Today we will be looking at the non-parametric test for

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.

__unrelated__samples:**Mann-Whitney U Test.**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

I've covered this in the previous post; if you remember it all, go on to the next section - or look through this one first to quickly refresh it in your mind.

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.

2.

3.

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

I have covered this in the previous post too, but in case you were specifically looking for the unrelated non-parametric test, I will go through this again; if you know how to rank your data already, feel free to skip this section.The basic process is really simple: you arrange your scores in ascending order and then rank them: 1, 2 and so on.

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

We simply calculate a mean for these ranks and assign it to each of the identical scores. The following table will make it clear:

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

Mann-Whitney U Test is an equivalent of t-test for Unrelated Samples. This is easy to remember if you think of

So, the basic formula is very easy and does not involve lots of maths:

**U**Test as referring to**U**nrelated.So, the basic formula is very easy and does not involve lots of maths:

where N1 is the size of the first sample, N2 - size of the second sample and R1 - sum of ranks of the bigger sample.

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!

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****Step 2: rank the data**

* Create one single group putting all the scores together

* Rank those scores as if they were in one group

**Step 3: sum the ranks of the larger 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.

**Step 3: Calculate your U**

Here, the calculation will be as follows:

(6 * 5) + (6 *(6+1)/2) - 48.5 =

__2.5__## Significance Testing

To test whether your result is statistically significant, you need:

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:

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:

Our U is 2.5 which is indeed between 0 and 3. Therefore, our result is statistically significant; we may now reject the Null Hypothesis and accept the Alternative Hypothesis.