One-Sample t-Test in SPSS

You have metric data and want to know whether the mean differs significantly from a specific value? That’s exactly what the One-Sample t-Test in SPSS is for.

For example: You record how many hours psychology students sleep per night. Now you want to test whether the average really is 7 hours—or whether that’s just wishful thinking.

Aim of the test

Definition:
The one-sample t-test examines whether the mean of a sample differs significantly from a specified value (e.g., a norm or target value).

Requirements for the test

Before you get started, check whether the following conditions are met:

• Your variable is measured on a metric scale (interval or ratio scale)
• The data are approximately normally distributed, especially for small samples
• You have one independent sample

Example: Students’ sleep duration

Suppose you have an SPSS data file with a variable schlaf (in hours per night). Now you want to know: Does the mean differ significantly from 7 hours?

Step-by-step guide in SPSS

1. Open the data

Open your SPSS file and make sure that your variable is numeric and entered correctly (e.g., schlaf).

2. Open the test

Go to:

Analyze → Compare Means → One-Sample T Test...

3. Select the variable

• Move the variable schlaf to the Test Variable(s) field.
• In the Test Value field, enter the comparison value, e.g., 7.

4. Click OK

Click OK to run the test. SPSS will now generate output in the Output Viewer.

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Interpreting the SPSS output

You will get two tables:

Table 1: Sample Statistics

Variable	N	Mean	SD	SE
sleep	20	6.74	0.25	0.056

Table 2: One-sample t-test

Test value = 7	t	df	Sig. (two-tailed)	Mean difference	CI (95 %)
	-4.62	19	0.0002	-0.26	[-0.37, -0.15]

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Interpretation of the results

Key metric	Meaning
t = -4.62	Test statistic – how far does the mean deviate from the test value (in standard error units)?
df = 19	Degrees of freedom: n – 1
Sig. (2-tailed) = 0.0002	p-value – probability of obtaining such a result under H0
Mean difference = -0.26	The observed difference from the reference value
Confidence interval	The range in which the true mean lies with 95% confidence

Conclusion: The p-value is very small – so the result is statistically significant. You can reject the null hypothesis: On average, the students sleep less than 7 hours.

Optional: One-tailed hypothesis

SPSS tests two-tailed by default. If you want to test a directional hypothesis (e.g., “they sleep less”), you must:

1. Halve the two-tailed p-value
2. Check the sign of t (to determine the direction)

Example:

• t is negative, two-tailed p = 0.02 → then one-tailed p = 0.01 for “less than”
• But be careful: This is only permissible if you justified the direction theoretically in advance

Summary

Step	What you do
1	Open the SPSS file
2	Analyze → Compare Means → One-Sample t Test
3	Select a variable and enter the test value
4	Interpret the output: t-value, df, p-value, confidence interval
5	Interpret the result substantively and write the report

Q&A to think through

Question 1: What does the one-sample t-test test?
Answer: Whether the mean of a sample differs significantly from a theoretical comparison value.

Question 2: What information does the SPSS output provide?
Answer: The t-value, the degrees of freedom (df), the p-value (Sig.), the observed difference, and the confidence interval.

Question 3: When can you formulate a one-tailed hypothesis?
Answer: Only if the direction has been justified in advance—for example, based on theory or previous research.

Question 4: How do you interpret a p-value of 0.0002?
Answer: It is very unlikely that this difference arose by chance. The null hypothesis is rejected.