Arthritis is a very commonly occurring affliction. It is a major cause of lost work time and often results in serious disability. Of the many types of arthritis, the most common type is osteoarthritis. This condition is frequently due to wear and tear in the joints and is more likely to be found in people over 50. It is very painful in the weight-bearing joints, such as the knees and hips. Cartilage wears away on the bone ends, causing pain and swelling. Osteoarthritis may develop after an injury such as bone fracture or a joint dislocation. In order to reduce the amount of time osteoarthritis patients are absent from work, it is important for them to have effective pain relief. An experiment was conducted to compare the effectiveness of three new analgesics, A1, A2, A3. A clinic evaluated a large group of patients and identified 24 patients with a moderate level of pain. Each of the 24 persons was then randomly assigned to one of the three analgesics. The patients were then placed on the therapies and the percentage reduction in pain level was assessed for each patient. You can download the data using the code:

reduction,analgesic 3.0,A1 1.2,A1 1.0,A1 0.7,A1 1.1,A1 0.6,A1 1.2,A1 0.1,A1 0.7,A1 1.9,A1 0.6,A1 0.0,A1 1.6,A1 4.0,A1 0.1,A1 1.8,A2 6.3,A2 5.2,A2 3.7,A2 5.4,A2 2.9,A2 6.0,A2 0.3,A2 3.6,A2 9.3,A2 2.8,A2 0.0,A2 8.1,A2 19.9,A2 0.3,A2 1.3,A3 12.6,A3 10.0,A3 10.5,A3 10.8,A3 5.9,A3 12.1,A3 0.6,A3 18.6,A3 18.7,A3 5.5,A3 0.0,A3 18.2,A3 22.3,A3 0.6,A3 

(a) Check the ANOVA assumptions to see if the data is not normal. That is, construct boxplots, residual plots and Levene's Test to see if the assumptions for running an ANOVA are violated. Comment on what you see for each of these? (b) Run a Kruskal-Wallis test to test for differences in the mean percentage reduction in pain level between the 3 analgesics. Give the hypotheses for the test, the output and a conclusion. (c) Run a Dunn test to see which analgesics differ. Give the output and a well written conclusion of your findings.