Which of the following statements are true?
A) The Wilcoxon rank-sum test for testing $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = \Delta _ { 0 }$
Is carried out by first combining the $\left( X _ { i } - Δ _ { 0 } \right) ^ { \prime } \text { sand } Y _ { i } ^ { \prime } \text { s }$
Into one sample of size m + n and ranking them from smallest (rank 1) to largest (rank m + n). The test statistic W is then the sum of the ranks of the $\left( X _ { i } - \Delta _ { 0 } \right) ^ { \prime \mathrm { s } }$
B) The Wilcoxon rank-sum interval is very similar to the Wilcoxon signed=rank interval; the later uses pairwise averages from a single sample, whereas the former uses pairwise differences from two samples
C) The Wilcoxon rank-sum interval is quite efficient with respect to the t interval.
D) For large samples, the Wilcoxon rank-sum interval will tend to be only a bit longer than the t interval when the underlying populations are normal, and may be considerably shorter than the t interval if the underlying populations have heavier tails than do normal populations.
E) All of the above statements are true.

Question

Which of the following statements are true?
A) The Wilcoxon rank-sum test for testing $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = \Delta _ { 0 }$
Is carried out by first combining the $\left( X _ { i } - Δ  _ { 0 } \right) ^ { \prime } \text { sand } Y _ { i } ^ { \prime } \text { s }$
Into one sample of size m + n and ranking them from smallest (rank 1) to largest (rank m + n). The test statistic W is then the sum of the ranks of the $\left( X _ { i } - \Delta _ { 0 } \right) ^ { \prime \mathrm { s } }$
B) The Wilcoxon rank-sum interval is very similar to the Wilcoxon signed=rank interval; the later uses pairwise averages from a single sample, whereas the former uses pairwise differences from two samples
C) The Wilcoxon rank-sum interval is quite efficient with respect to the t interval.
D) For large samples, the Wilcoxon rank-sum interval will tend to be only a bit longer than the t interval when the underlying populations are normal, and may be considerably shorter than the t interval if the underlying populations have heavier tails than do normal populations.
E) All of the above statements are true.

Quizplus · Accepted Answer

- Statement A describes the process of adjusting the values from one sample by a hypothesized difference before ranking, which is not accurate for the Wilcoxon rank-sum test. The correct procedure involves ranking the combined samples without adjusting for a hypothesized difference, making the statement as described incorrect. However, the question asks for true statements, and the error in interpretation led to an incorrect indication of the choices. The Wilcoxon rank-sum test does not involve adjusting the samples by a hypothesized difference before ranking; it directly ranks the combined samples.- Statement B correctly differentiates between the Wilcoxon rank-sum test, which is used for two independent samples, and the Wilcoxon signed-rank test, which is used for paired samples or matched pairs.- Statement C is true as the Wilcoxon rank-sum test can be more efficient than the t-test, especially when the assumptions for the t-test are not met.- Statement D is accurate because the efficiency of the Wilcoxon rank-sum test compared to the t-test can vary depending on the distribution of the population. It tends to be more efficient when the population distribution is not normal, especially with heavy-tailed distributions.

Which of the Following Statements Are True? A) the Wilcoxon H0:μ1−μ2=Δ0H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = \Delta _ { 0 }H0​:μ1​−μ2​=Δ0​

Which of the Following Statements Are True?
A) the Wilcoxon $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = \Delta _ { 0 }$