Two measurements on the same people, with differences that are not well behaved. What the test ranks, why the layout is the opposite of a two-group test, and how to report it in APA 7.
The Wilcoxon signed-rank test compares two measurements taken from the same people, using ranks rather than raw values. It is the rank-based counterpart to the paired-samples t test.
It works on the differences within each pair. Each difference is taken, the zeros are set aside, the remaining differences are ranked by size regardless of direction, and then the signs are put back. If the changes were random noise, the positive and negative ranks would roughly balance. When they do not, the test detects it.
That is more information than a sign test uses. A sign test only counts how many pairs went up. Wilcoxon also weighs how far each pair moved, which is why it detects a real change more readily.
The result opens with four figures: W+, labelled as the positive ranks, z, p stated as two-tailed, and r as the effect size.
W+ is the sum of the ranks for pairs that moved in the positive direction. On its own it is not comparable across studies, because it scales with the number of pairs. Do not read a large W+ as evidence of a large change.
The r effect size is what makes the result interpretable and is what most write-ups omit. A comparison returning W+ = 8124.0, z = 0.50, p = .620, r = 0.04 is not merely non-significant; the effect is essentially zero. A p value alone cannot distinguish those two statements.
The two-tailed label matters. A one-tailed p halves the apparent value, and stating it on the result removes any ambiguity about what was reported.
Reach for it when the differences are clearly skewed, when the outcome is ordinal, or when one or two pairs moved enormously and would dominate a mean difference.
Judge the differences, not the scores. This is the same trap as the paired t test. The condition concerns the distribution of the within-pair differences. Two skewed sets of scores can produce well-behaved differences, and two tidy-looking distributions can produce differences that are not.
The pairing must be real. Each row is one person or one unit measured twice, in a consistent order. If the two sets of scores come from different people, use Mann-Whitney U instead.
For three or more repeated measurements on the same people, use Friedman rather than running Wilcoxon on selected pairs, which inflates the error rate.
Lay the data out in wide format. One row per person, and the two measurements in two separate columns. This is the opposite of what a two-group test wants, and it is where most paired analyses break before they start.
Open Nonparametric & Categorical and select Wilcoxon signed-rank from the test list, then configure the two measurement columns in the Setup panel on the right. Results appear in the center.
Order determines the sign. Decide which measurement counts as the baseline before you run, since it sets whether an improvement reads as positive or negative.
Read the missing-cell count carefully. On a paired design a missing cell is a broken pair, and broken pairs are dropped entirely.
Use the action bar to add the result to a report, copy the table, or copy the APA text. Every result carries the ReliCheck Intelligence card for a plain-language explanation computed on your Mac.
Report the statistic, z, the two-tailed p, the effect size, and the number of pairs. Give medians for both measurements rather than means.
A Wilcoxon signed-rank test found no reliable difference between the two self-awareness items, W+ = 8124.0, z = 0.50, p = .620 (two-tailed), r = .04.
Include r. It is the difference between reporting an absence of evidence and reporting an effect near zero.
Report the number of pairs, and state how many were dropped for incomplete data. A reader cannot judge a change score without knowing who fell out of it.
Note how tied pairs were handled if there were many, since ties reduce the effective sample and the convention used affects the statistic.
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From the action bar you can add the result to a report, copy the table, or copy the APA text. Exported reports carry the APA table, its note, and a caution specific to that analysis beneath it.
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Paired-samples t test the parametric counterpart · Mann-Whitney U for two separate groups · Friedman for three or more repeated measurements · the complete list on the analyses page.