I'm practicing this test and I have a trouble with this question:

Students' scores on the mathematics test are given in the following table. The students are divided into two groups: those who are given study guide (group 1) and those who are not (group 2).

Group 1 Group 2
70 6 88 57 79 68 85 14 88 77 72 54 87 85 62 77 86 55 82 92 87 45 85 84 57 56
To test if the median of students' scores of group 1 is higher than that of group 2, which test is most appropriate between the Mann-Whitney Test or the Wilcoxon Signed-Rank test?

I believe that the best test to use is the Wilcoxon because of the paired samples but I'm not sure.

  • $\begingroup$ Please add the [self-study] tag & read its wiki. Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. $\endgroup$ Sep 25, 2015 at 0:24
  • $\begingroup$ Well i believe that the best test to use is the Wilcoxon because of the pair samples but im not sure @gung $\endgroup$
    – drezzy
    Sep 25, 2015 at 0:25
  • $\begingroup$ Add that to your question, & please add the tag & read the wiki. $\endgroup$ Sep 25, 2015 at 0:27
  • $\begingroup$ Well my question is basically how do you know for sure if the Wilcoxon is the best test to use for this problem? I mean arent the two groups consider a pair sample? and sorry im new to this website but i would appreciate your help @gung $\endgroup$
    – drezzy
    Sep 25, 2015 at 0:28
  • $\begingroup$ What makes you think the data are paired? $\endgroup$ Sep 25, 2015 at 1:33

1 Answer 1


The question does not suggest that the two samples are paired strategically. The Wilcoxon signed-rank test should be used when the two samples are paired strategically, otherwise use the Mann-Whitney U test.

An example of this: Suppose we have a classroom of 20 sets of twins. Group 1 contained the first-born twin, and group 2 contained the other twin. Group 1 was taught using method 1, and group 2 was taught using method 2. If we wanted to test for a difference in median test scores, we would use the Wilcoxon signed-rank test here.

In my example, the pairings are obviously strategic - group 1 has a corresponding member in group 2 (his/her twin).

In your example, there are no corresponding members between groups. To check this, ask yourself, is person 1 of group 1 tied to person 1 of group 2 in any relevant way?


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