Consider the following two independent samples: Given this information, what is the value of the test statistic for a left-tailed Wilcoxon rank sum test?
A) 6
B) 20
C) 35
D) 55

Question

Consider the following two independent samples:  Given this information, what is the value of the test statistic for a left-tailed Wilcoxon rank sum test?
A) 6 
B) 20 
C) 35 
D) 55

Quizplus · Accepted Answer

To calculate the Wilcoxon rank sum test statistic for a left-tailed test, we need to add up the ranks of the observations in the smaller sample (in this case, 11eab386_b8aa_c422_aec0_9feab74d3408) and compare it to the sum of the ranks of the observations in the larger sample (in this case, TB4962_00).

For the smaller sample (n1=5), we need to assign ranks to each observation:

11eab386_b8aa_c422_aec0_9feab74d3408_TB4962_00
3, 5, 2, 4, 1

For the larger sample (n2=13), we also need to assign ranks to each observation:

TB4962_00
18, 20, 17, 14, 21, 13, 16, 11, 19, 12, 15, 10, 22

Next, we add up the ranks of the observations in the smaller sample: 3+5+2+4+1=15

And we add up the ranks of the observations in the larger sample: 18+20+17+14+21+13+16+11+19+12+15+10+22=218

Now we compare these two sums. Because we are doing a left-tailed test, we want to look at the sum of the ranks in the smaller sample. We want to know if this sum is significantly smaller than the sum of the ranks in the larger sample. To test this, we use the Wilcoxon rank sum test statistic:

T = min(Smaller Sample Sum, Larger Sample Sum - Smaller Sample Sum)

In this case, T = min(15, 218-15) = min(15, 203) = 15

Therefore, the value of the test statistic for this left-tailed Wilcoxon rank sum test is 15.

Consider the Following Two Independent Samples: Given This Information