Dr. Pinker has worked with a lot of students who experience anxiety that interferes with their performance in college classes. He just read an article describing the reduction in anxiety achieved by having adults meditate 20 minutes a day. He would like to start offering a meditation program to students at the college counseling center where he works, but first, he wants to conduct some research to determine how effective the meditation program would be in his population of students.

Therefore, Dr. Pinker recruits 12 students to participate in a repeated-measures experiment. The students will complete a measure of anxiety as part of the recruitment process. Those whose scores indicate at least moderate anxiety (15 points or more) will be invited to participate. Participants will meet twice a week in a group to learn and practice mindfulness meditation (the same kind used in the study Dr. Pinker read about), and they will be expected to meditate for 20 min/day the rest of the week. After the 8-week treatment, the participants will complete the same measure of anxiety they completed before the treatment.

Dr. Pinker hopes to find that anxiety scores go down, but he knows that treatments sometimes have paradoxical effects (they sometimes have effects opposite of what you expect), so he uses a two-tailed test to evaluate the data he collects.

The data are below, including the value for D-bar and the sum of squares.