📈 Parametric
Student's t, ANOVA, correlation and regression. They rely on assumptions, e.g. ANOVA needs normal populations with equal variances.
When assumptions hold
Usually the most powerful choice.
No bell curve required.
When assumptions crumble or your data are just ranks and counts, nonparametric methods still deliver valid inference.
Methodology faceoff
Parametric vs. Nonparametric
🕊️ Nonparametric
Valid under very general assumptions, so they're the fallback when parametric assumptions fail.
Bonus
For small samples, many are almost as powerful as the parametric test.
Are “nonparametric” and “distribution-free” the same?
Not concerned with population parameters at all. The hypothesis itself makes no statement about a parameter such as μ or σ.
Examples: Goodness-of-fit tests, tests for randomness.
Diagnostic
Should I go nonparametric?
Tick every situation that applies to your data. Any one is a reason to consider nonparametric procedures.
Trade-offs
The Pros & Cons Seesaw
Toggle each point and watch the balance shift.
👍 Advantages · 2 active
Tilted toward the advantages.
⚠️ Limitations · 1 active
Tap a point to see what it means.
From Arbuthnot to Wolfowitz
- 1710John Arbuthnot
First use of a nonparametric method.
- 1710 – 1940sSparse use
Nonparametric methods stay rarely used for over two centuries.
- 1942Wolfowitz
The word "nonparametric" first appears in print.
- TodayEvery field
Widely used across the physical, biological and social sciences.
Speed quiz
5 True-or-False
1 / 5Score 0🔥 Combo 0
A nonparametric test wastes information when a parametric test would have been more appropriate.
§1.6–1.8 Roadmap & Toolkit →