I wanted to design an experiment to screen 18 factors against one response. I now understand that there are more modern, better designs to solve this problem, but at the time I used a 20-run Plackett-Burman design. I completed each run in duplicate, for 40 runs in total. I am attaching a .csv of the anonymised results, where I have standardised the factor levels (subtracted mean and divided by standard deviation).
I understand that because Plackett-Burman is a saturated design, I can't try to fit a linear model because the number of terms means it is almost certain to be overfit, so I should use 'two-level screening' (although maybe this changes because I have duplicates?) . I used this option, adding all 18 factors A-R as Xs and the response as Y. Screenshot of results below:
I expected A,M and D especially to have an effect, but I would find it quite surprising if F and K, were to have significant effects. Therefore I thought I would check here if I am interpreting these results properly. I'm especially confused with the fact that JMP adds 'Null' terms as part of the two-level screening. This page in the documentation describes the rationale:
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. For example, this situation occurs if there are exact replicate rows in the design.
I do have replicate rows in the design, but when I look at the plot above it seems to me that factors A and M are separate from the other factors, and that factors other than A and M only look significant because of the null terms being added.
Why would I question these results, apart from that it would be surprising if certain factors have effects? From the JMP documentation: "The analysis of screening designs depends on the principle of effect sparsity, where most of the variation in the response is explained by a small number of effects". I'm wondering if this is being broken here, if this many factors are coming out as significant?
Many thanks in advance for any help.
I'm using JMP Pro 17.0.0