A psychologist is designing a study to evaluate three new treatments for a behaviorial problem in children. The psychologist will include a second factor, which will classify the subjects according to four levels of socioeconomic status. There are 30 children available for each level of socioeconomic level, which will provide 10 replications of each of the treatments by socioeconomic combinations. At the end of the treatment period, the children will be assessed and assigned a score reflecting the degree of improvement in their behavior. There are five trained evaluators who will assign the scores to the children. The psychologist knows from past studies that some evaluators tend to assign uniformly higher scores than other evaluators, and, hence, he wants to be able to control for the evaluator effect in the analysis of the treatment– socioeconomic status effect.
a. Display how you would randomly assign the children to the 12 treatment– socioeconomic status combinations.
b. Provide an analysis of variance table for this experiment.