By identifying important sources of individual differences before the start of the experiment, we can select a homogeneous group of subjects to serve in the study. In doing so, we are reducing the within groups variance by restricting the variation due to a particular subject characteristic that would otherwise be unchecked in an SRD approach. The RBD includes groups of homogeneous subjects drawn from two or more ability levels. In addition, in the RBD, we can evaluate the presence of an interaction between the treatments and the subject characteristic that formed the basis for subject selection. If the Treatment x Blocks interaction is significant, then we will know that the effects of the treatments do not generalize across the abilities or classifications of subjects represented in the experiment. If the interaction is not significant, then we have achieved a certain degree of generalizability of the results.

The removal of this Treatments x Blocks interaction from the error term makes the error term smaller than the analogous error term in the SRD. The RBD error term also reflects the variability of subjects from populations in which variation in the blocking factor is greatly restricted. It should be noted that the degree to which blocking results in a reduction of the error term depends on the magnitude of the correlation between the scores forming the basis of the blocking and the scores on the DV. If the blocking factor is not highly correlated with the DV, we may actually lose power since we will have just as heterogeneous a population as in the SRD and we are needlessly giving up degrees of freedom to account for the blocking factor. Feldt (1958) says to use the unblocked design (SRD) when the correlation between the blocking factor and the DV is less than .2. But if the assessment of the Treatments by Blocks interaction is the primary purpose of the study, then a low correlation will not affect the decision to use RBD. Overall, the reduced error term makes the RBD more powerful than the SRD, but not quite as powerful as the RMD.

In the RBD, subjects are matched or blocked on a third variable that is related to the DV. Usually the 3^rd variable, or blocking variable, is a state variable which subjects either have or do not have (i.e. anxiety, IQ, gender, SES). In the RBD, we have a groups that are fixed and b fixed levels of the blocking factor. Within each Treatment by Block cell there are n subjects. Thus, N = (a)(b)(n).

Example: Age may be a factor in problem solving ability so we block on age. T1 involved an anagram task, T2 involved word problems, and T3 involved numerical problem solving.

This test, then, runs using several assumptions:

1. DV is interval and N.D.
2. Homogeneity of variance.
3. Blocking variable is related to the DV.

An important note: The RBD is what is essentially called a factorial design. Indeed, the calculation and interpretation of each are virtually identical.