Consider an experiment in which the treatments used are different in different blocks. In a conventional analysis, the sum of response measurements within the blocks give no information about the treatment effects since they are confounded with the block effect.
However if the block effects are assumed to be random variables instead of fixed constants, the block totals also provide information about the treatments. This chapter describes two types of experiment in which random block effects are used.
In some experiments, one or more factors cannot be varied at the level of the individual experimental units. If all units in a block get the same factor level, the factor would be confounded with blocks if the latter were treated as fixed effects, but with random block effects it is possible to estimate the factor effect. Such designs are called split plot designs.
In balanced incomplete block designs, the block totals provide a second estimate of the effects of each factor that is independent of the estimates that were described in the previous chapter. This is called inter-block analysis of balanced incomplete block designs. Combining the two estimates improves accuracy.