STA 402S98 Assignment 5: Quiz in tutorial Feb. 27th

Skip Chapter 18. Read Chapter 19; you are not responsible for the material of section 19.5, because it is just regression stuff you have seen in STA 302. We will not pool sums of squares as described in Section 19.8

Do problems 19.4, 19.7, 19.8, 19.29, 19.30 and 19.32. Also,

1. For a general a by b design, prove that there are no main effects for A if and only if all the marginal means for A are equal.

2. For a 2 by 2 design, prove that

• There are no interactions if and only if the effect of A does not depend on the value of B.
• There are no interactions if and only if the effect of B does not depend on the value of A.

3. For the design of Problem 19.14, make up a table showing how you would set up Factor Effects dummy variable coding, including the interactions. Your table should have 9 rows and 8 columns. Now make a 9th column, showing E(Y) for each row. This column should not have any "X" symbols, because the numerical values of the dummy variables and their products are completely known for each treatment combination. Notice that I am not asking you to do Problem 19.14; just use the example so you know the values of a and b.

4. Now continue the problem above by making a 3 x 3 table corresponding to the design of Problem 19.14. In each cell, write E(Y) using the notation of your regression model. Write the marginal means and total mean around the edges.

5. Still continuing the problem above, write the C and ß matrices for the following null hypotheses (H0: Cß=0):

• No main effects for Factor A.
• No main effects for Factor B.
• No A by B interaction effects.

Please note that problems 3 through 5 above are very typical of my test and exam questions. Questions 1 and 2 are good possibilities too.