Question

Antiviral Therapy. In the article "Improved Outcome for Children With Disseminated Adenoviral Infection Following Allogeneic Stem Cell Transplantation" (British Jourmal of Haematology, Vol. 130, Issue 4, p. 595), B. Kampmann et al. examined children who received stem cell transplants and subsequently became infected with a variety of ailments. A new antiviral therapy was administered to 11 patients. Their absolute lymphocyte counts (ABS lymphs) $\left(\times {10}^9/\mathrm{L}\right.$) at onset and resolution were as shown in the following table.

a. Obtain normal probability plots and boxplots of the onset data, the resolution data, and the paired differences of those data.

b. Based on your results from part (a), is applying a one-mean \(t\)-procedure to the onset data reasonable?

c. Based on your results from part (a), is applying a one-mean \(t\)-procedure to the resolution data reasonable?

d. Based on your results from part (a), is applying a paired \(t\)-procedure to the data reasonable?

e. What do your answers from parts (b)-(d) imply about the conditions for using a paired t-procedure?

Short answer

Part a)Given below

Part b)t-procedure is not reasonable.

Part c)t-procedure is not reasonable.

Part d)t-procedure is reasonable.

Part e)t-procedure is reasonable.

Step-by-step solution

Step 1:Given information

Step 2:Explaination Part a)

Using the MINITAB, we obtain normal probability plots and box plots for the Onset, Resolution and the paired difference of Onset and Resolution are:

Step 2:Explaination Part b)

The normal probability plot of the onset data indicates extreme deviation from normality. Therefore, in view of the small sample size, applying a one-mean$t$-procedure is not reasonable.

Step 2:Explaination Part c)

The normal probability plot of the resolution data is roughly linear and the boxplot suggests a potential outlier. Therefore, in view of the small sample size, applying a one-mean $t$-procedure is probably not reasonable.

Step 2:Explaination Part d)

Neither the normal probability plot nor the boxplot of the paired differences suggest the presence of outliers and furthermore, the normal probability plot of the paired differences is quite linear. Therefore applying a paired $t-$procedure is reasonable.

Step 2:Explaination Part e)

Whether applying a paired $t$-procedure is reasonable depends on the properties of the paireddifference variable and not on those of the individual variables that constitute the paireddifference variable.