Why do we use a balanced (equal number of replicates in each group) design? To maximize power. Let's verify this with simulation. Consider a simple example with 2 groups A and B and a total sample size of N = 10. Where should we place these samples (replicates) between A and B? Obviously, at least one replicate needs to be in each, but after that, we can choose. Consider the model yij = j + eij where eij N(0, 2 = 1). Here j = 1, 2, for A and B. The null hypothesis of the test we will run is: H0 : A = B Suppose that we're interested in an alternative where A = 0, B = 2 Calculate the power for each of the possible placements of the replicates with = 0.05. (Essentially, for na = 1, 2, . . . 9.) For each possibility, use at least 500 simulations. Plot the results. Does balance provide the best power? Before performing the simulations, set a seed value equal to your birthday, as was done in the previous homework assignments.

Using R