I have a 2 X 3 (levels of each factor) factorial experiment. This is about timings and levels of fertilization in corn. I also have a common check or control (no N added) between factors. How to include this check or control in the ANOVA?
If I was running a similar experiment, I would run an Optimal Factorial Design or an Optimal Response Surface design. I would set my levels on the fertilizer to 4 equally spaced values, say 0, 1, 2, 3 and the timing of the fertilizer the same way. I will have a combination that consists of zero fertilizer and a couple pairs of timings. These would be the "controls". If you split up your design, you end up losing the ability to interactions among your variables. The zero fertilizer plots should be added to your analysis as (fertilizer = 0, time = t1, t2, t3, etc.)
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