Problem 3. For the following problems, identify and describe the statistical test that you can use to answer the question of interest (you don’t need to actually conduct the test). Specifically,

• provide the name of the statistical test(s);

• rationale of your choice of the tests;

• what are the assumptions for that test;

• whether it’s a one-sided test or a two-sided test.

a) A study is designed to investigate whether there is a difference in response to various treatments in patients with rheumatoid arthritis. The outcome is patient’s self-reported symptoms, and a total of 60 patients are randomized to one of the three treatment groups. Summary table for these 60 patients are shown below. The goal is to assess whether there is a significant difference in effect of treatment.

b) An investigator wants to evaluate whether individuals, on average, experience a change in their systolic blood pressure level (SBP) in Treatment 1 eight weeks after the treatment started, as compared to study entry (the beginning of treatment)? Assume that the data has a normal distribution.

c) Use the information from part (b), but assume that the data is not normally distributed.