STA442/1008 Assignment 8

Quiz in Tutorial on Friday Nov 18th

This assignment is based on Chapter 5 of the class notes (the first part, say Pages 1-27, except you are not responsible for the multiple comparison tests) and associated lecture material. You will do the job described below, and bring your log file and your list file to the quiz. As usual, answers to the questions are not to be handed in. They are just practice for the quiz.

I know this is pretty gruesome, but the data are real -- from the U of T School of Dentistry.

An experiment in dentistry seeks to test the effectiveness of a drug (HEBP) that is supposed to help dental implants become more firmly attached to the jaw bone. This is an initial test on animals. False teeth were implanted into the leg bones of rabbits, and the rabbits were randomly assigned to receive either the drug or a saline solution (placebo). Technicians administering the drug were blind to experimental condition.

Rabbits were also randomly assigned to be "sacrificed" after either 3, 6, 9 or 12 days. At that time, the implants were pulled out of the bone by a machine that measures force in newtons and stiffness in newtons/mm. For both of these measurements, higher values indicate more healing. A measure of "pre-load stiffness" in newtons/mm is also available for each animal. This may be another indicator of how firmly the false tooth was implanted into the bone, but it might even be a covariate. Nobody can seem to remember what "preload" means, so we'll ignore this variable for now.

The data are available in the file bunnies.dat. The variables are

  1. Identification code
  2. Time (3,6,9,12 days of healing)
  3. Drug (1=HEBP, 0=saline solution)
  4. Stiffness in newtons/mm
  5. Force in newtons
  6. Preload stiffness in newtons/mm

Please do the following.

  1. Use proc freq to find out how many rabbits are in each experimental condition.
  2. Using proc glm, conduct a univariate two-way ANOVA, with force as the dependent variable. Use the means statement to get cell means and marginal means. Be prepared to answer the following questions about each of the significance tests that SAS produces by default (I count 4 default tests).
    1. What is the value of the test statistic? The answer is a number.
    2. What is the p-value? The answer is a number.
    3. Is the result statistically significant at the 0.05 level? Yes or No.
    4. What, if anything, do you conclude? This is not the place for statistical jargon. "What do you conclude" means say something about the drug, healing, time -- something like that.
  3. I know this is a bit redundant with the preceding item, but did the drug work? If the results justify an answer, then answer Yes or No.
  4. Now, make a table showing a dummy coding scheme with no intercept and 8 indicator dummy variables, one for each treatment combination. Give E[Y] for each treament combination. This is the full model.
  5. Consider a reduced model for testing the main effect of Drug. What restriction is placed on the parameters of the full model?
  6. Consider a reduced model for testing the main effect of Time. What restriction is placed on the parameters of the full model?
  7. Consider a reduced model for testing the Drug by Time interaction. What restriction is placed on the parameters of the full model? There is more than one natural (and correct) way to write the answer, but all correct answers will be algebraically equivalent.
  8. Now please return to SAS. Make the 8 indicator dummy variables, and fit a regression model with no intercept using proc reg. Conduct tests to answer the following questions. Just do regular one-at-a-time (custom) tests. Don't bother with any Bonferroni correction this time. Just consider one dependent variable: Force. As usual, we are guided by the alpha = 0.05 significnce level.
    1. Are the marginal means different at 3 and 6 days?
    2. Are the marginal means different at 6 and 9 days?
    3. Are the marginal means different at 9 and 12 days?
    4. Is there a difference between Drug and Placebo just at 3 days?
    5. Is there a difference between Drug and Placebo just at 6 days?
    6. Is there a difference between Drug and Placebo just at 9 days?
    7. Is there a difference between Drug and Placebo just at 12 days?
    As usual, be able to answer questions like these for each test:
    1. What is the value of the test statistic? The answer is a number.
    2. What is the p-value? The answer is a number.
    3. Is the result statistically significant at the 0.05 level? Yes or No.
    4. What, if anything, do you conclude? This is not the place for statistical jargon. "What do you conclude" means say something about the drug, healing, time -- something like that.