How to Perform a One‑Sample t‑Test in SPSS: Step‑by‑Step Guide

1. Problem and Data

A researcher plans a health survey and wants to know whether the BMI mean of the 40 recruited subjects is representative of the target population, whose mean BMI is reported as 24 kg/m².

2. Analysis of the Problem

The researcher intends to test whether the sample mean differs from the population mean, which calls for a one‑sample t‑test, provided four assumptions are met:

Assumption 1: The variable is continuous (BMI is continuous).

Assumption 2: Observations are independent (each subject’s data are independent).

Assumption 3: No significant outliers are present.

Assumption 4: The variable is approximately normally distributed.

Assumptions 1 and 2 are satisfied by the study design. The next steps are to test assumptions 3 and 4 and then conduct the t‑test.

3. SPSS Procedure

3.1 Testing Assumption 3: No Significant Outliers

In SPSS, choose Analyze → Descriptive Statistics → Explore , move BMI to the Dependent List, and click Plots .

In the Explore: Plots dialog, keep the default Boxplots option, deselect Stem‑and‑leaf, and check Normality plots with tests . Click Continue → OK .

SPSS produces a boxplot; points farther than 1.5 × IQR from the box edge are marked with a small circle (°) as outliers, and points farther than 3 × IQR are marked with an asterisk (*) as extreme values. In this dataset no significant outliers are observed, satisfying Assumption 3.

3.2 Testing Assumption 4: Approximate Normality

After checking Normality plots with tests , the Shapiro‑Wilk test results appear.

Generally, a P‑value greater than 0.05 indicates normality. Here P > 0.05, so the data are approximately normally distributed, satisfying Assumption 4.

3.3 One‑Sample t‑Test

Choose Analyze → Compare Means → One‑Sample T Test , move BMI to Test Variable(s), set the Test Value to 24, and click OK .

4. Result Interpretation

4.1 Descriptive Statistics

The sample size is 40 (N = 40). The mean BMI is 23.67 ± 0.88.

4.2 One‑Sample t‑Test

The mean difference is –0.3275 with a 95 % confidence interval of –0.6103 to –0.0447. The test yields t = –2.342, P = 0.024, indicating a statistically significant difference between the sample mean and the population mean.

5. Conclusion

The data contain no significant outliers and are approximately normally distributed. The one‑sample t‑test shows that the sample mean BMI (23.67 ± 0.88) differs significantly from the population mean of 24 (t = –2.342, P = 0.024).