STAT 101
M08 · L01
Module 8 · Lesson 1
Why Non-Parametric?
Most tests assume a distribution — usually normal. When that assumption breaks, distribution-free methods take over.
01 / 07
STAT 101
M08 · L01
When to reach for them
Four Warning Signs
- Small samples — can’t check normality or lean on the CLT
- Ordinal data — order but no meaningful arithmetic
- Heavy tails / outliers — wreck the mean and variance
- Strong skew — income, reaction time, survival
02 / 07
STAT 101
M08 · L01
The shared trick
Ranks, Not Values
Rank transform
R_i = \text{rank of } x_i
Replace values by their order. The magnitudes vanish, so the distribution’s shape no longer matters — and an outlier is just the biggest rank.
03 / 07
STAT 101
M08 · L01
What you pay
Power for Robustness
Asymptotic relative efficiency
\text{ARE}(W, t) = \tfrac{3}{\pi} \approx 0.955
On normal data, ~5% less power than the t-test. On non-normal data, often more — a bargain.
04 / 07
STAT 101
M08 · L01
Read the result right
Medians, Not Means
A rank test answers a question about medians or stochastic ordering, not means. State the conclusion in those terms.
05 / 07
STAT 101
Summary
Recap
What you learned
- Non-parametric = distribution-free; no normality assumption
- Use for small samples, ordinal data, heavy tails, or skew
- The rank transform makes tests distribution-free and outlier-robust
- Cost: ~5% power on normal data; often a gain otherwise
07 / 07