ABSTRACT
In this chapter we derive the analysis of three classes of designs under the models presented in Chapter 3: completely randomized designs, randomized complete block designs, and randomized Latin square designs. All of these are examples of orthogonal designs that can be analyzed in a straightforward manner. Under a completely randomized design, the precision of the estimates of treatment contrasts depends on the overall variability of the experimental units. Under a randomized block design, the overall variability is decomposed into between-block variability and within-block variability; we say that there are two strata (two error terms or two sources of error). If each treatment appears the same number of times in each block, then the precision of the estimates of treatment contrasts depends only on the within-block variability. Similarly, under a randomized row-column design there are three strata corresponding to between-row variability, between-column variability, and between-unit variability adjusted for the between-row variability and between-column variability. If each treatment appears the same number of times in each row and the same number of times in each column, then the precision of the estimates of treatment contrasts depends only on the adjusted between-unit variability.
