Statistical tests

When to Use a t-Test: A Simple Guide for Thesis Students

Q: When should I use a paired t-test instead of an independent samples t-test?

Use the paired samples t-test when the same participants are measured under both conditions — for example, before and after an intervention, or on two different tasks. Use the independent samples t-test when two completely separate groups are compared. The key question is whether the data points in the two groups are linked to the same individuals.

Q: What is the difference between a t-test and ANOVA?

Both compare group means, but the t-test is limited to exactly two groups. ANOVA handles three or more groups simultaneously without inflating the Type I error rate. If you have two groups, the t-test and a one-way ANOVA produce identical p-values — but once you have three or more groups, you must use ANOVA.

Q: How do I check normality for a t-test in SPSS?

Go to Analyze → Descriptive Statistics → Explore → move your DV to the Dependent List → click Plots → tick ‘Normality plots with tests’ → OK. Look at the Shapiro-Wilk result (recommended for n .05, normality is not significantly violated. Also inspect the Q-Q plot — points should lie approximately on the diagonal line.

Q: How do I calculate Cohen’s d for an independent samples t-test?

Cohen’s d = (M1 − M2) ÷ SDpooled, where SDpooled = √((SD1² + SD2²) ÷ 2). Benchmarks: d = 0.2 small, d = 0.5 medium, d = 0.8 large. SPSS does not calculate Cohen’s d automatically — compute it from the group means and SDs in the output.

Q: Can I use a t-test with Likert scale data?

A single Likert item (e.g. one question rated 1–5) is ordinal — use Mann-Whitney U or Wilcoxon instead. A computed composite score from multiple Likert items (e.g. a sum or mean of 10 items) is treated as metric, and a t-test is appropriate if the normality condition holds.

May 20267 min read

When to use a t-test is one of the first decisions every thesis student faces after collecting data. The t-test compares means — but only under specific conditions, and there are three different versions depending on your research design. This guide explains which type fits your situation, the four conditions your data must meet, and how to report results in APA format.

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Key takeaways

Use the independent samples t-test when comparing two different groups on a metric variable.
Use the paired samples t-test when the same participants are measured twice (pre-post design).
Use the one-sample t-test when comparing a group mean to a known reference value.
Check normality with Shapiro-Wilk (n < 50) and homogeneity of variance with Levene’s test before running any t-test.
When normality is violated and n < 30, switch to Mann-Whitney U (independent) or Wilcoxon signed-rank (paired).

What Is a t-Test? Plain English, No Formulas

A t-test answers one question: are the means of two groups (or time points) significantly different from each other, or could the difference be due to chance?

You have two stress scores — one for students who exercise regularly, one for those who don’t. The t-test tells you whether the gap between those averages is large enough to be real.

It does not require you to understand the formula. What matters is knowing which version to use, whether your data qualifies, and how to read the output.

The 3 Types of t-Test and When Each Applies

Choose based on your research design, not your data shape:

Independent samples t-test: two separate groups, different participants in each. Example: exercise group vs. no-exercise group. This is the most common t-test in thesis research.

Paired samples t-test (dependent t-test): the same participants measured at two time points. Example: stress score before and after an intervention. Also called a repeated-measures design.

One-sample t-test: one group compared against a known benchmark. Example: testing whether your sample’s mean differs significantly from the population average of 50. Less common in student theses.

Type	When to use	Example
Independent samples	Two separate groups	Exercisers vs. non-exercisers
Paired samples	Same participants, two time points	Pre-test vs. post-test
One-sample	One group vs. known reference value	Your sample vs. population norm

When to Use t-Test vs. ANOVA vs. Mann-Whitney

Use the t-test when you have exactly two groups or two time points. The moment you have three or more groups, switch to ANOVA (parametric) or Kruskal-Wallis (non-parametric).

Use Mann-Whitney U instead of the independent t-test when Shapiro-Wilk is significant (p < .05) and your sample is small (n < 30 per group). Use Wilcoxon signed-rank instead of the paired t-test under the same normality conditions.

Situation	Use this test
2 groups, metric DV, normality holds	Independent samples t-test
2 groups, metric DV, normality violated, n < 30	Mann-Whitney U
Same participants, 2 time points, normality holds	Paired samples t-test
Same participants, 2 time points, normality violated	Wilcoxon signed-rank
3+ groups	One-way ANOVA or Kruskal-Wallis

Checklist: 4 Conditions That Must Be Met Before Running a t-Test

Before you run any t-test, confirm these four conditions:

1. Metric dependent variable: your DV must be measured on an interval or ratio scale (e.g. a computed score, reaction time, grade). Ordinal data (e.g. a single Likert item) does not qualify.

2. Normal distribution: check with Shapiro-Wilk (Analyze → Descriptive Statistics → Explore → Plots → Normality plots with tests). If p > .05, normality is not significantly violated. With n > 100 per group, rely on the Q-Q plot and the Central Limit Theorem instead.

