1. I have run a full factorial design involving two discrete variables, A at 4 levels,and B at 5 levels. I have replicated the design once, i.e., I have two runs for each combination of these two variables. Further, I blocked the design by replicate; that is I ran the first replicate in Block 1, and the second replicate in Block 2. I randomized the order of runs within each block.

a. Write down the ANOVA table - just sources of variation and the associated degrees of freedom. Explain your answer.

b. Assume we did have the data, and could calculate the sums of squares, mean squares, and F ratios. Conceptually, what pattern would I expect to see in the set of mean squares if the null hypotheses concerning A, B, & their interaction were all true? That is, how would you expect these mean squares to compare to one another? Why?

c. What pattern would I expect to see in the set of mean squares if the null hypotheses concerning A, B, & their interaction were all false? Why?

d. What does the mean square error represent? Please be specific in your answer; for example, do not say "variation" - this is too general.

e. Suppose the null hypotheses about A, B, AB, etc. are false. How might this affect the mean square error? Please explain your answer.