TABLE OF CONTENTS In the discussion of factorial and nested experiments it was assumed that the whole experiment was performed in a completely randomized manner. In practice, however, it may not be feasible to have the entire experiment run several times in one day, or run by one experimenter, and so forth. It then becomes necessary to abandon the idea of complete randomization and block the experiment in the same manner used for the single-factor experiment in Chapter 4. Instead of running several replications of the experiment all at one time, it may be possible to run one complete replication on one day, a second complete replication on another day, a third replication on a third day, and so on. In this case each replication is a block, and the design is a randomized block design with a complete factorial or nested experiment randomized within each block.
Occasionally a second restriction on randomization is necessary, in which case a Latin square design might be used, with the treatments in the square representing a complete factorial or nested experiment.
Just as the factorial arrangements were extracted from the treatment effect in Equations (5.1) and (5.2), so can these arrangements be extracted from the treatment effect in the randomized complete block design of Chapter 4 (Section 4.2). For the completely randomized design, you will recall that
can be subdivided into
where A i + B j + AB ij = ? ij
