I have results of the experiments designed as you can see below (or in the attached file). What is your suggestion for analysis of such designed experiments? Actually my problem is with center points which were run separately and in different days otherwise the main experiments could be treated as split-plot design by taking A and B as hard-to-change factors.
Please note that:
- doing complementary experiments is impossible.
- Finding the significance of curvature is important.
- Estimating the effect of main factors and their 2nd order interactions is necessary.
A B C D
------------------------------------1st day
0 0 0 0
------------------------------------2nd day
-1 1 1 1
-1 1 1 -1
-1 1 -1 1
-1 1 -1 -1
------------------------------------3rd day
-1 -1 -1 -1
-1 -1 -1 1
-1 -1 1 -1
-1 -1 1 1
------------------------------------4th day
0 0 0 0
------------------------------------5th day
0 0 0 0
----------------------------------- 6th day
1 -1 -1 -1
1 -1 -1 1
1 -1 1 -1
1 -1 1 1
------------------------------------ 7th day
1 1 1 1
1 1 1 -1
1 1 -1 1
1 1 -1 -1
-------------------------------------8th day
0 0 0 0
-------------------------------------9th day
0 0 0 0
You can still analyze the experiments as a split-plot design (using the approach I gave in my paper). The problem is that because the design is not balanced, the test statistics will not have known distributions under the null hypothesis, i.e., the degrees of freedom at the subplot level are complicated.. You could use simulation to estimate the null distribution of the test statistics, and then compare the observed values of the test statistics from the experiments to this simulated distribution. You could also approximate the subplot degrees of freedom using the method of Kenward and Roger. Do you have your response data? I have another idea for analyzing unbalanced split-plot designs that I have been working on more recently. If you like, I can apply this to your data and see what results we find.
With you data, as presented, you cannot find quadratic effects. By running the center points by themselves, they are not of much help. I would skip them and analyze the rest of the data as a split plot.
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