. What are the similarities between these two types of designs especially regarding their balance and orthogonality properties?
b. What is the main difference between these two types of designs especially regarding 2 factor interactions?
I know the following:
2k-p fractional factorial design is only useful if we can be assured that the 2-way interactions are not important. If this is the case then we will find Resolution III designs to be very useful and efficient.
Plackett-Burman designs exist for N = 12, 20, 24, 28, 36, 40, 44, 48, ...... any number which is divisible by four. These designs are similar to Resolution III designs, meaning we can estimate main effects clear of other main effects. Main effects are clear of each other but they are confounded with other higher interactions.
When we have a 2k-p design, we have an alias structure that confounds some factors with other factors.
Plackett-Burman designs have partial confounding, not complete confounding, with the 2-way and 3-way and higher interactions. Although they have this property that some effects are orthogonal they do not have the same structure allowing complete or orthogonal correlation with the other two way and higher order interactions.
Any advice will be greatly appreciated.
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