Conceptual problems: Chapter 13: 2, 3, 4, 5, 6, 7, 10.
Chapter 14: 1, 2, 4.

Computational problems:
1) Chapter 13: 16 (Zinc data) The experiment is described in chapter 10, problem 14. The data in zinc.txt are slightly changed from what is given in the book.
a) the book's part a, as written
b) the book's part b, as written. Provide the ANOVA table and estimates of the marginal means (= lsmeans) for each level of the zinc factor and each level of the copper factor.
c) new part. Use a contrast to examine the linear effect of copper on protein.
(Hint: this will be a linear contrast between copper marginal means, with coefficients given by the copper level for that group - average of the five levels of copper).
d) Explain why the conclusions from the 4 df ANOVA test of copper and the 1 df contrast for the linear effect of copper are so different.

2) Chapter 13: 17 (Iridium data)
Note: the description in the book is longer than my questions and your answer. Do not treat this as a data problem. Do not worry about transforming the responses. Just do the following:
a) Use 2 way ANOVA to test whether there is evidence of an interaction.
b) Plot residuals vs predicted values. Is there anything to be concerned about?
c) Does the iridium concentration change with depth (or do all depths have the same mean iridium concentration)?
d) Use the appropriate multiple comparisons procedure to evaluate all pairwise differences between depths. Which depths are different from which others?

3) The data in range.txt come from a study of fertilizer effects on a particular pasture grass. The experiment was a randomized complete block design (RCBD) with 5 blocks and 5 treatments. The five treatments are given letters in the data file; there is also a short name. A: No fertilizer, B: 50 lb. Nitrogen, C: 100 lb Nitrogen, D: 50 lb Nitrogen + 75 lb P2O5, E: 100 lb nitrogen + 75 lb P2O5. Both Nitrogen and P205 are fertilizers. The response is the percent phosphorus in a plant tissue sample from each plot. All responses have been multiplied by 100 for convenience.

Note: Remember to include an additive effect of blocks in your model(s) for all parts except e.

a) Test the null hypothesis that the five treatments have the same mean. Report the F statistic and the p-value.
b) The data file includes an Ntrt variable with 0, L(ow), or H(igh) representing the amount of N and a Ptrt variable, with the 0 or H(igh) representing the amount of P added to the plot. Consider the treatment design for this study as a 2 way factorial. Is this is complete factorial treatment design? Explain why or why not.
c) Attempt to analyze the study as a two way factorial treatment design by fitting an ANOVA model with blocks, Ntrt, Ptrt, and the Ntrt*Ptrt interactions. Attempt to estimate the marginal means (LSMEANS) for each level of Ntrt and Ptrt. What is curious about the df in the ANOVA table? Can you estimate all 3 marginal means for Ntrt? Explain why the marginal mean for Ntrt = L can be estimated but the marginal mean for Ntrt = 0 can not.
d) The investigators are especially interested two contrasts:
1) the average effect of fertilizer, i.e. the difference between No fertilizer and the average of the four other treatments.
2) the average effect of P2O5, i.e. the difference between the average of the two treatments with P2O5 and the average of the two N only treatments.
Please estimate the value of each contrast. Report the estimate, its s.e., and the p-value for a test of that contrast = 0.
Hint: Ignore the 'almost' 2 way treatment structure, consider the study as involving 5 treatments, use 1 way ANOVA, then write the appropriate linear contrasts. This is probably most easily done using the letters (A,B,C,D,E) to define the groups. The treatment names get arranged in a curious order.
e) Calculate the s.e. of a treatment mean if blocks are ignored.
Hint: easiest way is to rerun proc glm without block in the model.
f) Are blocks a good idea for experiments conducted on this pasture?