One-Sample T Test in SPSS (Step-by-Step)

A one-sample t-test compares the mean of a sample to a known or hypothesized population value. Researchers often use this test to determine whether a sample average differs significantly from a specific benchmark or expected value. This guide explains what a one-sample t-test is, when to use it, and the key assumptions of the test. You will also learn how to run a one-sample t-test in SPSS step-by-step with an example, interpret the SPSS output tables, and report the results correctly in APA style.

What is a One-Sample t-Test?

A one-sample t-test is a statistical test that compares the mean of a sample to a known or hypothesized population value. Researchers use this test to determine whether the sample average differs significantly from a specific benchmark. The test evaluates whether the difference between the sample mean and the test value is large enough to conclude that the sample mean is not equal to the hypothesized value.

Researchers often apply a one-sample t-test when they want to compare observed data to a known standard or expected value. For example, a researcher may test whether the average study time of students differs from 5 hours per day, or whether the average customer satisfaction score differs from 4 out of 5. Statistical software such as SPSS allows researchers to run this test quickly and determine whether the difference is statistically significant.

When to Use a One-Sample t-Test

Use a one-sample t-test when your study involves one group of observations, and you want to evaluate the average value of a variable against a specific reference point.

This test is appropriate in situations such as:

• When you want to determine whether an average measurement meets a target or standard
• When you want to evaluate whether a policy, program, or intervention changes an average outcome
• When researchers want to verify whether observed results match expected benchmarks
• When analyzing sample data collected from one population group

For example, researchers may apply a one-sample t-test to evaluate whether the average exam score in a class meets a required pass mark, whether the average waiting time in a hospital exceeds a target limit, or whether the average production output meets a company standard.

Hypotheses

A one-sample t-test evaluates the hypotheses:

• Null hypothesis (H₀): the population mean is equal to the hypothesized value
• Alternative Hypothesis (H₁): the population mean is different from the hypothesized value.

For example, suppose a manufacturer claims that the average weight of a packaged product is 500 grams. A researcher collects a sample of products to test this claim. The null and alternative hypotheses for this example will be:

• H₀: μ = 500 grams (the average product weight is 500 grams)
• H₁: μ ≠ 500 grams (the average product weight is different from 500 grams)

By performing the one-sample t-test, you can determine whether there is enough evidence to reject the null hypothesis.

Assumptions of the One-Sample t-Test

Before using a one-sample t-test, researchers should ensure that several statistical assumptions are satisfied. These assumptions help ensure that the results of the test are reliable and valid.

1. The Dependent Variable Is Continuous

The variable being analyzed must be measured on a continuous scale. This means the values should represent quantities that can take many possible values within a range.

Examples of continuous variables include:

• Test scores
• Study hours
• Income
• Weight
• Blood pressure

Tip. A one-sample t-test is not appropriate for categorical variables such as gender, education level, or marital status.

2. Observations Are Independent

Each observation in the dataset should represent one independent measurement. The value recorded for one participant should not influence the value recorded for another participant.

For example:

• Each student in a study contributes one test score.
• Each patient contributes one measurement.

If the same participant appears multiple times in a way that affects independence, the results of the test may become unreliable.

3. The Data Are Approximately Normally Distributed

The one-sample t-test assumes that the distribution of the variable is approximately normal, especially when the sample size is small.

Researchers often check this assumption by examining:

• Histograms
• Q–Q plots
• Normality tests such as the Shapiro–Wilk test

When the sample size is reasonably large (for example, n ≥ 30), the t-test is generally robust to small deviations from normality.

4. The Data Are Collected from a Random Sample

The observations should come from a random sample of the population. Random sampling helps ensure that the sample represents the population fairly.

If the sample is biased or not representative, the results of the test may not generalize to the broader population.

5. The Data Should Not Contain Extreme Outliers

Extreme outliers can strongly influence the sample mean and may distort the results of the t-test. Researchers should examine the data for unusual values before performing the analysis.

Common ways to detect outliers include:

• Boxplots
• Z-scores
• Exploratory data analysis

If strong outliers are present, researchers should investigate whether they represent data entry errors or unusual observations.

Ensuring that these assumptions are reasonably satisfied helps researchers apply the one-sample t-test correctly and interpret the results with confidence.

How to Run A One-Sample-Test In SPSS: Step-by-Step

Running a one-sample t-test in SPSS is straightforward once your dataset is ready. The process involves entering the data, selecting the appropriate test in the SPSS menu, and specifying the value you want to compare the sample mean against. The example below demonstrates the exact steps you should follow to perform a one-sample t-test in SPSS.

