STA441s20 Assignment 2

Quiz on Monday Jan. 20th in tutorial

This assignment is based on Chapter 3, lecture slide sets 4 and 5, and earlier material.

  1. In a study of remedies for lower back pain, volunteer patients at a back clinic were randomly assigned to one of seven treatment conditions:
    1. OxyContin: A pain pill in the opiate family.
    2. Ibuprofin: A non-steroidal anti-inflammatory drug (Advil, Motrin)
    3. Acupuncture: The insertion and manipulation of thin needles into specific points on the body to relieve pain or for therapeutic purposes.
    4. Chiropractic: A form of therapy that includes manipulation of the spine, other joints and soft tissue.
    5. Stress management training based on thinking positive thoughts, a treatment that theoretically should not be effective. This is the non-drug control condition.
    6. Placebo: A sugar pill; patients were told that it was a pain killer with few side effects. This is the drug control condition.
    7. Waiting list control group: Patients were told that the clinic was overcrowded (true), and that they would were on a waiting list. This group received no treatment at all, not even a pretend treatment --- until the study was over, at which point they received the most effective treatment based on the results of the study. We'll call this the "No treatment" group.

    The idea is that the effectiveness of the drug treatments could be measured relative to the drug control (placebo), while the effectiveness of the non-drug treatments could be measured relative to the non-drug control (stress reduction training). Placebo effects from both control condition can be can be assessed relative to no treatment at all (wait list control).

    Degree of reported pain was measured by a questionnaire before treatment began, and again after six weeks. The response variable was Before-minus-After difference in reported pain, which will be called "improvement," or "effectiveness."

    The following questions can be answered by testing whether one or more contrasts of treatment means are different from zero. For each question below, first state the null hypothesis in terms of the population treatment means μ1 through μ7, and then give the weights of the contrast or contrasts. For null hypotheses involving more than one contrast, make a table. There is one column in your table for each treatment mean, and one row for each contrast. See the lecture slides and the text for examples of this format.

    Note that some of these questions ask whether certain treatments are better than others, while other questions just ask about a difference in effectiveness. In some courses, this would be a signal to choose between a one-tailed and a two-tailed test. But here, we will always use non-directional tests.

    1. Does OxyContin work better than the placebo?
    2. Does Ibuprofin work better than the placebo?
    3. Do Chiropractic treatment and Stress reduction training differ in their effectiveness?
    4. Which results in more mean improvement, Acupuncture or Stress reduction training?
    5. Is the average improvement from the two drug therapies different from the improvement from the placebo?
    6. Does either drug therapy differ from the placebo in its effectiveness? (This involves 2 contrasts.)
    7. Does either non-drug therapy differ in effectiveness from Stress reduction training?
    8. Is the Placebo better than no treatment at all?
    9. Is Stress reduction training better than no treatment at all?
    10. Is the average effectiveness of the drug therapies different from the average effectiveness of the non-drug therapies?
    11. Do Stress reduction training and the Placebo differ in their effectiveness?
    12. Does either control condition (Drug or Non-Drug) differ from no treatment at all?
    13. Is treatment condition (the full explanatory variable) related to improvement?
  2. It has been reported that drivers who talk more on their cell phones while behind the wheel are more likely to get into an accident. What is a possible confounding variable here? Briefly explain.
  3. In the Chick Weights data, newly hatched chickens were randomly allocated to six groups, and each group was given a different feed supplement. Their weights in grams after six weeks were recorded.
    1. Is this an experimental study, an observational study, both, or neither?
    2. Produce a table of means, standard deviations and sample sizes for the 6 feed types.
    3. Test whether the six mean weights are different. Get the F statistic, degrees of freedom, p-value and proportion of explained variation. These are all numbers on your printout.
    4. Carry out Tukey HSD tests for all pairwise differences between means. Which means are different from each other at the joint 0.05 level? In plain, non-statistical language, what do you conclude?
    5. If you were a chicken farmer, what kind of feed would you not want to buy for your chicks (assuming the cost of feed was fairly similar)?
    6. Test for differences among mean weights for the five feed types excluding horsebean. Please do this with contrast, and not by subsetting the data, though one could make a case for subsetting the data in this case.
      1. State the null hypothesis in terms of μ values.
      2. Give a table of contrasts: The null hypothesis is that all contrasts equal zero. There is one column in your table for each treatment mean, and one row for each contrast. There are examples of this format in the lecture slides and the text.
      3. Calculate the F statistic, degrees of freedom and p-value. Do you reject H0 at α=0.05?
      4. In plain, non-statistical language, what do you conclude from the F-test?

Bring your log file and your output (results) file to the quiz. You may be asked to hand them in. Do not write anything on the printouts except your name and student number. In particular, you are not allowed to write questions or answers from the homework on your computer output. This includes comment statements. You are not allowed to put conclusions from the analyses in your program file, or to otherwise cause them to appear on your printout.

The log file and output file must be generated by the same SAS program or you will lose a lot of marks. There must be no errors or warnings in your log files. Bring a calculator to the quiz.