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About crossed factorial design, two factors A and B are crossed, if every level of A can occur in every level of B.
A full factorial/crossed experiment is an experiment whose experimental units take on all possible combinations of these levels across all such factors.
If I am correct about the above, are crossed factorial design and full factorial design the same concept?
(Crossed) factorial design is not always equal to Full factorial design.
In this context, the word "crossed" is a synonym of "factorial" (see here). Both indicates the presence of interactions between factors.
A factorial design can be either:
Therefore, a "factorial design" does not necessarily implies it is "fully crossed".
In the OP's case, where:
two factors A and B are crossed, if every level of A can occur in every level of B
It will be a full factorial design.
crossed factorial design is redundant, because crossed and factorial means the same thing, i.e., an experiment has factors w/ usually 2 levels/factor. E.g., factor A = I (levels: with irrigation, without irrigation), factor B = F (with fertilization, without fert.). A full factorial design has all possible combinations between factors and levels (in this case $2^2$ --> I+F, no_I+no_F, I+no_F, no_I+F). Yet, a factorial design can be fractional, where there are interactions, but not all possible ones.
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Jul 6, 2014 at 15:15