As always, I will explain the calculation step by step using an example, and show how to test the result for statistical significance.
First though, I will quickly recap the general assumptions for Non-Parametric tests and remind how to rank the data to make it suitable for Non-Parametric tests.
Recap: When to use Non-Parametric Tests
Try to use Parametric tests whenever possible as they are much more powerful and reliable. However, Non-Parametric tests have to be used in cases when one/several of assumptions for Parametric tests are broken:
1. The data are seriously NOT normal; very skewed.
2. The data are ordinal/categorical instead of being ratio/interval.
3. The variance is not homogenous (in between-subjects (unrelated samples) design).
Recap: Ranking your data
So, for example, for the scores set of 10, 5, 2, 8 we need to arrange them in 2, 5, 8, 10 and assign ranks to them: 2 will have rank 1; 5 is 2; 8 is 3; 10 is 4.
However, sometimes we have to deal with tied ranks. This happens when our data has several identical scores. For example, we might have arranged our scores and found that our set is as follows: 1, 4, 6, 6, 6, 8, 10, 10, 24. How do we rank these identical scores?
We simply calculate a mean for these ranks and assign it to each of the identical scores. The following table will make it clear:
Non-Parametric test for Unrelated Samples:
Mann-Whitney U Test
So, the basic formula is very easy and does not involve lots of maths:
However, despite the easy maths, many steps are actually involved in the calculation, and it is easy to mix them up or to forget one of them - so pay attention!
Step 1: arrange the data
* Create one single group putting all the scores together
* Rank those scores as if they were in one group
* Separate the two groups again (keeping their ranks) and calculate the sum for each of them; the sum of the larger group is your R1. If the groups are equal in size, then you can take either and use it as your R1.
Here, the calculation will be as follows:
(6 * 5) + (6 *(6+1)/2) - 48.5 = 2.5
1. your N1 (size of the larger group; 6 in our case)
2. your N2 (size of the smaller group; 5 in our case)
3. your U value (our 2.5)
4. set the level of significance (p<0.05)
Using these data locate the critical range from the significance table: