Paired Data• Many statistical applications use paired data samples to draw conclusions about the difference between two population means.• Data pairs occur very naturally in “before and after” situations, where the same object or item is measured both before and after a treatment. • Other situations: identical twins, a person’s left and right foot
Paired Data• When a test involves comparing two populations for which the data occur in pairs, the proper procedure is to run a one-sample test on a single variable consisting of the differences from the paired data. • Note: we did one-sample testing in 8.1 – 8.3
Example: Paired DifferencesA team of heart surgeons at Saint Ann’s Hospital knows that manypatients who undergo corrective heart surgery have a dangerousbuildup of anxiety before their scheduled operations. The staffpsychiatrist at the hospital has started a new counseling programintended to reduce this anxiety. A test of anxiety is given to patientswho know they must undergo heart surgery. Then each patientparticipates in a series of counseling sessions with the staff psychiatrist.At the end of the counseling sessions, each patient is retested to determine anxiety level. Table 8-8 indicates the results for a random sample of nine patients. Higher scores mean higher levels of anxiety. Assume the distribution of differences is mound-shaped and symmetric. From the given data, can we conclude that the counseling sessions reduce anxiety? Use a 0.01 level of significance.