Problem Set # 3 (Experimental Design)HST.583Problem Set # 3 (Experimental Design)October 6, 2004Due on October 18, 2004Problem #1: The term “expectation” can refer to many things, but the specific meaning that we wish to examine now is exemplified in the following story: “You are thirstyand decide that orange juice (complete with the pulp) is just what you wish to drink. You imagine what it will taste like and how satisfying it will be. Upon goingto the refrigerator, however, you find that there is only an apple juice container. After a moment, you resign yourself to the idea of enjoying a cool drink of apple juice. You put the container to your mouth and drink---but some devilish experimenter has put orange juice in the container instead of apple juice!" How will this taste? ....It will almost certainly taste awful (at least initially), despite the fact you had previously wanted orange juice. Your expectation of tasting apple juice will alter your experience of what would have been the perfect drink.How can we study this kind of “expectation” using the imaging methods we have been learning about this year? Consider the practical problems of doing this experiment with fMRI. Within the constraints imposed by the imaging environment, propose one specific testable hypothesis about expectation and the associated feasible experiment to test it. Include the specific details for the experimental paradigm (e.g. conditions, order, timing, etc.) and image acquisition parameters.Problem #2: In Chapter 12 (“The Parietal Lobes”) of the text “Fundamentals of Human Neuropsychology”, there is a discussion of a parietal lobe syndrome called “acalculia”. This discussion (on page 270, attached) includes an error: “acalculia”is defined as the ability to do arithmetic, when it is in fact the INABILITY to do arithmetic. In any case, the authors attribute to A.R. Luria the speculation that acalculia is seen in patients who have lesions in the parietal lobe because there is a spatial component to arithmetic tasks. (a) Using the information in the excerpt you have been given from Chapter 12, summarize the basis for thinking that the parietal lobe has special properties concerning spatial information.(b) Also using information from Chapter 12, describe some of the practical difficulties in “...constructing watertight experimental designs in brain imaging studies”.-p. 270(c) How could we design a combination (or a series) of fMRI studies to test whether “acalculia” is likely to be in the exclusive domain of the parietal cortex.Problem #3:Data has been collected for a "castle paradigm" experiment with three conditions,F,G, H, as shown below. (Note: the diagram below indicates the conditions schematically, as usual. It does not represent data.) _______ _______ | | | | _______ | | _______ | | | | | | | | | |_______| |_______| |_______| |_______| |_______ F G F H F G F H FThe experimenters planned to compute three statistical maps, based on the following comparisons: F vs G F vs H G vs HF vs G showed no areas of significant activation.F vs H showed no areas of significant activation.Then the computer crashed. While waiting for it to reboot, the following discussion ensued:Experimenter 1: "We don't have to wait for the computer—we can stop now. If neither of the interesting conditions (G&H) show any difference from our baseline(F), there is no way that there can be a statistically significant difference betweenconditions G&H, so we don't have to run the third comparison."Experimenter 2: "Experimenter 1 is wrong. There are more images collected during the F condition, and it might be that, with fewer images, the G vs H comparison could be significant."Experimenter 3: "Experimenter 1 is wrong. Differences in amount of noise in therecorded signal during various conditions might make it possible for the G vs H comparison to be significant."Experimenter 4: "Experimenter 1 is wrong. Independent of any aspect of the data collected during the F condition, the G vs H comparison might be significant."*****************************************************************State which of each of these Experimenters (1-4) was right or wrong, and why.*****************************************************************For extra credit, state whether Experimenter 5 was right or wrong, and why.Experimenter 5: "I just arrived and don't even know what modality of experiment is being used. I see the diagram of the design, but this could be a PET, fMRI, rTMS, EEG or MEG experiment. The question of whether a G vs H comparison might be significant depends on the modality of the