• Wilcoxon signed ranks test of difference

The Wilcoxon signed-rank test is a non-parametric statistical test used to compare the difference between two related, but not necessarily dependent, samples. In psychology, it is often used to compare the difference in scores between two groups on a single measure (e.g. pre- and post-test scores on a single questionnaire). Here’s how to use it:

  1. Determine the hypothesis: State the null and alternative hypotheses being tested.
  2. Organise the data: Pair up the observations from the two groups and calculate the difference between each pair.
  3. Rank the differences: Assign a rank to each difference, treating positive and negative differences separately.
  4. Calculate the test statistic: The test statistic is the sum of the ranks for the positive differences.
  5. Determine the significance level: Compare the test statistic to a critical value from the Wilcoxon table to determine the p-value.
  6. Draw conclusion: If the p-value is less than the significance level (e.g. alpha = .05), reject the null hypothesis and conclude that there is a significant difference between the two groups.

Past Paper Questions

  • Determine whether this result is significant or not (Wilcoxon). (1) June 2016
  • Explain whether Zulikhat’s result is significant or not (Wilcoxon). (2) June 2019
  • Complete Table 4 and calculate the Wilcoxon Signed Ranks test. (4) January 2020