How to Run and Interpret t Tests in SPSS

What does a t test test?

A t test compares means. Depending on your data design, you can compare the mean of one group with a benchmark value, the means of two independent groups, or the means of two measurements taken from the same subjects. In SPSS, the three common forms are One-Sample t Test, Independent-Samples t Test, and Paired-Samples t Test.

Choose the test according to your research question. If you have one group and want to know whether its Mean differs from a fixed value, use One-Sample t Test. If you are comparing two different groups of people, such as men and women, use Independent-Samples t Test. If you measure the same group before and after an intervention, use Paired-Samples t Test.

A t test answers two questions: how large is the difference between the means, and is that difference statistically significant? If the grouping variable has three or more levels, also consider ANOVA, because running several separate t tests can increase the risk of an incorrect conclusion. You can also consult the materials in the Statistics topic to match the test to the type of variable.

H0 and H1 hypotheses

For every t test, define H0 and H1 before looking at the p-value. H0 usually states that there is no difference between the means. H1 states that the means differ, or that they differ in a direction specified in advance.

For Independent-Samples t Test, H0 states that the two group means do not differ in the population. H1 states that the two group means differ. For example, if the grouping variable is gender and the dependent variable is satisfaction, H0 states that the mean satisfaction of men and women is equal, while H1 states that the two means differ.

For Paired-Samples t Test, H0 states that the means of the two measurements taken from the same subjects do not differ. H1 states that the two measurements differ. For example, H0 states that evaluation scores did not change before and after a training program, while H1 states that the two time points show a change.

If your study has a one-tailed hypothesis, determine the direction of the test from the theoretical basis and research design before running the analysis. In many theses, results are read using a two-tailed test at the 5% significance level. Do not change H1 to “higher” simply because the Mean in the output is higher when the original hypothesis only stated that the means “differ.”

Conditions for applying a t test

Before running the test, check the variable type, group structure, independence, and data distribution. The table below is a practical checklist. Any threshold with a source is shown directly in the table so you can explain the decision if the committee asks.

For Independent-Samples t Test, Levene's Test only helps you choose the appropriate result row. It does not tell you whether the two groups have different means. For Paired-Samples t Test, the two variables must be two measurements of the same subjects. When checking distribution, pay attention to the distribution of the difference between the first and second measurements.

Steps for running a t test in SPSS

Step 1: Prepare the data and code the groups

In Variable View, set the outcome variable to Numeric and check Measure. For Independent-Samples t Test, the grouping variable must have exactly two codes, such as 1 and 2. Enter clear Value Labels, for example 1 for Men and 2 for Women, so the output is easy to read.

If the dependent variable represents a concept measured by several items, calculate the representative score using the method stated in your methods chapter. Usually, this is the mean of the acceptable items. Do not replace a composite scale with one item without a methodological reason.

Step 2: Run Independent-Samples t Test

Select Analyze > Compare Means > Independent-Samples T Test. Move the quantitative variable to Test Variable(s). Move the grouping variable to Grouping Variable, click Define Groups, and enter the correct two group codes. Click Continue and OK.

SPSS usually produces two main tables, Group Statistics and Independent Samples Test. Group Statistics shows N, Mean, standard deviation, and standard error for each group. Independent Samples Test contains Levene's Test and the t test results.

Step 3: Run Paired-Samples t Test

Select Analyze > Compare Means > Paired-Samples T Test. Select the first and second measurement variables as one pair. Click OK to create the Paired Samples Statistics, Paired Samples Correlations, and Paired Samples Test tables.

The main decision table is Paired Samples Test. Read the Mean of the difference, confidence interval, t value, df, and Sig. 2-tailed. If you have several pairs of variables, run and present them by hypothesis so that Chapter 4 is easier to follow.

Step 4: Run One-Sample t Test

Select Analyze > Compare Means > One-Sample T Test. Move the variable to be tested to Test Variable(s) and enter the benchmark value in Test Value. Use this value only when it matches the coding scheme and research question, such as testing whether the Mean differs from the midpoint of a scale.

One-Sample t Test does not replace a two-group comparison. If the question is whether men and women differ, use Independent-Samples t Test.

Step 5: Save the output and record your choices

Save the Output Viewer file together with the .sav data file. Record the t test type, dependent variable, grouping variable, group codes, and result row selected. If you rerun the analysis after cleaning the data, name each version clearly so that you do not copy an old table into Chapter 4.

Reading the results and drawing a conclusion

Read the output from description to test. First, look at N and Mean in Group Statistics or Paired Samples Statistics. Mean shows the direction of the difference, while Sig. (2-tailed) shows whether the difference is statistically significant at the selected alpha level.

The following is illustrative output, not the result of a real study. Column names are kept as SPSS prints them in the output.

For Independent-Samples t Test, start with Levene's Test for Equality of Variances. If Sig. is greater than or equal to 0.05, read the Equal variances assumed row. If Sig. is less than 0.05, read the Equal variances not assumed row. Then take Sig. (2-tailed) from that same row.

For Paired-Samples t Test, read the Paired Samples Test table directly. If Sig. (2-tailed) is less than 0.05, reject H0 at the 5% significance level and conclude that the two measurements differ statistically. If Sig. is greater than or equal to 0.05, there is not enough statistical evidence to reject H0. This wording is more careful than saying that “H0 is true.”

In the illustrative example, Independent-Samples t Test has Sig. equal to 0.046. If this is the appropriate variance row, the result is statistically significant at the 5% level. The Mean of Group 1 is approximately 0.24 points higher than that of Group 2. For Paired-Samples t Test, Sig. is 0.002, so the two measurements differ statistically in the illustrative sample, with the Mean after the intervention higher than the Mean before it.

