Paired t-Test vs Wilcoxon in SPSS: Which to Use?

Two Measurements, One Question: Which Test Fits Your Data?

You measured the same people twice — before and after a training course, at baseline and follow-up, under two conditions — and now you need to know whether the scores really changed. Two tests compete for this job in SPSS: the paired-samples t-test and the Wilcoxon signed-rank test. They answer the same question, but they make different assumptions about your data, and picking the wrong one can weaken an otherwise solid analysis.

This guide explains the difference, shows you how to run both tests in SPSS with click-by-click steps and syntax, and shows you how to report the result in APA style (7th ed.).

Paired t-Test vs Wilcoxon: The Core Difference

The paired-samples t-test compares the means of two related measurements. It asks: is the average difference between the two time points reliably different from zero? It is a parametric test, which means it works best when the differences between the paired scores are approximately normally distributed.

The Wilcoxon signed-rank test compares the ranks of the differences instead of their raw values. It asks a similar question — do the scores tend to shift in one direction? — but it does not assume the differences follow a normal distribution. That makes it the safer choice when your data are skewed, contain outliers, or are measured on an ordinal scale.

The t-test uses every point of information in your numbers, giving it more power when its assumptions hold. Wilcoxon trades some of that power for robustness: when the data are well behaved, the t-test wins; when they are not, Wilcoxon is the honest choice.

When to Use the Paired t-Test

Choose the paired t-test when all of the following are true:

Your data are paired. Each case contributes two scores — the same person, the same matched pair, or the same unit measured twice.
The variable is continuous. Scores are measured on an interval or ratio scale, such as test marks, reaction times, or blood pressure readings.
The differences are approximately normally distributed. It is the distribution of the difference scores that matters, not the distribution of each variable on its own.
There are no extreme outliers in the differences. A single wild difference can drag the mean — and the t-test — off course.

If these conditions hold, the paired t-test is the standard, most powerful option, and it is the one most readers and reviewers will expect to see.

When to Use the Wilcoxon Signed-Rank Test

Reach for the Wilcoxon signed-rank test when any of these apply:

The differences are clearly non-normal. A Shapiro-Wilk test on the difference scores is significant, and a histogram or Q-Q plot shows strong skew.
Outliers are present and meaningful. The extreme values are real data, not errors, so you do not want to delete them — but you do not want them to dominate the result either.
Your data are ordinal. Likert-scale ratings, ranked preferences, or any score where the gaps between values are not equal in meaning.
Your sample is small. With very few pairs, normality is hard to verify, and the rank-based test is the more defensible choice.

One caution: Wilcoxon assumes the differences are roughly symmetric around the median. If they are heavily skewed, even Wilcoxon can mislead, and a sign test — which assumes still less — may be worth considering.

Quick Decision Checklist

Question	If yes
Are the two scores from the same people or matched pairs?	Either test applies — both are for paired data. If the groups are independent, you need an independent-samples t-test or a Mann-Whitney U test instead.
Is the variable continuous (interval or ratio)?	Paired t-test is possible; check normality next.
Is it ordinal, such as Likert ratings?	Use the Wilcoxon signed-rank test.
Are the difference scores approximately normal, with no severe outliers?	Use the paired t-test.
Are the differences skewed, or do they contain outliers you cannot remove?	Use the Wilcoxon signed-rank test.
Is the sample very small (for example, fewer than 15 pairs)?	Prefer the Wilcoxon test unless normality is clear.

How to Check the Normality of the Differences First

Before choosing, create the difference scores and inspect them. This one-minute check is what separates a defensible choice from a guess.

Go to Transform > Compute Variable.
Name the target variable Diff and enter the numeric expression as After – Before (replace with your own variable names), then click OK.
Go to Analyze > Descriptive Statistics > Explore.
Move Diff into the Dependent List and click Plots.
Tick Histogram and Normality plots with tests, then click Continue and OK.

Read the Shapiro-Wilk row: a non-significant result (p > .05) supports normality, as does a roughly straight line on the Q-Q plot. A significant result (p < .05), a skewed histogram, or points bending away from the diagonal point toward Wilcoxon. With large samples Shapiro-Wilk can flag trivial departures, so always read the plots alongside the p-value.

Syntax for the difference scores and the normality check:

COMPUTE Diff = After - Before.
EXECUTE.

EXAMINE VARIABLES=Diff
  /PLOT HISTOGRAM NPPLOT
  /STATISTICS DESCRIPTIVES
  /CINTERVAL 95
  /MISSING LISTWISE
  /NOTOTAL.

How to Run the Paired t-Test in SPSS

Go to Analyze > Compare Means > Paired-Samples T Test.
Click the first variable (for example, Before) and move it into the Pair 1 Variable 1 slot, then click the second variable (After) and move it into Pair 1 Variable 2.
Click Options to confirm the confidence interval is set to 95%, then click Continue.
Click OK to run the test.

Syntax:

T-TEST PAIRS = Before WITH After
  /MISSING = ANALYSIS
  /CRITERIA = CI(.95).