Example. Suppose a researcher wants to determine whether the average daily study time of university students differs from 5 hours. The researcher collects study time data from 30 students and records the number of hours each student studies per day.

The dataset contains one variable called StudyHours, which stores the number of study hours for each student.

Student	StudyHours
1	4
2	6
3	5
4	7
5	5
6	6
7	4
8	8
9	5
10	6
11	7
12	5
13	6
14	4
15	5
16	7
17	6
18	5
19	4
20	6
21	7
22	5
23	6
24	4
25	8
26	5
27	6
28	7
29	5
30	6

We will now use SPSS to test whether the sample mean differs significantly from 5 hours. The following steps show how to run a one-sample t-test in SPSS using this dataset.

Step 1: Enter or Import Your Data in SPSS

The first step is to enter your dataset into SPSS. In SPSS, the data file works like a spreadsheet.

• Each row represents one participant (in this case, one student).
• Each column represents a variable measured in the study.

For this example, the dataset contains a single variable called StudyHours, which records the number of hours each student studies per day.

Variable View

Start by defining the variable in Variable View.

Create a variable with the following settings:

Name	Type	Label	Measure
StudyHours	Numeric	Daily study hours	Scale

This tells SPSS that StudyHours is a numeric variable measured on a continuous scale. Your variable view should be as shown below.

Data View

Next, switch to Data View and enter the study hours for the 30 students. Each row should contain one value for the variable StudyHours.

The Data View should be as shown below.

Alternatively, instead of entering the data manually, you can enter the data in Excel and save it either as CSV or Excel format. You can then use the procedure below to import it into SPSS.

File → Import Data → Excel if you saved it as a .xlsx data, or File → Import Data → CSV Data if you saved it as a .csv data.

Then browse the location and select the Excel or CSV file containing your dataset.

Step 2: Click Analyze → Compare Means → One-Sample T Test

After entering the dataset, go to the top menu bar in SPSS and follow this path:

Analyze → Compare Means → One-Sample T Test

Clicking this option opens the One-Sample T Test dialog box. This window allows you to choose the variable you want to analyze and enter the test value that SPSS will use to compare against the sample mean.

You should see the following dialog box.

Step 3: Select the Test Variable and Enter the Test Value

In the One-Sample T Test dialog box, select the variable you want to analyze and specify the value you want to compare the sample mean against.

First, select the variable StudyHours from the list on the left. Then click the arrow button to move it into the Test Variable(s) box.

Next, enter the Test Value. The test value is the number that SPSS will use to compare against the sample mean. In this example, the researcher wants to test whether the average study time differs from 5 hours, so the test value is 5.

Therefore, enter:

Test Value = 5

Once you select the test variable and enter the test value, the setup for the one-sample t-test is complete.

The dialog box should be as shown below.

Step 4: Click OK to Run the Test

After selecting the test variable and entering the test value, click OK to run the analysis.

SPSS will process the request and generate the results in the Output Viewer. The output will include tables that summarize the sample statistics and the results of the one-sample t-test.

The SPSS output produced for this example is shown below.

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SPSS Output Tables Explanation

After you run a one-sample t-test in SPSS, the results appear in the Output Viewer. SPSS generates several tables that summarize the data and show the results of the hypothesis test. In this example, the main tables are:

• One-Sample Statistics
• One-Sample Test
• One-Sample Effect Sizes

Each table provides different information that helps you interpret the results.

1. One-Sample Statistics Table

The One-Sample Statistics table summarizes the descriptive statistics of the sample. It shows basic information about the data before the hypothesis test is evaluated.

In this example, the table reports:

• N = 30 → the number of observations included in the analysis
• Mean = 5.6667 → the average study time of the students
• Std. Deviation = 1.15470 → the amount of variation in study hours among the students
• Std. Error Mean = 0.21082 → the estimated standard deviation of the sampling distribution of the mean

This table helps you understand the characteristics of the sample data.

For this study:

• The average study time is about 5.67 hours per day.
• The standard deviation (1.15) shows that study hours vary across students.
• The standard error (0.21) indicates how precisely the sample mean estimates the population mean.

Researchers typically use the mean and standard deviation from this table when reporting results in APA style.

2. One-Sample Test Table

The One-Sample Test table contains the main results of the hypothesis test. It shows whether the sample mean differs significantly from the hypothesized value.

In this example, SPSS compares the sample mean to the test value of 5 hours.

