Independent, Paired or One-Sample t-Test: Which One Fits Your Paper
The three kinds of t-test, how to tell which one your hypothesis needs, the assumptions to check, how to read the SPSS output and how to report it in APA - with full examples.
Part of the series: Statistical Analysis for a Seminar Paper or Thesis: The Complete Guide
The t-test is the most common test in seminar papers: it compares two means. There are three kinds, and one question decides between them: which two means are you comparing?
The three kinds in one table
| Situation | Test | Example |
|---|---|---|
| Two different groups of people | independent-samples t | anxiety, men vs women |
| The same people, measured twice | paired-samples t | scores before and after training |
| One group against a known value | one-sample t | sample mean vs a national norm of 100 |
With three or more groups it is no longer a t-test but an ANOVA - see One-way ANOVA and post-hoc tests.
Independent-samples t-test
Compares a continuous variable between two separate groups; each participant belongs to one group only.
Assumptions: a continuous dependent variable (or a questionnaire total/mean); roughly normal distribution in each group, or about 30+ per group; equal variances - check Levene's test. If Levene is significant (p < .05), read the "Equal variances not assumed" row in SPSS (Welch's correction).
In SPSS: Analyze → Compare Means → Independent-Samples T Test; outcome in Test Variable, group in Grouping Variable, Define Groups with the codes (e.g. 1 and 2).
Paired-samples t-test
Compares two measurements of the same people: before/after, two conditions, or matched pairs. The test works on the difference within each person, which makes it more sensitive - differences between people no longer add noise.
Main assumption: the differences are roughly normal. With a small, skewed sample, use Wilcoxon instead.
In SPSS: Analyze → Compare Means → Paired-Samples T Test, select the two variables as a pair.
Common mistake: running an independent t-test on before/after data. It throws the pairing away and costs power.
One-sample t-test
Compares one group's mean with a known value: a questionnaire norm, a national average, or a scale midpoint (e.g. 3 on a 1-5 Likert: "do participants tend to agree?"). In SPSS: Analyze → Compare Means → One-Sample T Test, with the value in Test Value.
Effect size: don't skip it
APA 7 asks for an effect size. For t-tests it is Cohen's d: 0.2 small, 0.5 medium, 0.8 large. Recent SPSS versions print it in an Effect Sizes table; otherwise divide the mean difference by the pooled standard deviation.
Reporting in APA
Independent: "Women reported significantly higher anxiety (M = 3.45, SD = 0.62) than men (M = 3.12, SD = 0.71), t(98) = 2.47, p = .015, d = 0.49."
Paired: "Knowledge scores rose significantly from before the training (M = 62.3, SD = 11.4) to after it (M = 71.8, SD = 9.9), t(39) = 5.12, p < .001, d = 0.81."
Degrees of freedom in parentheses, no leading zero on p, means and SDs for each group. With Welch's correction the df are not whole numbers (e.g. t(87.4)) - report them as they are.
Common mistakes
- Several t-tests instead of one ANOVA when there are more than two groups.
- Ignoring Levene's test and reading the wrong row.
- Switching to one-tailed after the fact to reach significance. Decide on a directional test in advance and say so.
- Reporting t and p without the means, so the reader can't tell the direction.
FAQ
My data isn't normal. With 30+ per group the t-test is robust. With a small, skewed sample: Mann-Whitney instead of independent, Wilcoxon instead of paired.
Unequal group sizes? Fine, as long as you check equal variances and use Welch when needed.
Where does this fit in the whole analysis? Step 4 of 7 - see Statistical analysis for a seminar paper: the complete guide. Not sure which test your hypotheses need? Send us your hypotheses.
Tell us what you need, and we'll come back with an expert in Statistical analysis and a quote.
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