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During my study about experimental design, I detect from some examples that factorial design is a sub-step in an experimental design. However till now the idea seems not fully clear for me.

What is an experimental design? what is a factorial design? and how they differ?

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Mostly, experimental design is a large subject, which topic is the planification of experiments in general. Then factorial design is a sub-topic among many others within this large field.

For some authors, experimental design is about the plot layout, terminology coming from layout of experimental plots on land in agricultural experimentation. This will often include choice and construction of blocks.

Factorial design is then subtly different, it is about the layout of the various regressor variables, that is, how to combine/choose the possible values for the regressor variables. Literally, it is about how to construct the design matrix. The 'experimental design' then is about how to run this design matrix, for instance, how to do blocking, deciding the time sequencing of the runs (maybe by randomization) etc.

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