In Example 8.4.1, we examined data from a study by Licciardone et al. (A-15) on osteopathic manipulation as a treatment for chronic back pain. At the beginning of that study, there were actually 91 subjects randomly assigned to one of three treatments: osteopathic manipulative treatment

(OMT), sham manipulation (SHAM), or non-intervention (CONTROL). One important outcome variable was the rating of back pain at the beginning of the study. The researchers wanted to know if the treatment had essentially the same mean pain level at the start of the trial. The results are displayed in the following table. The researchers used a visual analog scale from 0 to 10 cm where 10 indicated “worst pain possible.” Can we conclude, on the basis of these data, that, on the average, pain levels differ in the three treatment groups? Let a ¼ :05 and find the p value. If warranted, use Tukey’s procedure to test for differences between individual pairs of sample means.

CONTROL SHAM OMT 2.6 5.8 7.8 3.5 5.6 1.3 4.1 3.4 3.3 2.4 1.7 1.1 4.6 1.0 3.3 0.5 8.4 3.2 4.3 5.1 0.0 0.4 6.5 1.9 2.5 5.4 5.4 2.0 5.0 4.5 4.0 2.8 1.7 1.5 4.1 3.7 3.8 0.0 2.6 1.6 2.4 0.6 3.2 0.0 1.1 0.0 2.8 0.2 0.7 7.6 3.4 7.3 2.4 3.5 6.7 1.7 3.3 3.9 7.3 7.5 6.6 7.0 2.1 1.6 0.4 7.4 3.7 3.0 0.4 6.5 2.3 6.5 0.9 1.6 4.4 3.0 6.0 1.3 2.8 3.3 6.6 0.4 7.3 6.3 0.7 4.6 7.0 7.9 4.8 1.3 4.9 Source: Data provided courtesy of J. C. Licciardone, D.O.