The answer is b). The Wilcoxon signed-ranks test is a non-parametric test for assessing whether two related or paired samples of observations come from the same distribution. It is a non-parametric alternative to the paired Student’s t-test.

 The answer is a). As the outcome variable is skewed and the sample size small, a non-parametric test is required. The Wilcoxon signed-ranks test is the test to use. The Mann Whitney U would be used if we had two independent groups where we wished to compare the WBC counts from a sample of sick patients with the WBC counts from a sample of healthy patients.

 The answer is b). a) is False. There a no assumption about the distribution, so you could use the Wilcoxon signed-ranks test on Normally distributed differences of paired observations, however a paired t-test would be more powerful. b) is True. The Wilcoxon signed-ranks test makes no assumptions about the distribution of the data. c) is False. The Mann-Whitney U test considers the differences in medians of two independent groups. The Wilcoxon signed-ranks test considers the difference between paired observations where the two groups are not independent. d) is False. The Sum-Rank Test is the same as the Mann Whitney U test it tests for differences in the medians of independent groups. However because of the confusion between Sum Rank and Signed Rank, most people use the terms Mann Whitney for independent groups and Wilcoxon (Signed-Rank Test) for paired groups of data.

 The answer is d). a) is False. If the differences in CD4 counts (value at 6 weeks minus value at baseline) were Normally distributed we would expect a paired t-test to be used. Since it was not we must conclude the differences showed a skewed distribution and this is why the Wilcoxon signed-ranks test was chosen. Note if the distribution of the CD4 counts taken at baseline was skewed or the distribution at 6 weeks was skewed this would not be a reason to choose the Wilcoxon signed-ranks test, it is the distribution of the difference that is important. b) is False. This is because it does not consider that we are using paired observations. It implies we will use a Mann-Whitney U test because we will be comparing medians. However we should consider the difference so a better hypothesis would be ‘There is no median difference in the value of CD4 counts after six weeks of treatment with a PI in patients with HCV and HIV.’ c) is False. The value were not independent, they were paired. If they were independent we would use the Mann-Whitney U test. d) is True. The P-value is less than 0.05 so the result is statistically significant. What we are not told is by how much the CD4 counts increased and whether this was clinically significant. e) is False. We assume that the distribution of the differences is skewed, so a t-test would not be appropriate because the assumption of a Normality of the difference is not satisfied.