How to Run a Paired Samples T-Test in SPSS and Interpret Results

The paired samples t-test compares the means of two related measurements from the same group of participants. It is the standard test for pre-test/post-test designs, before-and-after studies, and matched-pair experiments. If you measured the same people twice under different conditions, this is the test you need.

When to Use the Paired Samples T-Test

Use this test when:

• You have one group of participants measured at two time points (pre and post)
• You are comparing two related conditions measured on the same participants (e.g., test performance under noise vs. silence)
• You have matched pairs where each participant in one group is matched with a participant in the other group
• The dependent variable is continuous (interval or ratio scale)

Example research questions:

• Did the training program significantly improve employee performance scores?
• Is there a significant difference in anxiety levels before and after the intervention?
• Do students score differently on math versus reading assessments?

Assumptions

Before running the test, verify these assumptions:

1. Continuous Dependent Variable

The dependent variable must be measured on an interval or ratio scale (e.g., test scores, time, weight, rating scales treated as continuous).

2. Related Pairs

Each observation in one condition must be meaningfully paired with an observation in the other condition. Typically, this means the same participant is measured twice.

3. No Significant Outliers in the Difference Scores

Calculate the difference between paired observations. There should be no extreme outliers in these difference scores.

How to check: Create the difference variable (Transform → Compute Variable), then use Analyze → Explore to generate a boxplot. Cases beyond the whiskers are potential outliers.

4. Approximate Normality of the Difference Scores

The distribution of the difference scores should be approximately normal. This is especially important for small samples (n < 30).

How to check: Run the Shapiro-Wilk test on the difference scores (Analyze → Explore → Plots → Normality plots with tests). If p > .05, the normality assumption is met.

For samples larger than 30, the paired samples t-test is robust to mild violations of normality due to the Central Limit Theorem.

Step-by-Step in SPSS

Step 1: Set Up Your Data

Your data should have one row per participant and two columns — one for each measurement. For example:

Participant	Pre_Score	Post_Score
1	42	58
2	55	61
3	38	49
4	47	52

Step 2: Run the Test

1. Go to Analyze → Compare Means → Paired-Samples T Test
2. Select your two variables and move them into the Paired Variables box
   • Variable 1: Pre-test measurement
   • Variable 2: Post-test measurement
3. Click OK

Step 3: Optional — Enable Effect Size

In newer versions of SPSS (Version 27+):

1. Click Options before running the test
2. Check Effect size (Cohen's d)
3. Click Continue, then OK

Interpreting the Output

SPSS produces three tables. Here is what each one tells you.

Table 1: Paired Samples Statistics

This table shows the descriptive statistics for each variable:

• Mean: The average score for each time point
• N: The number of valid pairs
• Std. Deviation: The standard deviation for each variable
• Std. Error Mean: The standard error of the mean

Look at the means to see the direction of change. If the post-test mean is higher than the pre-test mean, scores increased on average.

Table 2: Paired Samples Correlations

This table shows the Pearson correlation between the two measurements.

• A positive correlation means participants who scored high at pre-test tended to score high at post-test as well
• The correlation should typically be positive and significant in a pre-test/post-test design, confirming that the measurements are indeed related

If the correlation is very low or negative, consider whether the paired design is appropriate.

Table 3: Paired Samples Test

This is the most important table. It tests whether the mean difference between the paired measurements is significantly different from zero.

Key values:

• Mean (of the difference): The average difference between paired observations. If Pre was subtracted from Post, a positive mean indicates an increase
• Std. Deviation: The standard deviation of the difference scores
• Std. Error Mean: The standard error of the mean difference
• 95% Confidence Interval of the Difference: If this interval does not contain zero, the difference is significant at the .05 level
• t: The t-statistic
• df: Degrees of freedom = N − 1 (number of pairs minus 1)
• Sig. (2-tailed): The p-value

Decision rule:

• If Sig. (2-tailed) < .05, there is a statistically significant difference between the two measurements
• If Sig. (2-tailed) > .05, the difference is not statistically significant

Calculating Effect Size

Effect size tells you how large the difference is in practical terms. The most common measure for paired samples t-tests is Cohen's d.

If SPSS Reports It

In SPSS Version 27 and later, Cohen's d appears in the output if you enabled it in Options.

Manual Calculation

If your version of SPSS does not report it, calculate it yourself:

Cohen's d = Mean difference ÷ Standard deviation of the difference scores

Both values are available in the Paired Samples Test table.

Interpretation:

• d = 0.2: Small effect
• d = 0.5: Medium effect
• d = 0.8: Large effect

APA Reporting

Format

A paired samples t-test was conducted to compare [DV] before and after [intervention/condition]. There was a significant difference in scores between pre-test (M = [mean], SD = [SD]) and post-test (M = [mean], SD = [SD]); t(df) = [t-value], p = [p-value], d = [Cohen's d].

Example

A paired samples t-test was conducted to compare anxiety scores before and after the mindfulness intervention. There was a significant reduction in anxiety from pre-intervention (M = 42.30, SD = 8.15) to post-intervention (M = 35.60, SD = 7.42); t(29) = 4.87, p < .001, d = 0.89, indicating a large effect.

When Results Are Not Significant

A paired samples t-test indicated no significant difference in job satisfaction between the first assessment (M = 3.85, SD = 0.92) and the second assessment (M = 3.91, SD = 0.88); t(44) = 0.72, p = .476, d = 0.11.

One-Tailed vs. Two-Tailed Tests

By default, SPSS reports a two-tailed p-value. If you have a directional hypothesis (e.g., "scores will increase after the intervention"), you can use a one-tailed test:

One-tailed p-value = Two-tailed p-value ÷ 2

Only use a one-tailed test when your hypothesis was directional before you collected the data and this is stated in your proposal.

What to Do When Assumptions Are Violated

Outliers in Difference Scores

If you find extreme outliers:

1. Verify they are not data entry errors
2. Run the analysis with and without the outliers
3. If results differ substantially, report both and discuss the impact
4. Consider using a non-parametric alternative

Non-Normal Difference Scores

If the Shapiro-Wilk test is significant (p < .05), indicating non-normality:

Use the Wilcoxon Signed-Rank Test — the non-parametric equivalent of the paired samples t-test.

1. Go to Analyze → Nonparametric Tests → Legacy Dialogs → 2 Related Samples
2. Move your paired variables into the Test Pairs box
3. Check Wilcoxon
4. Click OK

Common Mistakes to Avoid

1. Using an independent samples t-test instead — If the same participants are measured twice, you must use the paired test. An independent test treats the observations as unrelated and produces incorrect results
2. Ignoring the direction of the difference — The sign of the mean difference depends on which variable SPSS subtracted from which. Always check the Paired Samples Statistics table to confirm the direction
3. Not checking assumptions — Especially normality of difference scores in small samples. Violations may require a non-parametric alternative
4. Reporting the wrong means — Report the means for each time point from Table 1, not the mean difference from Table 3
5. Forgetting effect size — Statistical significance tells you whether the difference is real, but effect size tells you whether it matters. Always report Cohen's d

Paired Samples T-Test vs. Other Tests

Scenario	Correct Test
Two related measurements, continuous DV, normal differences	Paired samples t-test
Two related measurements, ordinal DV or non-normal differences	Wilcoxon signed-rank test
Two independent groups, continuous DV	Independent samples t-test
Three or more related measurements	Repeated measures ANOVA
Two related categorical measurements	McNemar's test

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