WHAT IS THE MANN-WHITNEY U TEST?
This is an inferential test created by Henry Mann (left) and Donald Whitney (below, left). It is used when:
(* it’s easy to turn interval/ratio level data into ordinal data: you just put the scores into rank order)
The Edexcel exam might ask you about the appropriateness of the Mann-Whitney U test – when you would use it. But you could be asked to calculate the test. The equation and tables are provided at the front of the exam booklet.
If you are using a Matched Pairs or Repeated Measures design, use the Wilcoxon test instead.
MAKING THE CALCULATIONS
Of course, most researchers use computers to do their statistical tests. There are lots of websites that will let you input your data from an experiment and carry out the Mann-Whitney U test for you.
The Exam expects you to be able to work out the Mann-Whitney U test "by hand" and, although it's fiddly, it's not that difficult.
You are trying to work out the value of U and to do this you need to calculate two scores called Ua and Ub and choose the lowest of the two.
The test uses ordinal level data, so you will probably need to turn your interval/ratio data into ordinal data. You do this by “ranking” the scores in each condition; the top scores gets rank 1, the next score gets rank 2 and so on; identical scores get the mean rank they share (so if there are 3 scores sharing 1st place, instead of getting ranks 1, 2 and 3, they all get rank 2).
You will need to know na and nb; na is the total number of scores you have in Condition A and nb is the number of scores in Condition B.
The first step is to calculate Ua:
The next step is to calculate Ub:
Your observed value (U) will be the lower of Ua and Ub. You will compare U to the critical value and you are looking for U to be lower than the critical value.
Before you can look up the critical value, you need to know two things:
Once you know these two things, you can finish the calculation:
If you look closely at these tables, you'll notice that the critical values for 2-tailed tests are a bit lower than the values for 1-tailed tests. This reflects the fact that, being a bit more vague, 2-tailed tests require stronger evidence of difference.
If your value of U is equal to or less than the critical value, you can refute your null hypothesis (and cautiously accept your hypothesis).
If the value of U is greater than the critical value, you must accept your null hypothesis and refute your experimental hypothesis.
A STATEMENT OF STATISTICAL SIGNIFICANCE
You can sum up your statistical test with a statement of statistical significance. This will include:
The results were subjected to a Mann-Whitney U test
The observed value (U) was 17, which is lower than the critical value of 20 for a 1-tailed test where p≤0.05
Therefore, the null hypothesis can be refuted
APPLYING MANN-WHITNEY U TEST IN PSYCHOLOGY