How to write this in your thesis

You need to report both descriptive statistics and the test result. A sentence that only says “Sig. is less than 0.05, so the hypothesis is accepted” is incomplete, because the reader needs to know which group has the higher Mean, how large the difference is, and which result row you read.

You can adapt the following paragraph to your actual data: “The Independent-Samples t Test shows that the Mean of [group 1 name] is [Mean 1], while the Mean of [group 2 name] is [Mean 2]. Levene's Test has Sig. = [value], so the result is read from the [Equal variances assumed/Equal variances not assumed] row. Sig. (2-tailed) is [p-value], [less than/greater than or equal to] 0.05, indicating [that there is/that there is not] a statistically significant difference in [variable name] between the two groups.”

For Paired-Samples t Test, you can write: “The Mean of [measurement 1] is [Mean 1] and the Mean of [measurement 2] is [Mean 2]. The Paired-Samples t Test shows t([df]) = [t], Sig. (2-tailed) = [p-value]. Because [p-value] is [less than/greater than or equal to] 0.05, [H0 is rejected/there is not enough basis to reject H0], leading to the conclusion that [there is/there is not] a statistically significant change in [variable].”

If this test evaluates a hypothesis in your model, state clearly whether H1 is supported or not supported according to your department's convention. Use “there is a difference in the study sample” when the data come from only one survey sample.

What to use when assumptions are violated

If the data are strongly skewed, contain many outliers, or come from a small sample, examine the cause before changing the test. Check the histogram, Q-Q Plot, boxplot, and unusual records at Analyze > Descriptive Statistics > Explore. An outlier may be a data-entry error, but it may also be a valid response that must be retained and explained.

For two independent groups, a commonly used nonparametric option is Mann-Whitney U Test. In SPSS, go to Analyze > Nonparametric Tests > Legacy Dialogs > 2 Independent Samples. This test does not assess a Mean difference in exactly the same way as a t test, so your report should state clearly that you are comparing distributions or ranks between the two groups.

For two paired measurements, you can use Wilcoxon Signed-Rank Test at Analyze > Nonparametric Tests > Legacy Dialogs > 2 Related Samples. This is a more suitable option when the difference between the two measurements does not meet the assumptions required by Paired-Samples t Test.

If there are three or more groups, consider One-Factor ANOVA instead of running several Independent-Samples t Tests. If the variable is categorical and the question concerns the relationship between frequencies, Chi-square test may be more appropriate. You can also review the ANOVA table when the grouping variable has more than two levels.

Common errors

Choosing the wrong t test. Two different groups of people require Independent-Samples t Test. Two measurements from the same person require Paired-Samples t Test. Using Paired-Samples t Test for men and women creates data pairs with no meaningful basis.

Misreading Levene's Test. Levene's Sig. only determines which row to read in Independent Samples Test. It is not the p-value for the hypothesis about the difference between the means.

Looking only at Mean and ignoring Sig. (2-tailed). A higher Mean is not enough to conclude that the difference is statistically significant. Compare the p-value with the selected alpha level.

Using incorrect group codes. If Grouping Variable has codes 0 and 1 but you enter Group 1 as 1 and Group 2 as 2, SPSS may exclude the group coded 0. Run Frequencies before running the t test.

Deleting an outlier only to obtain a smaller p-value. Every excluded record needs a clear methodological reason, such as an invalid response or data-entry error. Do not remove an observation simply because its result is inconvenient.

Calling a nonsignificant result proof that H0 is true. The appropriate wording is “there is not enough evidence to reject H0.”

Frequently asked questions

What is a t test?

A t test is a group of tests used to compare means. In SPSS, choose One-Sample, Independent-Samples, or Paired-Samples according to whether you are comparing one group with a benchmark, two independent groups, or two measurements from the same subjects.

Which row should I read for an independent sample t test in SPSS?

Check Levene's Test for Equality of Variances first. If Sig. is greater than or equal to 0.05, read the Equal variances assumed row. If Sig. is less than 0.05, read the Equal variances not assumed row, then use Sig. (2-tailed) from the selected row.

Where do I run a paired samples t test in SPSS 26?

In SPSS 26, select Analyze > Compare Means > Paired-Samples T Test. Select the two measurements from the same subjects as one pair, then read the Paired Samples Test table. The interface may vary slightly between versions, but the path and logic are similar.

What p-value indicates that a t test is significant?

At the 5% significance level, a p-value below 0.05 is commonly used to reject H0 and conclude that there is a statistically significant difference. If the p-value is greater than or equal to 0.05, there is not enough evidence to reject H0. Consider the p-value alongside the Mean, sample size, and research design.

Can I run a t test when the data are not normally distributed?

Assess the degree of skew, outliers, sample size, and the distribution of the differences rather than deciding from one check alone. If the assumption is not suitable, you can use Mann-Whitney U Test for two independent groups or Wilcoxon Signed-Rank Test for two paired measurements, then explain the choice in your thesis.

How is a t test different from ANOVA?

A t test is usually used to compare one benchmark value, two independent groups, or two paired measurements. ANOVA is suitable for comparing means across three or more groups. When the grouping variable has more than two levels, also inspect the ANOVA table and appropriate post hoc tests.

Open the .sav file again, check the group codes, run the correct t test, and save Group Statistics, Independent Samples Test, or Paired Samples Test together with the version of the data you used. If you need to run the analysis on your own file and track each step from output to conclusion, see M4 SPSS and SmartPLS data analysis from DoThesis.