Wilcoxon Signed-Rank Test Assignment Help — Paired Non-Parametric SPSS Test

What Is the Wilcoxon Signed-Rank Test and When Do You Use It?

The Wilcoxon signed-rank test is the non-parametric alternative to the paired samples t-test. It compares two related measurements from the same subjects (a pre/post design or matched pairs) using ranked differences rather than assuming those differences are normally distributed. Use it when your paired-difference scores are ordinal, or clearly violate the paired t-test’s normality assumption.

If your difference scores are reasonably normal, use the paired samples t-test instead. It has more power when its assumption holds.

Assumptions You Must Check Before Running It in SPSS

The two measurements must be genuinely paired: same subject, or a deliberately matched pair.
The dependent variable should be at least ordinal.
No normality assumption on the differences: that’s the reason to use this test instead of the paired t-test.
The distribution of differences should be reasonably symmetric for the “median difference” interpretation to be clean, though the test itself remains valid more broadly.

How to Run It in SPSS (Step by Step)

Go to Analyze > Nonparametric Tests > Legacy Dialogs > 2 Related Samples.
Select your two related variables and move them into Test Pair(s) List as Variable 1 and Variable 2.
Ensure Wilcoxon is checked under Test Type, then click OK.

How to Interpret the Output

Check the Ranks table first: it shows how many pairs had negative ranks (decreased), positive ranks (increased), and ties (no change). This tells you the direction of change before you even look at significance.
In the Test Statistics table, read the Z-value and Asymp. Sig. (2-tailed), your p-value.
Calculate effect size as r = Z ÷ √N (where N is the number of pairs, not individuals): 0.1 small, 0.3 medium, 0.5 large.

How to Report the Results in APA Format

A Wilcoxon signed-rank test showed that post-intervention scores were significantly higher than pre-intervention scores, with 24 positive ranks, 4 negative ranks, and 2 ties, Z = −3.41, p < .001, r = .48.

Wilcoxon Signed-Rank vs Paired Samples T-Test: Understanding the Difference

Both compare the same subjects measured twice. The paired t-test compares the mean difference and assumes it’s normally distributed; the Wilcoxon test compares ranked differences and makes no such assumption. With a small sample and visibly skewed or ordinal difference scores, Wilcoxon is the safer default. The paired t-test’s normality assumption is harder to defend with few observations.

If the Wilcoxon test doesn’t quite fit your design, one of these related non-parametric tests likely will:

Mann-Whitney U Test: the independent-groups version of this same rank-based comparison
Kruskal-Wallis H Test: for three or more independent groups instead of two related measurements
McNemar’s Test: for paired binary or categorical data instead of a continuous outcome
Spearman’s Rank Correlation: for testing a relationship between two ordinal or non-normal variables, rather than a paired difference

Not sure which one your data needs? See the full SPSS statistical test guide, or get help with this specific assignment.