Paired-samples t-test in SPSS

Do you have data from the same people at two points in time – e.g., before and after a training session – and need to analyze it in SPSS? Then you need the t-test for dependent samples. This test examines whether the two measurements differ significantly. It is typically used for pre–post measurements, but also for measurements of pairs or twin studies.

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What is the paired t-test about?

Definition:
The t-test for dependent samples examines whether the means of two related measurements differ from each other.
Null hypothesis: $H_0: \\mu_{\\text{diff}} = 0$
Alternative hypothesis: $H_1: \\mu_{\\text{diff}} e 0$

The difference is calculated for each person, and then we test whether the mean of these differences deviates significantly from zero.

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Assumptions

Before conducting the test, you should make sure that:

• The measurements are metric (e.g., scale values from 1–10)
• Each person has two values (e.g., before and after)
• The differences are approximately normally distributed

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Example: Stress level before and after a seminar

You measure the perceived stress of 20 participants before and after a mindfulness training. The two variables are called:

• stress_vorher
• stress_nachher

Goal: Did the average stress level change after the seminar?

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Step-by-step guide in SPSS

1. Prepare the file

Make sure that both variables (e.g., stress_vorher and stress_nachher) are available in two columns and have been entered correctly.

2. Open the test

Go to:

Analyze → Compare Means → Paired-Samples T Test...

3. Select the variables

• Drag stress_vorher into the Variable 1 column
• Drag stress_nachher into the Variable 2 column

Confirm by clicking OK.

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Interpreting the SPSS output

You will receive two tables:

Table 1: Statistics

Variable 1	Variable 2	Mean 1	Mean 2	Difference	SD of the difference
stress_vorher	stress_nachher	7.00	6.00	1.00	0.80

Table 2: Test results

t	df	Sig. (2-tailed)	Confidence interval
5.123	19	.00005	[0.60; 1.40]

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Interpreting the results

Statistic	Meaning
t = 5.123	Test statistic – magnitude of the deviation from the mean
df = 19	Degrees of freedom: n – 1
Sig. (2-tailed) = .00005	Very small p-value → very likely not due to chance
Confidence interval	With 95% confidence, the true mean difference lies between 0.60 and 1.40

Conclusion: Stress levels have decreased significantly after the seminar.

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Optional: One-tailed hypothesis

SPSS tests two-tailed hypotheses by default. If you have a directional hypothesis (e.g. “Stress will decrease”), you must:

1. Justify the direction (e.g. with theory or previous studies)
2. Halve the p-value if the sign points in the expected direction

Example:

• p (two-tailed) = 0.00005
• Positive difference → Stress_vorher > Stress_nachher
• → p (one-tailed) = 0.000025 → highly significant

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Summary

Step	What you do
1	Prepare a file with two columns: e.g. before, after
2	Analyze → Compare means → Paired-samples t-test
3	Select variables and run the test
4	Interpret the result: t, p-value, confidence interval
5	Optional: Justify a directional hypothesis and interpret the result one-tailed

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Q&A to think along with

Question 1: When do you use the t-test for dependent samples?
Answer: When you have two related measurements per case—e.g. before-and-after comparisons or measurements from twins.

Question 2: What is the purpose of the test?
Answer: To determine whether the mean of the differences differs significantly from zero.

Question 3: What does a p-value of 0.00005 indicate?
Answer: It is very unlikely that this difference occurred by chance. The difference is statistically highly significant.

Question 4: How can you take a directional hypothesis into account?
Answer: Only if it is justified beforehand. In that case, you may halve the p-value if the result is in the expected direction.