STA442/1008 Assignment 5

Quiz in tutorial on Friday Feb. 29th

Note: This assignment was revised Feb. 3d to include multiple comparisons.

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.data. 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 the significance tests produced by default (I count 4; my overall F = 5.23).
   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. Based just on the one-at-a-time tests (no multiple comparisons yet), do you think this drug shows promise for clinical use in humans? Please answer Yes or No and briefly explain.
4. Now, go back to your data step and make a single independent variable consisting of all combinations of time and drug. Using contrast statements in proc glm, conduct tests to answer the following questions. Start by just doing regular one-at-a-time tests. You'll employ a Scheffé correction later. Just consider one dependent variable: Force. As usual, we are guided by the α = 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?
   8. Is there a difference between Drug and Placebo at any time period? Under this reduced model, there is no difference between Drug and Placebo at 3 days, none at 6 days, none at 9 days, and none at 12 days. (Your contrast matrix will have four rows. Just a comment: Notice how this reduced model is even more reduced than the one for testing the main effect of drug, because no main effect just specifies the marginal (average) means equal.
5. Now consider all the sets of contrasts you've tested (including the standard tests for main effects and interactions) as followups to the initial, overall F test. Produce a table of Scheffé critical values, and answer the questions above again, with reference to the Scheffé tests this time. How do your conclusions change? Would your recommendation change about trying the drug with humans?