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To study the effects of physical discomfort on attention, Dr. Lopez conducted the following study: A group of participants were required to keep one hand submerged in cold water (52 degrees). Half of the participants kept their hand in the water for 2 minutes, and half of the participants kept their hand in the water for 4 minutes. In addition, half of the participants were given a placebo pill and told it would reduce the pain of the water (pain relief assumed). The other half were given a placebo pill and told that it would have no effect (no pain relief assumed). While their hands were in the water, participants were asked to watch a video where a ball is quickly passed between and underneath three cups. At the end of the video, participants were asked to indicate under which cup the ball could be found. Whether or not the participant picked the correct cup was recorded (as a measure of whether they were paying attention). The results are below.
Imagine that Dr. Lopez decides to manipulate the pain duration differently. He now has three levels of this variable: 2 minutes, 4 minutes, and 6 minutes. Using factorial notation, describe Dr. Lopez's study. Given this new study design, how does this change the number of cells, main effects, and interactions in Dr. Lopez's study?
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