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Our World Statistics Day conversations have been a great reminder of how much statistics can inform our lives. Do you have an example of how statistics has made a difference in your life? Share your story with the Community!
In one sense, what you may be describing is the process of sequential experimentation as a guiding principle to problem solving. If so, there is much in the literature on this process. I suggest reading the first few chapters of Box, Hunter and Hunter "Statistics for Experimenters" as a starting place. In a very real sense, all practitioners of sequential experimental design as a process always leverage earlier experimentation with subsequent experimentation. No quarrel at all with this method. All up all in my experience is it's the most efficient problem solving process for DOE centric investigations.
If what you are really after is merging two or more experimental designs into one Mother of All Experiments and then analyzing, this method is fraught with many many pitfalls and watch outs. Not the least of which could be inconsistent hypotheses, experimental goals, and objectives for each of the ingredient experiments...with the hypothesis, goals and objectives of the 'Mother' inspired investigation. So above and beyond maybe using the 'Mother' experiment for exploratory data analysis I'd be leery of much beyond that.
I don't have 2 cents to add to @P_Bartell 's great post, but here's a penny. I am a proponent of the sequential DOE strategy. In fact, I think it is ridiculous to think that in your first experiment you will have chosen all of the most important factors, tested them at optimal levels and over appropriate noise (inference). It is more efficient and I think long-term effective to PLAN on sequential work (this goes for sampling as well). The first design you design is to help design a better experiment! Consider what you think you learned from those previous experiments (how did those increase your understanding of the phenomena?), but realize those experiments may have been executed in entirely different inference space.