10.5. Modify the multiple imputation approach of Problem 10.4 to give the correct answer for large r and N=r. (Hint: For example, add sRr 1=2zd to the imputed value for observation i, where the zd are independent standard normal deviates.) 1 0.6. Consider the situation where the complete-data analysis is nonparametric, and produces no estimates but just a P value for a null hypothesis, for example, the P value for a Wilcoxon test in a randomized two-treatment experiment. Suppose that the missing data in this experiment have been multiply imputed with D ¼ 2, and the two P values are p1 and p2. Let z1 and z2 be such that Prðz < z1Þ ¼ p1; Prðz < z2Þ ¼ p2, where z is standard normal, and a ¼ 3ðz1 z2Þ 2 =4. Show that a multiple-imputation combined P value can be found from treating ffiffiffiffiffiffiffiffiffiffiffi z1z2 1 þ a r as a t random variable with ð1 þ a 1Þ degrees of freedom. (Hint: consider Eq. (10.22) in this setting.)