Parametric vs non-parametric
Every powerful statistical test asks something of your data in return — usually that it be normally distributed and evenly spread. When your data can’t promise that, forcing the test anyway is how precise-looking, wrong answers are born.
What “parametric” assumes
Parametric tests — the t-test, ANOVA, Pearson correlation — are the workhorses of applied statistics, and they’re powerful precisely because they assume a lot. Chiefly, they assume your data follows a known distribution (usually the normal, bell-shaped curve) and that the groups being compared have similar variances. When those assumptions hold, parametric tests extract the most information from your data and detect effects with the fewest participants.
When the assumptions break
Real data is often less tidy. Reaction times are skewed; survey responses are ranks, not real numbers; a small sample makes normality impossible to verify. Running a parametric test on data that violates its assumptions doesn’t just weaken the result — it can produce a confident, precise-looking p-value that is simply wrong. This is where non-parametric tests earn their place. They make far fewer assumptions, typically by working on the ranks of the data rather than its raw values.
Non-parametric tests trade a little statistical power for a lot of honesty when your data won’t behave.
The map of swaps
Nearly every parametric test has a non-parametric counterpart that answers the same question with weaker assumptions:
- Independent t-test → Mann–Whitney U test
- Paired t-test → Wilcoxon signed-rank test
- One-way ANOVA → Kruskal–Wallis test
- Pearson correlation → Spearman’s rank correlation
The trade-off
Non-parametric tests aren’t automatically “safer” — if your data does meet the parametric assumptions, the parametric test is more powerful, and avoiding it throws away sensitivity. The right move is not to pick one camp for good, but to check the assumptions and follow the evidence: use the parametric test when it’s licensed, switch when it isn’t.
Checking, not guessing
Deciding this by eye is where a lot of analyses quietly go wrong. thericerca tests normality and variance on your actual data and switches from Pearson to Spearman, or ANOVA to Kruskal–Wallis, automatically — and tells you it did, and why. If you’re still choosing the test, the free which-test tool walks you through it, and how to choose the right test covers the bigger picture.
The rule of thumb. Parametric when the assumptions hold; non-parametric when they don’t. The mistake isn’t choosing one — it’s never checking which one your data actually calls for.