Assignment Four: Quiz on Friday Feb. 3d

The quiz will be based on Chapter 3 and associated lecture material. But that does not mean you are allowed to forget everything you learned earlier.

  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 reduction 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: 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 should be measured relative to the drug control (placebo), while the effectiveness of the non-drug control (stress reduction training). Placebos can be measured relative to no treatment at all.

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

    1. Does OxyContin work any better than the placebo?
    2. Does Ibuprofin work any 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 independent 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 chicks 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 with where (though where does work with proc glm, and one could make a case for where and not contrast.)
      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.
      3. Calculate the F statistic, degrees of freedom and p-value. Do you reject H0 at α=0.05?
      4. What proportion of the variation in weight is explained by the differences among these five means?
      5. In plain, non-statistical language, what do you conclude from the F-test?
      6. Carry out a non-parametric test to answer the same question. This time you will have to use where.
        1. What is the value of the test statistic? The answer is a number from your printout.
        2. What is the p-value for the non-parametric test? The answer is on your printout.
        3. Do you reject H0? Answer Yes or No.
        4. Are the results statistically significant? Answer Yes or No.
        5. Does the non-parametric test lead to the same conclusion as the parametric test? Answer Yes or No.

    On your list file for the Chick Weights data, you may (or may not) have noticed that the names of the feed types are truncated to 8 characters, which is the SAS default. You won't directly lose any marks if you don't fix this, but if you want to fix it, you can include a line like the following before your input statement:   length feed $ 9;

  4. This question uses the Furnace data of Assignment Three.

    The independent variable here is chimney shape and the dependent variable is average amount of energy consumption (mean of consumption with vent damper active and vent damper inactive).

    1. First, we will consider whether the independent variable and the dependent variable are related.
      1. What is the value of the test statistic? The answer is a single number from the printout.
      2. What is the p-value? The answer is a single number from the printout.
      3. Do you reject the null hypothesis at the 0.05 level? Answer Yes or No.
      4. Are the results statistically significant at the 0.05 level? Answer Yes or No.
      5. Carry out this same test using the contrast statement. Make sure you obtain the same value of F and the same p-value.
    2. Use contrast statements to carry out all pairwise comparisons of treatment means. Using a calculator, convert all the p-values to Bonferroni adjusted p-values -- but do not write the adjusted p-values on your printout. Check your work with the lsmeans statement (there will be a little bit of rounding error).
      1. Which means are different from which other means?
      2. State any conclusions in plain, non-statistical language.
    3. Use lsmeans to carry out all pairwise comparisons of treatment means using Scheffé-corrected p-values.
      1. How do your conclusions compare to what you got from Bonferroni?
      2. What is the critical value for all possible Scheffé-corrected tests of single contrasts? Use proc iml. Your answer will be a single number on your printout.
      3. Now use a contrast statement to test whether average energy consumption of houses with rectangular and square chimneys is different from those with round chimneys. What is the value of the test statistic? The answer is a single number from the printout. What is the p-value? The answer is a single number from the printout. Are the results statistically significant at the 0.05 level? Answer Yes or No.
      4. Is this last comparison still significant when converted to a Scheffé test? Answer Yes or No. How did you decide? ("I looked at the ...")
      5. Based on your list file, how would you do the Scheffé pairwise comparisons without using lsmeans?

Bring your two log files and your two list files to the quiz. Do not write anything on the printouts except your name and student number. You may be asked to hand one or both of them in. The log and list files for each data set must be generated by the same SAS program or you may lose a lot of marks. There must be no errors or warnings in your log files. Bring a calculator to the quiz.