An experiment is to be designed as a randomized complete block experiment with three blocks and a split-plot treatment assignment. Each block is divided into four units. Suppose the wholeplot treatment (A) has four levels and the split-plot treatment (B) has three levels with both factors having fixed levels. The researcher wants to have two replications of each level of factor B in each block.
a. Describe a method of randomizing the experimental units to the levels of factors A and B in this experiment.
b. Write a linear model for this experiment. Make sure to identify each of the terms in the model and list the range of values for all subscripts.
c. Construct an analysis of variance table for this experiment, including columns for sources of variation, degrees of freedom, and expected mean squares.