STA305s14 Computer Assignment Six
Quiz in lecture on Monday March 24th

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.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. Using proc glm, conduct a two-factor ANOVA, with force as the dependent variable. Use the means statement to get cell means and marginal means. You should also be able to tell how many rabbits were in each experimental condition. 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 from your printout.
    2. What is the p-value? The answer is a number from your printout.
    3. Do you reject the null hypothesis 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.
  2. Now, make a table with a row for each treatment combination. Give the coefficients of the constrast or contrasts that would be used to test for
    1. The main effect of Drug
    2. The main effect(s) of Time
    3. The Drug by Time interaction.
  3. Make another table with a row for each treatment combination. Make columns showing the dummy variables for effect coding.
  4. Give E[Y|X=x] for a regression model with both main effects and the interaction. Use your variable names from the preceding question.
  5. In terms of the β values of your regression model, give the null hypothesis you would test in order to answer each of the following questions.
    1. Averaging across time periods, is there a differnece between the drug and placebo in mean force required to extract the tooth?
    2. Averaging across drug and placebo, is does elapsed time affect the mean force required to extract the tooth?
    3. Does the effect of the drug depend upon elapsed time?
  6. Now please return to SAS. Using either proc glm or proc reg (do it the way you find easiest), conduct tests to answer the following questions. Just do regular one-at-a-time tests. Don't bother with any Bonferroni or Scheffé correction yet. Just consider one dependent variable: Force. As usual, we are guided by the α = 0.05 significance level.
    1. Are the marginal means for time different at 3 and 6 days?
    2. Are the marginal means for time different at 6 and 9 days?
    3. Are the marginal means for time 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 day? This is a combination of the last four tests.
    Be able to answer questions like these for each test:
  7. It would be possible to treat all the tests you've done as Scheffé follow-ups to the first test on the printout -- the test for equality of the eight treatment means. But if you think carefully about it, that's wasteful (almost nothing is significant). The only reason for doing this experiment was to see the effect of the HEBP drug, and the only reason for including time as a factor was to discover the way that time affected the drug's effectiveness. The null hypotheses says there is no effect of drug at any time, which is the same as saying the drug had no effect at all. So, a good initial test would be the test for the drug's effect at any time period; that's the four-degree-of-freedom test.

    Using this as the initial test, use proc iml to obtain the appropriate Scheffé critical value or values. Then, answer these questions based on Scheffé tests. Of course you will use the F statistics you already computed.

    1. Is there a difference between Drug and Placebo just at 3 days?
    2. Is there a difference between Drug and Placebo just at 6 days?
    3. Is there a difference between Drug and Placebo just at 9 days?
    4. Is there a difference between Drug and Placebo just at 12 days?

     

  8. Based on the Scheffé tests you've just carried out, would you advise the dentists running this study to proceed to clinical trials with humans? Answer Yes or No and explain in one sentence.

 

 

Bring both your log file and your procedure output file to the quiz. You will be asked to hand them in with your quiz. Please put your name and student number in the title statement.

Please be reminded of the rules for computer assignments and quizzes. See the syllabus for more detail.

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