Investigation 2: Reducing Back Pain, due Mon, Sept 27)

You may work with one other person on this, handing in one report with both names. Word-processed reports are preferred to hand-written ones.

A study published in the journal Neurology examined whether the drug botulinum toxin A is helpful for reducing pain among patients who suffer from chronic low back pain. Thirty-one subjects participated in the study. They were randomly assigned to one of two treatment groups: 15 received the drug itself, and the other 16 received a placebo of normal saline. The subjects’ pain levels were evaluated at the beginning of the study and again after three weeks and after eight weeks. Naturally, the researchers were looking for evidence that the drug was more effective than the placebo for reducing back pain. The results of the study after eight weeks were that 9 of the 15 subjects who received the drug experienced a substantial reduction in pain, compared to 2 of the 16 subjects in the placebo group.

a) Create a two-way table to present these data. Put the medication received in columns, the response in rows.

b) What proportion of those who received the drug experienced a substantial reduction in pain? What proportion of those who received a placebo reported such a pain reduction? Do these proportions differ in the direction expected if the drug is effective?

c) Use the Java applet to conduct a simulation analysis to investigate whether the observed sample data would support the drug’s effectiveness by this much if in fact the drug were no more effective than a placebo. [Start with the :friendly observers” applet but follow the link to the applet that allows you to change the entries in the table.] Run the applet to simulate 1000 random assignments of subjects to treatment groups. Report a tally of the number of simulated “successes” randomly assigned to the botulinum group and comment on this distribution.

d) How many and what proportion of the 1000 simulated randomizations produced a result as extreme as the actual data (i.e., 9 or more successes in the botulinum group)?

e) Based on the approximate p-value that you calculated in (d), would you say that the experimental data provide strong evidence that botulinum is more effective than a placebo for reducing back pain? Explain the reasoning process on which your answer is based.

f) Determine the exact p-value using hypergeometric probabilities. [You are welcome to use Minitab to do this calculation, but be sure to specify what parameter values you enter.]