 The Man-Whitney-U test is used when you want to find if two independent groups differ significantly on an ordinal measure. Here's an example. Do math majors and psychology majors differ in their sense of humor? Five math majors, Group A, and six psychology majors, Group B, are asked to rate a comedy movie on a scale of 1 to 10, where 1 is not at all funny and 10 is extremely funny. Here are the scores for the two groups. We want to find out if the ratings of Group A are significantly different than the ratings in Group B. More formally, the Man-Whitney-U test is testing the null hypothesis that the distribution of both groups is equal. Here's how the calculation works. Let's pretend that we have a competition where every person in Group A competes against every person in Group B. In this case, that would make a total of 30 matches. The null hypothesis is that the teams are equally skilled, so there should be 15 wins for each team. The further you get away from this even split, the more likely it is that one team is better than the other. The Man-Whitney-U test compares every score from one team against every score from the other team. If your score is greater than your opponent's, your team gets one point. If it's a tie, your team gets a half point. The rule is to start with the group that seems to have the lower scores. In this case, it's pretty clear that that's Group B. Looking at the score of two, you can see that it doesn't beat any one score in Group A, so that earns zero points for Group B. Now look at the five. It beats only one score from Group A, the four, so that means one point for Group B. The three doesn't beat any one in Group A, so it earns zero points for Group B. The six ties one of the scores in Group A, so that's one half point for Group B. And the six beats the four, and so that's one more point for Group B. The four ties Group A's four, so that earns one half point for Group B. Finally, look at Group B's score of seven. How many points does it earn for Group B? Stop the video now and see if you can figure it out. It scores two and a half points for Group B because it ties the seven in Group A and it beats the six and the four. Add up the points and you get a total of five point five. That's the man Whitney used statistic. If you look up that value in a table, you'll see that a value of five point five has a probability of one tenth point one. So there isn't a statistically significant difference between these two groups. What would have happened if you had started with Group A? You would have come up with a total of 24 and a half. The rule is to choose the smaller total as you. Once you have one total, you can easily figure out the other one, since the totals have to add up to the 30 possible matches. And that's the theory and the calculation behind man Whitney U test.