A crossover study comparing d = 2 drugs observes a continuous response

(yi1, yi2) for each subject for each drug. Let ????1 = E(yi1) and ????2 = E(yi2) and consider H0: ????1 = ????2.

a. Construct the normal linear mixed model that generates a paired-difference t test (with test statistic t = √nd̄∕s, using mean and standard deviation of the differences {di = yi2 − yi1}) and the corresponding confidence interval for ????1 − ????2.

b. Show the effect of the relative sizes of the variances of the random error and random effect on corr(yi1, yi2). Based on this, to compare two means, explain why it can be more efficient to use a design with dependent samples than with independent samples.