The table includes the following values:

• t = 3.162 → the t-statistic that measures how far the sample mean is from the test value
• df = 29 → the degrees of freedom for the test (calculated as n − 1)
• Sig. (2-tailed) = .004 → the p-value used to determine statistical significance
• Mean Difference = 0.66667 → the difference between the sample mean and the test value
• 95% Confidence Interval = 0.2355 to 1.0978 → the range of plausible values for the true mean difference

These values help determine whether the difference between the sample mean and the hypothesized value is statistically significant.

From the table, we can observe:

• The sample mean is higher than the test value by about 0.67 hours.
• The p-value (.004) is smaller than 0.05, which indicates a statistically significant difference.
• The confidence interval does not include zero, which supports the conclusion that the true mean is different from 5 hours.

This table is the most important table for interpreting the results of the one-sample t-test.

3. One-Sample Effect Sizes Table

The One-Sample Effect Sizes table provides information about the magnitude of the difference between the sample mean and the hypothesized value. While the p-value shows whether the difference is statistically significant, the effect size shows how large the difference is in practical terms.

In this example, SPSS reports two effect size measures:

• Cohen’s d = 0.577
• Hedges’ correction = 0.562

SPSS also provides 95% confidence intervals for these estimates:

• Cohen’s d CI = 0.186 to 0.960
• Hedges’ correction CI = 0.181 to 0.935

These values indicate the strength of the difference between the sample mean and the test value.

Using common interpretation guidelines for Cohen’s d:

• 0.2 → small effect
• 0.5 → medium effect
• 0.8 → large effect

In this example:

• 0.577 indicates a moderate effect size

This means that the difference between the sample mean and the hypothesized value is not only statistically significant but also meaningful in size.

Which Tables Are Most Important?

When interpreting a one-sample t-test in SPSS, focus mainly on these tables:

• One-Sample Statistics → provides the sample mean, standard deviation, and sample size
• One-Sample Test → shows the t-value, degrees of freedom, p-value, mean difference, and confidence interval
• One-Sample Effect Sizes → indicates the practical magnitude of the difference

Together, these tables allow researchers to summarize the sample data, test the hypothesis, and evaluate the practical importance of the results.

How to Interpret One-Sample T-Test Results

To interpret the results of a one-sample t-test, focus on the Sig. (2-tailed) value in the One-Sample T-Test table. This value represents the p-value of the test.

Decision Rule

• If p ≤ 0.05 → there is a statistically significant difference between the sample mean and the test value.
• If p > 0.05 → there is no statistically significant difference.

From the SPSS output:

• Sample mean = 5.67 hours
• Test value = 5 hours
• t(29) = 3.162
• p = 0.004

Since p = 0.004, which is less than 0.05, the result is statistically significant. This means the average study time of the students differs significantly from 5 hours.

Therefore, you can write the interpretation as follows:

The sample mean study time was 5.67 hours per day. A one-sample t-test showed that the average study time of students was significantly higher than 5 hours, t(29) = 3.162, p = 0.004. This result suggests that students in the sample study more than the hypothesized average of 5 hours per day.

How to Report a One-Sample T-Test SPSS Outputs in APA Style

When reporting the results of a one-sample t-test, you should include the sample mean (M), standard deviation (SD), t-statistic, degrees of freedom (df), and p-value.

Based on the SPSS output in this example:

• Mean (M) = 5.67
• Standard deviation (SD) = 1.15
• t statistic = 3.162
• Degrees of freedom (df) = 29
• p-value = .004

Here’s how you should report the results from the SPSS Outputs in APA style.

A one-sample t test was conducted to determine whether the average daily study time of university students differed from the hypothesized value of 5 hours. The results showed that students studied significantly more than 5 hours per day (M = 5.67, SD = 1.15), t(29) = 3.16, p = .004. These results indicate that the mean study time of the sample is significantly higher than the hypothesized average of 5 hours.

Key Takeaways

A one-sample t-test compares the mean of a sample to a known or hypothesized value. Researchers often use this test to determine whether the average of a variable differs significantly from a specific benchmark.

Running a one-sample t-test in SPSS is straightforward. Once your dataset is ready, you only need to follow a few simple steps to perform the analysis and interpret the results.

1. Enter the dataset and define the variable in SPSS
2. Click Analyze → Compare Means → One-Sample T Test
3. Move the variable into the Test Variable(s) box and enter the test value (the hypothesized mean)
4. Click OK to run the test

Once you have the outputs, you can either interpret them or write a report in APA style if needed.

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