Note: For all the problems, please provide minimal output from SPSS that is necessary to assist you answering questions. Please interpret your results, especially conclusions, in the context of the problem.
1. Suppose we have a situation where there are a=5 treatments of interest, and we are restricted to k=3 EU per block.
a) How many blocks (b) is needed for a combinatoric BIB design? Calculate r and λ for this BIB. State the meaning of r and r(k-1).
b) Suppose I tell you that the design below will work for fewer number of EU needed. Is this design a BIB? Why or why not? If it is not, what disadvantage does this have, as compared to a BIB design?
(A, B, C) (B, C, D) (C, D, E) (A, D, E) (A, B, E)
2. Midterm exam considered a study for testing if a new drug and an old drug perform the same in lowering bad cholesterol. Let m1=mean cholesterol decrease of the new drug, and m2=mean cholesterol decrease of the old drug. The standard deviation of random error is s=1.9. Now consider an AB/BA crossover design for this study. Calculate the number of subjects you would recruit for this study, in order to detect the differences listed in the table. Use alpha=0.05. Desire power of 0.9. Show all work. Hint: For each mean difference, find the τ1 and τ2, so that τ1+ τ2=0.
3. Consider a Latin Rectangle design with t=3 treatments, A, B, and C, and each subject receives all three treatments in some order. Find the minimum number of subjects needed so that the overall F test for treatment effect will have a power of at least 0.7, if we use alpha=0.05, and in fact a particular set of treatment effects is:
τA = -σ, τB = 0, τC = σ
Organize the resulting design in a Latin Rectangle design table as used in class. Consider all aspects of being balanced and randomized, including balanced for the carry-over effect.
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