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Suppose I am running a $2^2$ factorial design in two blocks. Denote the factors as A and B and the four treatment combinations as $(1), a, b$ and $ab$. Consider the blocking arrangement:
------------------- | Block1 | Block2 | |---------|--------| | (1) | a | | ab | b |
Now usually we assume that within each block, the treatment combinations are randomly assigned. However, suppose I impose the restriction that instead, within each block, the treatment combinations must be assigned in the order as above (e.g. in Block 1, assign $(1)$ first, then $ab$. Similarly for Block 2). How can this design be analyzed? Does some kind of Order factor need to be considered?

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