Wilcoxon Signed Rank Test: Concept, Interpretation, Reporting Wilcoxon Signed Rank Test

Wilcoxon signed-rank test is presented as a non-parametric alternative to the paired-samples t test for detecting whether an intervention changes outcomes measured on the same people before and after. Instead of relying on normality assumptions, it ranks the size of within-subject differences and then tracks whether those differences trend positive or negative. That makes it useful in practical “before–after” scenarios such as testing whether a new math-focused TV program boosts children’s interest, whether sleep duration changes after clinical treatment, or whether seminar-based learning shifts preferences.

The walkthrough centers on a market-research question: whether preference for watching social media ads changes after attending a seminar on learning through social media. The setup uses paired observations—each respondent provides a “pre-seminar” preference score and a “post-seminar” preference score. The analysis is framed with an alternative hypothesis that expects a significant change in preference after the seminar. The data are entered as two related samples (social media preference 1 for before, social media preference 2 for after), and the Wilcoxon signed-rank test is run under the “two related samples” option.

Results are interpreted through the sign and magnitude of the ranks. The output shows zero negative ranks, which would indicate post-seminar scores are lower than pre-seminar scores; that pattern does not occur here. Instead, all observed changes are in the positive direction: 11 respondents show an increase in preference, while 4 report no change. This directionality matters because it aligns the statistical conclusion with the substantive story—preferences rise rather than fall.

Statistical significance is reported using the test’s p-value. The significance value is given as 0.03, indicating a statistically significant change in preference after the seminar. The test statistic is summarized with a Z value of -3.17 (the negative sign reflects the direction coding used by the software; the interpretation focuses on the positive change shown by the rank counts). The p-value of 0.03 supports rejecting the null of no change.

Finally, the effect size is calculated to judge practical importance, not just statistical significance. The effect size formula used is r = Z / √n, with n taken as 30 because there are 15 pre and 15 post observations (paired, treated as 30 total cases in the calculation). Using Z = -3.17 yields r = 0.55. The magnitude is interpreted as a large effect size, leading to the conclusion that the seminar produced a significantly large positive shift in how people perceive or prefer watching social media advertisements.

Overall, the transcript ties together concept, direction of change, statistical significance, and effect size—showing how Wilcoxon signed-rank test can evaluate intervention impact in paired before–after designs when parametric assumptions are not appropriate.