1. A chiropractor wants to help her patients who suffer from chronic back pain reduce their pain levels. To do this, the doctor investigates whether different chiropractic treatments are more effective at reducing pain levels over time. Thirty people volunteer to participate in the experiment and are randomly assigned to one of three treatment groups. One group receives a massage treatment for their back pain (treatment=1); a second group participates in an acupuncture program (treatment=2), and the third group participates in an online mindfulness program (treatment=3). Each program lasts for six weeks. Over this six-week period, back pain is measured at three time points, with higher scores representing more pain: at the beginning of the program (time 1), after three-weeks (time 2), and at the end of the program (time 3). The data for this study are presented below. Use an alpha of .05 to answer the questions below.
a) What is the most appropriate statistical analysis we discussed this semester to analyze these data?
b) Identify the between-subject and within-subject factors.
c) Do we meet the assumption of Sphericity? What information did you use to come to this conclusion?
d) Were the three treatment programs equally effective in reducing back pain? What information did you use to come to this conclusion?
e) Perform the simple effects analysis comparing treatment programs at each time period. Briefly describe the results of this analysis.
f) Perform the simple effects analysis examining change over time for each treatment program. Briefly describe the results of this analysis.
g) Why did the chiropractor randomly assign participants to treatment groups?
h) To whom, if anyone, can we generalize the results of this study? Why?
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