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I went through a "design of experiment" course recently, but there are still things that I haven't sorted out yet regarding which types of experiment to choose when facing a real world problem.

I understand that experiments can be costly, so one may be inclined to use a fractional design over a full factorial design (Taguchi, Box-Benkhen) for instance. But are there general guidelines to which types of design to choose ? Is cost the only issue ?

I come across many theoretical designs through books, but I can't grasp why some types of experimental designs are used instead of others. I am probably lacking something here, so if anyone can help me sort this out it will be deeply appreciated.

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    $\begingroup$ Typically, the penalty for the reduced numbers of observations in fractional factorial designs is the inability to test for certain interactions or reduced power in testing interactions. $\endgroup$ – BruceET Mar 11 '19 at 19:54
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It depends on what you want to do. Without knowing the specifics of what you want to investigate (or if you want compare two specific types of experimental design and the merits of each for a particular process / application), it's difficult to give a precise answer.

At a broad level, Box Hunter and Hunter define three types of experimental investigations:

  1. screening studies. These tell you which of a large number of variables affects the response.

  2. empirical studies. Produces an empirical model showing how the variables affect the response. You don't know the true nature of the response function, f.

  3. mechanistic studies. Produces a model that leads to the correct functional form of the response f, and enables you to explain why the response is the way it is.

The same authors also advise not worrying too much about your first experimental design, as once the first part of the experiment has been completed you will know more about the process, so you can plan a better second experiment, and then plan a better third experiment and so on, in an iterative process.

Box, G.E., Hunter, W.G. and Hunter, J.S., 1978. Statistics for experimenters.

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