3. Homogeneity of variance (independent samples only): check Levene’s test in the t-test output. If Levene’s p < .05, use the "Equal variances not assumed" row (Welch’s t-test) instead.

4. Independence of observations: each participant contributes only one data point per group. If the same person appears in both groups, use the paired design instead.

[TIP] SPSS runs Levene’s test automatically when you request a t-test. You do not need a separate step — just read the correct row in the output.

Step-by-Step Example: Independent Samples t-Test in SPSS

Research question: Do students who exercise ≥3 times per week have lower perceived stress scores than those who do not exercise?

SPSS path: Analyze → Compare Means → Independent-Samples T Test → move PSS score to "Test Variable", physical activity group to "Grouping Variable" → Define Groups → OK.

Reading the output:
Step 1 — Levene’s test: p = .269 (not significant) → use "Equal variances assumed" row.
Step 2 — t-test result: t(119) = 3.42, p = .001 → significant difference.
Step 3 — Effect size: Cohen’s d = (M1 − M2) ÷ SDpooled. d = 0.62 = medium effect.

Conclusion: Exercising students (M = 21.4, SD = 5.1) had significantly lower stress than non-exercising students (M = 24.8, SD = 5.6), t(119) = 3.42, p = .001, d = 0.62.

How to Report t-Test Results in APA Format

Significant result:
"Students who exercised regularly (M = 21.4, SD = 5.1) reported significantly lower stress than non-exercising students (M = 24.8, SD = 5.6), t(119) = 3.42, p = .001, d = 0.62."
Non-significant result:
"No significant difference in stress was found between exercising and non-exercising students (M = 21.4, SD = 5.1 vs. M = 22.1, SD = 5.3), t(119) = 0.81, p = .418, d = 0.13."
For paired samples t-test — significant:
"Stress scores decreased significantly from pre-test (M = 26.3, SD = 4.8) to post-test (M = 22.7, SD = 5.0), t(44) = 4.11, p < .001, d = 0.74."

[INFO] Always report: group means and SDs, t-statistic, degrees of freedom, p-value, and Cohen’s d. A result without effect size is incomplete in APA 7th edition.

Common Mistakes Students Make With t-Tests

Using a t-test with three or more groups: run ANOVA instead. A t-test on groups A vs. B, then B vs. C, then A vs. C inflates the Type I error rate.

Ignoring Levene’s test: always check which row to read. Using the wrong row can change whether your result is significant.

Reporting p = .000: SPSS shows .000 when p is very small, but the true value is never exactly zero. Always write p < .001.

Omitting effect size: t-statistic and p-value alone are not enough. Calculate Cohen’s d and report it. A p = .03 with d = 0.08 is statistically significant but practically meaningless.

Frequently asked questions

When should I use a paired t-test instead of an independent samples t-test?

▾

Use the paired samples t-test when the same participants are measured under both conditions — for example, before and after an intervention, or on two different tasks. Use the independent samples t-test when two completely separate groups are compared. The key question is whether the data points in the two groups are linked to the same individuals.

What is the difference between a t-test and ANOVA?

▾

Both compare group means, but the t-test is limited to exactly two groups. ANOVA handles three or more groups simultaneously without inflating the Type I error rate. If you have two groups, the t-test and a one-way ANOVA produce identical p-values — but once you have three or more groups, you must use ANOVA.

How do I check normality for a t-test in SPSS?

▾

Go to Analyze → Descriptive Statistics → Explore → move your DV to the Dependent List → click Plots → tick ‘Normality plots with tests’ → OK. Look at the Shapiro-Wilk result (recommended for n < 50 per group): if p > .05, normality is not significantly violated. Also inspect the Q-Q plot — points should lie approximately on the diagonal line.

What do I do if my data fails the normality check for a t-test?

▾

With n ≥ 30 per group, the Central Limit Theorem means the t-test is robust and you can proceed. With n < 30 and Shapiro-Wilk p < .05, switch to the non-parametric alternative: Mann-Whitney U for independent groups, or Wilcoxon signed-rank for paired data.

How do I calculate Cohen’s d for an independent samples t-test?

▾

Cohen’s d = (M1 − M2) ÷ SDpooled, where SDpooled = √((SD1² + SD2²) ÷ 2). Benchmarks: d = 0.2 small, d = 0.5 medium, d = 0.8 large. SPSS does not calculate Cohen’s d automatically — compute it from the group means and SDs in the output.

Can I use a t-test with Likert scale data?

▾

A single Likert item (e.g. one question rated 1–5) is ordinal — use Mann-Whitney U or Wilcoxon instead. A computed composite score from multiple Likert items (e.g. a sum or mean of 10 items) is treated as metric, and a t-test is appropriate if the normality condition holds.

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