To add an effect size, tick the Estimate effect sizes box in the dialog (available in recent SPSS versions), or compute Cohen’s dz by hand from the output: divide the t-value by the square root of the number of pairs (dz = t / √N). Values around 0.2, 0.5 and 0.8 are conventionally described as small, medium and large, but those labels are only rough guides — interpret the size in the context of your field.

How to Run the Wilcoxon Signed-Rank Test in SPSS

Go to Analyze > Nonparametric Tests > Legacy Dialogs > 2 Related Samples.
Move your two variables (Before and After) into the Test Pairs list.
Make sure Wilcoxon is ticked under Test Type, then click OK.

Syntax:

NPAR TESTS
  /WILCOXON = Before WITH After
  /MISSING ANALYSIS.

For an effect size, use the Z value from the output: r = Z / √N, where N is the total number of observations (twice the number of pairs). Values around .1, .3 and .5 are conventionally described as small, medium and large. Note that SPSS reports the Z statistic based on the negative ranks by default; use its absolute value when computing r, and report the direction of the change in words.

How to Interpret the Output

Paired t-test output

SPSS produces three tables. Paired Samples Statistics gives the mean and standard deviation for each time point — report these. Paired Samples Correlations shows how strongly the two measurements are related; a high correlation is expected and confirms the pairing was useful, but it is not the test result. Paired Samples Test holds the answer: the mean difference, its 95% confidence interval, the t-value, degrees of freedom (number of pairs minus one), and the two-tailed significance (p-value). If p < .05, the mean difference is statistically significant. The confidence interval tells you the plausible range of the true mean difference — if it excludes zero, that agrees with a significant result.

Wilcoxon output

The Ranks table shows how many pairs decreased (negative ranks), increased (positive ranks), and stayed tied, along with the mean rank and sum of ranks for each direction. The Test Statistics table gives the Z value and the asymptotic two-tailed significance. If p < .05, the shift between the two measurements is statistically significant. To describe the size of the change, report the medians of the two measurements alongside the Z value, the p-value, and the effect size r.

If the two tests disagree, trust the one whose assumptions your data meet, and report the assumption check that led you there — so the choice reads as principled, not a search for a smaller p-value.

Reporting in APA Style (7th ed.)

Report the test you ran, the descriptive statistics, the test statistic with degrees of freedom where applicable, the exact p-value (or p < .001 when it is very small), and an effect size. State the direction of the change in plain words.

Paired t-test example (illustrative values): “Scores increased from pre-test (M = 62.4, SD = 8.1) to post-test (M = 68.9, SD = 7.6), t(29) = 4.12, p < .001, dz = 0.75. The mean increase of 6.5 points, 95% CI [3.3, 9.7], was statistically significant.”

Wilcoxon example (illustrative values): “A Wilcoxon signed-rank test showed a significant increase from pre-test (Mdn = 61.0) to post-test (Mdn = 69.0), Z = −3.45, p < .001, r = .45.”

Also report the assumption check in a sentence: “Difference scores were approximately normally distributed, Shapiro-Wilk W(30) = .97, p = .42, so a paired-samples t-test was used” — or, when the check fails: “Difference scores departed from normality, Shapiro-Wilk W(30) = .88, p = .003, so a Wilcoxon signed-rank test was used instead.” Replace the numbers with your own output values.

Key Takeaways

Use the paired t-test when the differences between paired scores are approximately normal and free of extreme outliers — it is the more powerful option.
Use the Wilcoxon signed-rank test when the differences are skewed, contain real outliers, or the data are ordinal.
Always check the distribution of the difference scores — not the two variables separately — with a histogram, a Q-Q plot, and the Shapiro-Wilk test before deciding.
Report medians with Wilcoxon and means with the t-test, and always include an effect size (Cohen’s dz or r).
If the two tests disagree, trust the one whose assumptions your data meet, and say so in your write-up.

FAQs

Can I run both tests and report the one that is significant?

No. Choose the test before looking at the results, based on the distribution of the difference scores and the measurement scale. Running both and picking the significant one is a form of selective reporting that reviewers will rightly challenge.

What if my differences are normal but my sample is very small?

The t-test can still be appropriate if the differences look normal, but normality is hard to verify with few pairs. With fewer than about 15 pairs, many analysts prefer Wilcoxon as the safer choice — either way, justify it in the write-up.

What is the difference between the Wilcoxon signed-rank test and the sign test?

The sign test only counts how many differences are positive versus negative, ignoring how large they are. The Wilcoxon test also uses the size of the differences through their ranks, which makes it more powerful. Use the sign test only when the differences are strongly asymmetric and even Wilcoxon’s symmetry assumption is in doubt.

Do I need equal variances for a paired t-test?

No. Equal variances between groups is an assumption of the independent-samples t-test, not the paired version. The paired t-test only assumes the difference scores are approximately normally distributed.

Can I use the paired t-test on Likert-scale data?

It is commonly done, but strictly the t-test assumes interval-level data. For single Likert items, Wilcoxon is the more defensible choice; for composite scores averaged across many items, many researchers treat the scale as approximately continuous and use the t-test, provided the differences are normal.

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