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Screening Replicated factorial DOE - Half normal plot - null space terms?

I create a 2x2 full factorial DOE, with 1 replication. Sorting my data from right to left, my responses are 10, 11, 20, 19, 30, 28, 37, 40.

I run the screening script and a half normal plot is created - so far so good. But there are 7 points in the half normal plot, but just 3 effects (2 x main effects and 1 x 2 factor interaction). One of the null terms 'Null7' is even highlighted as significant.

Finally, a Lenth PSE is quoted.

The Stat and Graph guide for the Screening analysis says "The process continues until n effects are obtained, where n is the number of rows in the data table, thus fully saturating the model. If complete saturation is not possible with the factors, JMP generates random orthogonalized effects to absorb the rest of the variation. They are labeled Null n where n is a number. This situation occurs, for example, if there are exact replicate rows in the design."

My questions:

1. Why do it this way? I have no idea if this is the most statistically correct approach to analyse a replicated factorial design, but it is confusing to say the least to see extra null terms in the half normal plot, where I expect just to see main effects and interactions. I have not seen this in text books nor in Minitab.

2. Lenth's procedure, I thought, was a method to analysed UNREPLICATED data, where no degrees of freedom for the error term existed. In Minitab, for example, Lenth's method is used (and a PSE quoted) when the design is unreplicated only.

Any comments appreciated (I would love to learn that I'm doing replicated DOEs incorrectly on JMP).
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Staff (Retired)

Re: Screening Replicated factorial DOE - Half normal plot - null space terms?

Feels like you set it up correctly. I would just run the Fit Model script which should give you the main effects and two-way interaction terms. If the default model has not been scripted to the data table then I would add the terms to the Fit Model dialog box accordingly. When I do that with your data I get an R square value of 0.991 and an adj. R square of 0.985. Also the Anova gives me a p-value of 0.0001. X2 is your biggest driver followed by X1. There does not seem to be any interaction.
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