Wilcoxon’s Signed Ranks Test

When is a Wilcoxon’s the correct test?

  • When you are testing to see whether there is a significant difference between two groups/conditions
  • When the experimental design is repeated measures
  • 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)

How do I do it?


If you are allowed to use an online calculator, try this one: https://www.socscistatistics.com/tests/signedranks/default2.aspx

If not you will need to work it out by hand following the instructions above which are taken form the Edexcel A Level exam booklet. Use the practice questions below and worked examples to guide yourself through.

  1. Researchers Bianco and Lecce (2016) believe they have discovered a way to train 8-9 year old children in “the theory of mind” (ToM), that is, the ability to think about the thoughts and perspectives of others. This is an ability  which is often thought to be lacking in children with autism and therefore any breakthrough in how to help children to develop their sills in this area would have major practical applications in society. They believe they can improve children’s test scores in just 4 x 50 minute sessions. They trained teachers in how to run the intervention for children at their schools and tested their “theory of mind” skills before and afterwards, by testing their comprehension of three stories involving “double bluff”, persuasion and misunderstanding. They also had a control group of children who completed an intervention unrelated to ToM and looked at how much the ToM skills developed over the course of the project without a specific ToM intervention.

The table below provides some made-up data about the children’s test scores so that you can practice your Wilcoxon’s skills!

ToM test scores (max score 120)
Pp Before ToM intervention After ToM intervention Before control intervention After control intervention
1 75 85 89 76
2 48 55 68 69
3 63 62 57 58
4 84 95 75 77
5 79 69 82 84
6 59 58 65 62
7 62 79 54 59
8 95 101 101 102
9 35 45 27 35
  1. Bianco and Lecce (2016) want to see whether the children who received the ToM intervention have made significant progress over the course of project by comparing their scores before and after the intervention. They have decided to use a Wilcoxon’s test. Explain why a Wilcoxon’s is a suitable test choice for them. (3)


2. Calculate the observed value of T by completing the following table and use the space to show the rest of your workings. (5)

Condition A Condition B Difference (d)




T value:


c. State whether Bianco and Lecce (2016) should use a one or a two tailed test when checking for significance and why (2)

d. State the appropriate critical value  (1)

e. State whether Bianco and Lecce (2016) would reject the null hypothesis based on this analysis and why (3)


If you want to practice another Wilcoxons, try this worksheet on the research by Olsson et al, that we looked at when studying phobias: method-and-stats-practice-question-based-on-olsson1 (1)