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A Researcher Wishes to Determine Whether the Controversial Healing Touch \quad

question 17

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A researcher wishes to determine whether the controversial healing touch therapy is successful when the patients are unaware that the therapist is using "healing touch." Twenty patients with acute back pain are randomly assigned to either an unaware condition, where the patients sleep through the sessions, or an aware condition, where they are awake. The patients then receive three sessions each of healing touch therapy. After each session, the patients are asked to rate their pain on a 1 to 10 scale, where 1 = no pain and 10 = maximum pain. \quad Unaware Sessions \quad\quad\quad\quad\quad Aware Sessions
123123 Patient 1 889 Patient 11 532 Patient 2 778 Patient 12 674 Patient 3 543 Patient 13 532 Patient 4 464 Patient 14431 Patient 5 796 Patient 15 421 Patient 6 554 Patient 16 311 Patient 7 8910 Patient 17333 Patient 81099 Patient 18 432 Patient 9989 Patient 19 242 Patient 10899 Patient 20 221\begin{array}{lccccccc}&1&2&3&&1&2&3\\\hline \text { Patient 1 } & 8 & 8 & 9 & \text { Patient 11 } & 5 & 3 & 2 \\\text { Patient 2 } & 7 & 7 & 8 & \text { Patient 12 } & 6 & 7 & 4 \\\text { Patient 3 } & 5 & 4 & 3 & \text { Patient 13 } & 5 & 3 & 2 \\\text { Patient 4 } & 4 & 6 & 4 & \text { Patient } 14 & 4 & 3 & 1\\\text { Patient 5 } & 7 & 9 & 6 & \text { Patient 15 } & 4 & 2 & 1 \\\text { Patient 6 } & 5 & 5 & 4 & \text { Patient 16 } & 3 & 1 & 1 \\\text { Patient 7 } & 8 & 9 & 10 & \text { Patient } 17 & 3 & 3 & 3\\\text { Patient } 8 & 10 & 9 & 9 & \text { Patient 18 } & 4 & 3 & 2 \\\text { Patient } 9 & 9 & 8 & 9 & \text { Patient 19 } & 2 & 4 & 2 \\\text { Patient } 10 & 8 & 9 & 9 & \text { Patient 20 } & 2 & 2 & 1\end{array}
-The df for the interaction is


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