Assignment Four: Quiz on Friday Oct. 9th

This quiz is 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.

    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. This question uses the TV data of Assignment Two. If you got no marks off for your SAS program on Assignment Two, you may use %include if you wish (but you don't have to). If you got any marks off for your SAS program on Assignment Two, please do not use %include this time.
    1. Make a binary variable that indicates whether or not a household has any children (11 and younger). Is location (Rural, Small town or Urban) related to presence of children in the household?
      1. What is the independent variable? What is the dependent variable?
      2. What percent of rural households have no children? The answer is a number from your printout.
      3. What is the value of the test statistic? The answer is a single number from the printout.
      4. What is the p-value? The answer is a single number from the printout.
      5. Do you reject the null hypothesis at the 0.05 level? Answer Yes or No.
      6. Are the results statistically significant at the 0.05 level? Answer Yes or No.
      7. In plain, non-technical language, what do you conclude, if anything?
    2. Is reported price willing to pay for cable TV related to location?
      1. What is the independent variable? What is the dependent variable?
      2. What is the mean reported price willing to pay for rural households? The answer is a number from your printout.
      3. What proportion of the variation in reported price willing to pay is explained by location? The answer is a single number from the printout.
      4. What is the value of the test statistic? The answer is a single number from the printout.
      5. What is the p-value? The answer is a single number from the printout.
      6. Do you reject the null hypothesis at the 0.05 level? Answer Yes or No.
      7. Are the results statistically significant at the 0.05 level? Answer Yes or No.
      8. In plain, non-technical language, what do you conclude, if anything?
    3. Carry out a "planned comparison" of Rural vs Small Town in mean reported price willing to pay for cable TV.
      1. Give the weights of the contrast. Your answer is three numbers, a1, a2 and a3.
      2. What is the value of the test statistic? The answer is a single number from the printout.
      3. What is the p-value? The answer is a single number from the printout.
      4. Do you reject the null hypothesis at the 0.05 level? Answer Yes or No.
      5. Are the results statistically significant at the 0.05 level? Answer Yes or No.
      6. In plain, non-technical language, what do you conclude, if anything?
    4. Carry out a "planned comparison" of Urban vs the Average of Rural & Small Town in mean reported price willing to pay for cable TV.
      1. Give the weights of the contrast. Your answer is three numbers, a1, a2 and a3.
      2. What is the value of the test statistic? The answer is a single number from the printout.
      3. What is the p-value? The answer is a single number from the printout.
      4. Do you reject the null hypothesis at the 0.05 level? Answer Yes or No.
      5. Are the results statistically significant at the 0.05 level? Answer Yes or No.
      6. In plain, non-technical language, what do you conclude, if anything?
    5. Consider the comparison of Rural vs Small Town.
      1. How do you know this would not be significant by a Scheffe test, without even bothering to try it?
      2. How do you know this would not be significant by a Bonferroni test, without even bothering to try it?
      3. So try a Tukey test. What is the adjusted p-value? Are the two means significantly different by this criterion?
  4. This question uses the Furnace data of Assignment Three. If you got no marks off for your SAS program on Assignment Three, you may use %include if you wish (but you don't have to). If you got any marks off for your SAS program on Assignment Three, please do not use %include this time.

    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 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. There is no harm in checking 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 linear combinations? Use proc iml.
      3. Now use a contrast statement to test whether average energy consumption o 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 can you tell?

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.