To study the effects of physical discomfort on attention, Dr. Ate conducted the following study: A group of participants were required to keep one hand

To study the effects of physical discomfort on attention, Dr. Ateş conducted the following study: A group of participants were required to keep one hand submerged in cold water (10 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), and the results are presented in the table below.

Duration

2 Minutes 4 Minutes

Expecting to experience pain relief 32 18

Not expecting to experiencepain relief 25    25

a) Name the independent variables in this study and describe their levels.

b) Using factorial notation, describe Dr. Ateş’s study. Given this information, how many main effects and interactions will Dr. Ateş need to examine?

c) Using the marginal means, state whether it appears that the main effects in Dr. Ateş’s study are important. (You do not need to say whether the main effects are statistically significant but simply whether a difference appears to exist.)

d) Discuss whether Dr. Ateş should conclude that an interaction exists in his study.

e) Provide a graph of the possible interaction in Dr. Ateş’s study and discuss whether Dr. Ateş should conclude that an interaction exists in his study.

f) Imagine that Dr. Ateş 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. Ateş’s new study. Given this new study design, how does this change the number of cells, main effects, and interactions in Dr. Ateş’s study?