Incomplete factorial experiments in completely randomized and randomized complete block designs

The estimation of main and interaction effects is considered, when some treatment combinations are excluded from the experiment and one or more factorial contrasts can be assumed to be negligible. For equal treatment replication, it is shown that the increase in variance due to the exclusion of some treatment combinations depends on the degree of involvement of the effect of the excluded treatment combinations in the negligible factorial contrasts. Further, linear combinations of the set of negligible contrasts are identified which maximizes the precision of the estimators of the contrasts of interest.