Finding significant parameters in factorial experiments

What is it about?

In design of experiments, normal probability plots are often used to determine which parameters are significant. Most of the results focus on the simple 2-level case, where the factors (variables of interest) only have 2 values (often denoted as +1 and −1). This paper focuses on creating appropriate normal probability plots for higher level experiments, where the factors can take additional levels. There exist two different approaches: using an orthogonal basis and using an orthonormal basis. It is shown that for properly constructing a normal probability plot to determine significant factors for higher level experiments it is necessary to use an orthonormal basis.

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Why is it important?

This paper generalises the commonly used 2-level normal probability plot to a general multilevel normal probability plots that can then be used to determine significant parameters for the given experiment.