When is the use of a t-test inappropriate?

A t-test is a powerful tool for comparing means, but it only works well when its underlying assumptions hold. Here are key situations where using a t-test is inappropriate:

🚫 When You Should Not Use a t‑Test

Non‑numeric or ordinal data

• T-tests require continuous, interval-scale outcomes (e.g., height, weight, temperature).
• If your data are rankings or categories — like Likert scale (e.g., “agree,” “neutral,” “disagree”) — a t-test isn’t suitable.

Severely non‑normal distributions with small sample sizes

• T-tests assume data in each group is normally distributed.
• With small nnn (say n❤0n❤0n❤0), non-normal data (e.g., heavily skewed, long tails, outliers) can invalidate results.
• In such cases, **non-parametric tests** (e.g., Mann–Whitney U, Wilcoxon signed-rank) are safer.

Major variance inequality (heteroscedasticity)

• The classic Student’s t-test assumes both groups have similar variances.
• If that isn’t true and you don’t use **Welch’s t-test **(which adjusts for unequal variances), results can be misleading.

Dependent observations treated as independent (or vice versa)

• Using an independent-sample t-test when samples are actually paired (e.g., pre‑ vs post‑measurement) ignores within-subject correlation and reduces statistical power.
• Conversely, using a **paired t-test** on independent samples inflates Type I error risk.

Very small sample sizes

• With extremely small groups (e.g., n=2n=2n=2 or 3), the t-test lacks power and variance estimates are unstable.
• Even if data appear normal, it’s often better to increase sample size or use more **robust exploratory statistics**.