Chapter 1 · §1.5

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

📈 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.

🕊️ 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

PROS 2CONS 1

Tilted toward the advantages.

⚠️ Limitations · 1 active

Tap a point to see what it means.

Historical arc

From Arbuthnot to Wolfowitz

  1. 1710
    John Arbuthnot

    First use of a nonparametric method.

  2. 1710 – 1940s
    Sparse use

    Nonparametric methods stay rarely used for over two centuries.

  3. 1942
    Wolfowitz

    The word "nonparametric" first appears in print.

  4. Today
    Every 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.

Up next

§1.6–1.8 Roadmap & Toolkit →