Chapter 2 of 10All chapters
Chapter 2 of 10
The central limit theorem
Why normality keeps appearing.
What it says
Averages of many independent observations tend towards a normal distribution regardless of the shape of the original data. It concerns the mean, not the data itself.
- This is why methods assuming normality often work on skewed data.
- With heavy tails or dependence, the approximation degrades.
Standard error
It shrinks with the square root of sample size, so quadrupling the sample halves the uncertainty. That relationship governs how much extra data is worth.