STA429/1007 Makeup Assignment

Quiz on April 9th (Last class meeting)

This quiz will substitute for your lowest two quiz marks, or your lowest one quiz mark, or it will not be counted at all -- whichever will help you most. My preference is that you take it in class on April 9th, but it is a religious holiday, and also some people are going to conferences. Therefore, whatever your reason, you may just give clear answers (preferably typed) to all the questions below (numbered, in order) and hand them in, along with your log and list files.

I just remembered that because this course does not have a final exam, they are giving me only a few days to turn in the marks for STA429. Therefore, I can't give any extensions. If you choose to do this optional assignment, you must either take the quiz in person or hand it in by 1:00 pm on Monday April 9th. I will stay in the classroom until then.

It is okay to hand it in early; tomorrow is acceptable.

This one time, I will also take it as an email attachment, with the same deadline. If it is an email attachment, it must be a single PDF document or I will not look at it. You can save a Microsoft Word document as PDF, so this should not be a hardship. The log and list files can be pasted in after your answers. Please put them in the courier font. If this is too much trouble, then you may take the quiz or give me hard copy.

I know this study is pretty gruesome, but the results are interesting.

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 answer these questions.

  1. How many rabbits are in each experimental condition? (Use proc freq.)
  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. When I look at the F tests produced by default (I count four), one of them is a lot more interesting than the others. Which one is it? For this one test only,
    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 do you conclude? This is not the place for statistical jargon. "What do you conclude" means say something about how firmly teeth are implanted into bone.
  3. Now make a combination independent variable, whose 8 values are the combinations of drug and healing time. Treating all tests as Scheffé followups to the initial test for difference among the 8 treatment means,
    1. Using custom contrasts, test all pairwise differences between marginal means for healing time. Which ones are significantly different from one another? Again, that's marginal means, and we are comparing them with Scheffé tests.
    2. For those pairwise tests, what was the Scheffé critical value? Give a number. You don't have to give all the F statistics, though you might be asked for one on the quiz.
    3. Is the main effect for drug still significant, when it is considered as a Scheffé test? You don't have to do a custom contrast for this one, because the F statistic is part of your default output from the 2-way ANOVA. Answer Yes or No, and give the F statistic and the Scheffé critical value.
    4. Is there a difference between Drug and Placebo just at 3 days? Answer Yes or No, and give the F statistic and the Scheffé critical value. If the answer is Yes, say which mean is higher.
    5. Is there a difference between Drug and Placebo just at 6 days? Answer Yes or No, and give the F statistic and the Scheffé critical value. If the answer is Yes, say which mean is higher.
    6. Is there a difference between Drug and Placebo just at 9 days? Answer Yes or No, and give the F statistic and the Scheffé critical value. If the answer is Yes, say which mean is higher.
    7. Is there a difference between Drug and Placebo just at 12 days? Answer Yes or No, and give the F statistic and the Scheffé critical value. If the answer is Yes, say which mean is higher.
    8. Is there a difference between Drug and Placebo at any time period? Under the 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. (You are testing 4 contrasts) 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.

      Answer Yes or No, and give the F statistic and the Scheffé critical value.

    9. Finally, does this drug show promise for treating dental patients? Answer Yes or No.