The most common question in student research: should I use a t-test or an ANOVA? The answer is straightforward once you understand what each test does.
The simple rule
- Comparing two groups: use a t-test
- Comparing three or more groups: use one-way ANOVA
That is it. The number of groups determines which test to run.
Types of t-test
Independent samples t-test — comparing two separate groups (e.g. male vs female, treatment vs control). Each participant appears in only one group.
Paired samples t-test — comparing the same group at two time points (e.g. before and after a training programme, pre-test vs post-test). Each participant appears in both measurements.
One-sample t-test — comparing a sample mean to a known population value (e.g. testing whether your sample's average score differs from the national average).
One-way ANOVA
When you have three or more groups, a t-test is not appropriate — running multiple t-tests inflates the Type I error rate (the chance of a false positive). ANOVA compares all groups simultaneously while controlling this error rate.
After a significant ANOVA, run a Tukey HSD post-hoc test to find which specific pairs of groups differ from each other.
The normality assumption
Both t-tests and ANOVA assume your data is approximately normally distributed. Check this with Shapiro-Wilk before running the test.
If normality is violated:
- Instead of independent t-test: use Mann-Whitney U
- Instead of paired t-test: use Wilcoxon signed-rank
- Instead of one-way ANOVA: use Kruskal-Wallis (followed by Dunn's post-hoc)
ResearchScope handles this automatically — it runs normality and variance tests first, then selects the correct parametric or non-parametric test and explains the decision in plain English.
APA reporting examples
Independent samples t-test:
t(58) = 2.45, p = .017, d = 0.63, 95% CI [0.29, 1.14]
Paired samples t-test:
t(29) = 3.12, p = .004, d_z = 0.57, 95% CI [0.18, 0.95]
One-way ANOVA:
F(2, 87) = 6.83, p = .002, eta-squared = .14
Tukey HSD post-hoc:
Group A vs Group C: MD = 4.21, p = .003, 95% CI [1.89, 6.53]
Effect sizes
APA 7th Edition requires effect sizes alongside every hypothesis test.
- For t-tests: Cohen's d (0.2 = small, 0.5 = medium, 0.8 = large)
- For ANOVA: eta-squared (.01 = small, .06 = medium, .14 = large)
- For Mann-Whitney / Wilcoxon: r = z / sqrt(N) (0.1 = small, 0.3 = medium, 0.5 = large)
- For Kruskal-Wallis: report H statistic and eta-squared
ResearchScope computes all effect sizes automatically and includes them in every APA result string.