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Statistical Design and Analysis. The assignment is expected to be the joint work of all of the members of the group.

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This assignment is worth 5% of your marks for the subject. You may do the assignment in groups of up to three students. The assignment is expected to be the joint work of all of the members of the group. You must attach the assignment cover sheet to your assignment. Students who have not signed the assignment cover sheet will not be given a mark for the assignment. Please do not submit the assignment in a plastic cover, folder or envelope. Multiple pages should be securely fastened with a clip or staple. 1. Two clinical trials were designed to test the e ectiveness of laser treatment for...

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This assignment is worth 5% of your marks for the subject. You may do the assignment in groups of up to three students. The assignment is expected to be the joint work of all of the members of the group. You must attach the assignment cover sheet to your assignment. Students who have not signed the assignment cover sheet will not be given a mark for the assignment. Please do not submit the assignment in a plastic cover, folder or envelope. Multiple pages should be securely fastened with a clip or staple. 1. Two clinical trials were designed to test the e ectiveness of laser treatment for acne. In one trial the subjects were divided into two groups. One group received the laser treatment and one group received a sham treatment. In the other trial each participant received laser therapy to one side of the face, randomly chosen, and the sham treatment to the other side of the face. (a) Under what circumstances do you think that the second approach is better? (b) Why might the rst approach have been used? 2. A strain of corn has been genetically modify with a gene from the bacterium Bacillus thuringien- sis (Bt) to express the protein Cry1Ab, which is toxic to any caterpillars that eat the leaves. The pollen of such corn also contains the protein. Suppose that non-pest caterpillars feed on one of two di erent sorts of plants. One sort has been exposed to Bt-modi ed corn pollen which may have negative e ects on non-pest caterpillars. The other sort has been exposed to unmodi ed corn pollen. Suppose that you want to use enough caterpillars to be able to detect a di erence between mean weights of 0.25 gm with power at least 0.8 when the signi cance level is 0.05. The estimated standard deviation is 0.25 gm. How many caterpillars should you use in each group? 3. In conservation biology an important issue is how dispersal among populations in uences the persistence of species in a fragmented landscape. Molofky and Ferdy (2005) measured this in the annual plant Cardamine pensylvanica which produces explosively dispersed seeds. The layout of the 4 treatments appears in Figure 1 below.

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Second approach will be better in case of presence of heterogeneity in the subjects. Heterogeneity may be in terms of skin types, colour, texture or it can be in terms of Age and sex which might affect the results if first approach is used. Comparing two subjects of different age, sex or skin type will in itself give different results. Thus in this case second approach is better, in which subjects are homogenous, since two sides of a face are used to compare the treatment.

First approach might have been used because of availability of a large sample which might have been of homogeneous i.e. the subjects might have had the similar characteristics. Or it might not have been possible to administer two different treatments on two sides of a face.

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