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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.