T-Test for Your Thesis: Complete Guide with Assumption Checks, Effect Size, and APA Copy-Paste Templates
5 min read
The t-test is the most reported statistical test in student theses - and the one most often reported incorrectly. Skip the Shapiro-Wilk normality check and your supervisor will flag it in your defense. Report p < .05 without Cohen's d and you are missing half the story. This guide gives you exact software menu paths for three t-test types, a step-by-step assumption checklist, Cohen's d benchmarks, and ready-to-paste APA sentences for every outcome.
Key takeaways
- Always run Shapiro-Wilk before a t-test - if p < .05, switch to Mann-Whitney U (independent) or Wilcoxon (paired) instead.
- Welch's t-test handles unequal variances automatically - most software reports it alongside the standard version; use it when Levene's p < .05.
- Cohen's d is mandatory - small = 0.2, medium = 0.5, large = 0.8 - always report it next to your p-value.
- For paired t-tests check normality of the difference scores, not the raw scores - this is the assumption that matters.
- Your methods section must state the test type, software version, and results of Shapiro-Wilk and Levene's - not just the final t and p.
What the T-Test Actually Measures
A t-test compares two means and asks: is the difference between them large enough - relative to the variability in the data - to be unlikely due to chance?
The result is a t-statistic and a p-value. A significant result (p < .05) means you reject the null hypothesis that the two means are equal in the population.
- Three versions exist for three different designs:
- - Independent samples t-test: two separate groups
- - Paired samples t-test: same subjects measured twice
- - One-sample t-test: one group compared to a known value
Independent Samples T-Test: Software Menu Paths and What to Check
Use when: comparing two distinct, non-overlapping groups on a metric outcome.
Examples: male vs. female on exam score; treatment vs. control group; two university programmes.
- Software paths:
- SPSS → Analyze → Compare Means → Independent Samples T Test
- Jamovi → Analyses → T-Tests → Independent Samples T-Test
- JASP → T-Tests → Independent Samples T-Test
| Assumption | Test to Run | What to Check | If Violated |
|---|---|---|---|
| Normality | Shapiro-Wilk (each group) | W statistic, p > .05 | Use Mann-Whitney U |
| Equal variances | Levene's test | F statistic, p > .05 | Use Welch's t-test |
| Independence | Study design review | No subject appears twice | Cannot fix post-hoc |
| Metric scale | Variable type check | Interval or ratio scale | Use Mann-Whitney U |
[WARNING] Never skip Shapiro-Wilk. A t-test on non-normally distributed data without justification is one of the most common thesis defense questions. Run it, report it, and note if the assumption is met.
Paired T-Test: Same Subjects Measured Twice
Use when: the same participants are measured at two time points, or you have matched pairs.
Examples: pre-test vs. post-test scores; scores before and after an intervention; matched sibling pairs.
Key assumption: normality applies to the difference scores (post − pre), not the raw scores. Run Shapiro-Wilk on the computed difference variable.
- Software paths:
- SPSS → Analyze → Compare Means → Paired-Samples T Test
- Jamovi → Analyses → T-Tests → Paired Samples T-Test
If normality of differences fails → use Wilcoxon signed-rank test.
The paired test is more powerful than independent because it removes between-subject variability from the error term - you need fewer participants to detect the same effect.
One-Sample T-Test: Comparing Against a Known Value
Use when: you have one group and want to test whether its mean differs from a known reference value.
Examples: "Does my sample's mean (M = 67) differ from the population mean of 70?" or "Is customer satisfaction in my sample above the industry benchmark of 3.5 on a 5-point scale?"
- Software paths:
- SPSS → Analyze → Compare Means → One-Sample T Test → enter Test Value
- Jamovi → T-Tests → One Sample T-Test → set the test value
This test is less common in theses but useful when comparing against published norms, national statistics, or theoretical benchmarks.
Effect Size: Cohen's d - What It Means and How to Calculate It
Cohen's d measures how many standard deviations the two means differ by. It tells you the practical importance of your finding, independent of sample size.
| Cohen's d Value | Effect Size | Plain-Language Meaning |
|---|---|---|
| 0.2 | Small | Means differ by 0.2 SDs - subtle, may need large N to detect |
| 0.5 | Medium | Means differ by 0.5 SDs - noticeable in practice |
| 0.8 | Large | Means differ by 0.8 SDs - clearly visible difference |
| > 1.0 | Very large | Means differ by more than 1 SD - strong, practical effect |
APA Reporting Templates (Copy and Adapt)
- Independent t-test - significant result:
- "An independent samples t-test revealed a significant difference between Group A (M = 74.2, SD = 8.1) and Group B (M = 68.5, SD = 9.3), t(48) = 2.31, p = .025, d = 0.65."
- Independent t-test - non-significant result:
- "No significant difference was found between Group A (M = 72.1, SD = 8.4) and Group B (M = 70.3, SD = 9.1), t(48) = 0.72, p = .476, d = 0.21."
- Paired t-test - significant result:
- "A paired samples t-test indicated that scores increased significantly from pre-test (M = 61.3, SD = 9.4) to post-test (M = 71.8, SD = 8.7), t(29) = 5.42, p < .001, d = 0.99."
- Welch's t-test (unequal variances):
- "Levene's test indicated unequal variances (p = .018), so Welch's correction was applied. A significant difference was found, t(41.3) = 2.67, p = .011, d = 0.73."
Common T-Test Mistakes in Thesis Research
These are the errors supervisors flag most often during thesis reviews.
| Mistake | Why It Is Wrong | How to Fix It |
|---|---|---|
| Skipping Shapiro-Wilk | Cannot justify parametric assumption | Always run and report W and p |
| Reporting p = .000 | Mathematically impossible value | Write p < .001 instead |
| No Cohen's d | Statistical without practical significance | Calculate d and benchmark it |
| Using t-test on 3+ groups | Inflates Type I error rate | Use one-way ANOVA instead |
| Ignoring Levene's test | Variance inequality distorts results | Check and use Welch's if p < .05 |
Frequently asked questions
What is Welch's t-test and when do I use it?
▾
How do I interpret Cohen's d?
▾
Is a t-test really robust to non-normality?
▾
Further reading
Free tool
Not sure which statistical test to use?
Answer 5 quick questions about your research design and get the right test - with an explanation of why - in under two minutes.
Statoria Team
Statistics educators & software developers
We build Statoria to help bachelor and master students get through their thesis data analysis without stress. Our guides are written by researchers with experience in social science statistics and student supervision.