Which of the following statements are true?
A) In large-sample problems, the Wilcoxon signed-rank test is never very much less efficient than the t test and may be much more efficient if the underlying distribution is far from normal.
B) The Wilcoxon signed-rank test statistic for large-sample is $Z = \frac { S _ { + } - n ( n + 1 ) / 4 } { \sqrt { n ( n + 1 ) ( 2 n + 1 ) / 24 } }$
Where n is the sample size and $S _ { + }$
Is the sum of the ranks associated with the positive observations.
C) When the sample size n 20, the Wilcoxon signed-rank test statistic $S _ { + }$
Has approximately a normal distribution with mean and variance given by $n ( n + 1 ) / 4 \text { and } n ( n + 1 ) ( 2 n + 1 ) / 24$
, respectively
D) All of the above statements are true.
E) None of the above statements are true.

Question

Which of the following statements are true?
A) In large-sample problems, the Wilcoxon signed-rank test is never very much less efficient than the t test and may be much more efficient if the underlying distribution is far from normal.
B) The Wilcoxon signed-rank test statistic for large-sample is $Z = \frac { S _ { + } - n ( n + 1 ) / 4 } { \sqrt { n ( n + 1 ) ( 2 n + 1 ) / 24 } }$
Where n is the sample size and $S _ { + }$
Is the sum of the ranks associated with the positive observations.
C) When the sample size n > 20, the Wilcoxon signed-rank test statistic $S _ { + }$
Has approximately a normal distribution with mean and variance given by $n ( n + 1 ) / 4 \text { and } n ( n + 1 ) ( 2 n + 1 ) / 24$
, respectively
D) All of the above statements are true.
E) None of the above statements are true.

Quizplus · Accepted Answer

All the statements provided are true regarding the Wilcoxon signed-rank test. Statement A correctly describes the efficiency of the Wilcoxon signed-rank test compared to the t-test, especially under non-normal distributions. Statement B accurately provides the formula for calculating the Z statistic for large samples in the Wilcoxon signed-rank test. Statement C correctly describes the approximate distribution of the test statistic $S_+$ for sample sizes greater than 20, including its mean and variance.

Which of the Following Statements Are True? A) in Large-Sample Z=S+−n(n+1)/4n(n+1)(2n+1)/24Z = \frac { S _ { + } - n ( n + 1 ) / 4 } { \sqrt { n ( n + 1 ) ( 2 n + 1 ) / 24 } }Z=n(n+1)(2n+1)/24​S+​−n(n+1)/4​

Which of the Following Statements Are True?
A) in Large-Sample $Z = \frac { S _ { + } - n ( n + 1 ) / 4 } { \sqrt { n ( n + 1 ) ( 2 n + 1 ) / 24 } }$