Mann Whitney

When is Mann Whitney U the correct test?

  • When you are testing to see whether there is a significant difference between two groups/conditions
  • When the experimental design is independent measures/groups
  • When the level of measurement of the data is at least ordinal, e.g. it can be used with interval/ratio as well (NOT nominal)

mann whitney formualHow do I do it?

If you are allowed to use an online calculator, try this one:

If not follow the formula using the steps below.

  1. Rank all of the scores from both groups/conditions as one set (when there are tied ranks, you give both scores the median of the ranks) – be careful with ranking easy to make mistakes at this point!
  2. Add up the sum of the ranks in condition A (the one with the smaller sample, if they are both the same size don’t worry!); this gives you RA
  3. You then need to use the formula at the front of the exam booklet to work out your Ua value; in the formula Na means the number of Pps in condition A and Nb is the number of Pps in condition B (the larger sample)
  4. Start with the bit in the brackets na+1 🙂 easy so far!
  5. Multiply the answer by Na 🙂 going well!
  6. Divide the answer by 2 🙂 who said stats was hard!
  7. Now do Na multiplied by Nb and add the answer to the bit you just worked out 🙂 easy-peasy but make sure your workings are all neat and tidy
  8. Last bit subtract the total of the ranks in condition A (we called it Ra earlier) 🙂 Okay that’s you done for calculating Ua
  9. Now its time to work out Ub, follow the formula carefully just like you did above and write your workings really neatly so the examiner can award to lots of lovely marks!
  10. Okay last bit now you have Ua and Ub decide which is smaller, let’s call it U!
  11. Now you have your observed/calculated value you need to find the correct critical values table according to whether your hypothesis is directional or non-directional (one or two tailed), start with the 0.05 level of significance. To find the correct critical value you will need to know Na and Nb again.
  12. Circle the critical value; use two pieces of paper one vertical/one horizontal to guide you and make sure your eye does not wander off the the wrong row or column!
  13. Now compare your observed value and the critical value, if your value is less than the critical value, you can accept your experimental hypothesis and reject the null (p<0.05). If your value is bigger than the one in the table , you have to reject your hypothesis and accept the null, (p>0.05).
  14. Remember when answering questions about interpreting the results of a stats test always use both the critical value and the observed value in your answer and always relate your answer to the actual hypothesis that they have outlined in the scenario, (contextualise!)
Rosie placed a sign saying “keep off the grass” in a local park. She put it in an area which was a popular short cut to the train station. She watched the passers-by and noted whether they obeyed the sign or not. She then asked them to complete a short questionnaire, which they could access on their mobile phone, to measure their “desire for personal control”. The questionnaire was out of 20, where 0 indicated no desire for personal control and 20 indicated a very high desire for personal control.
a. Write a suitable directional alternative hypothesis for Rosie’s study (3)
b. What participant design is Rosie using? (1)

Rosie’s results were as follows:

Did not obey the sign (walked across the grass) Obeyed the sign (stayed off the grass)
Pp1 14 13
Pp2 17 8
Pp3 15 12
Pp4 11 13
Pp5 14 6
Pp6 16 9
Pp7 10 12

c. Rosie thinks she ought to do a Chi Squared test but her friend April tells her she needs to do a Mann Whitney U test. April is right, what might she say to convince Rosie to the Mann Whitney U test? (3)

d. Rosie decides to go ahead with the Mann Whitney U test. Use the data table above to work out the observed value of U. The formula is at the front of the booklet.( 4)

Show ALL your workings:

U is equal to:

e. Should Rosie reject her null hypothesis? (1)

f. Explain your answer, making reference to the critical values tables at the front of this booklet (3)