Statistics · Maths EE idea · Accessible
Why divide by n − 1?
A research question to start from
Why is dividing by n − 1 rather than n needed for an unbiased estimate of variance, and when does the biased estimator actually perform better?
A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.
Why it works as a maths EE
A short proof followed by a genuine trade-off (bias against mean squared error) to evaluate.
Mathematics you would need
- Expectation algebra
- Bias of an estimator
- Mean squared error
- Simulation as a check
Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.
One possible line of attack
- Prove the expectation of the sample variance with divisor n.
- Compare bias and mean squared error for different divisors.
- Check with simulated samples.
Scope and difficulty
Accessible. Accessible; the MSE comparison adds depth.
Pitfalls
- Only simulation.
- Confusing population and sample.
Where to start reading
Search a library catalogue or a university's open lecture notes for: sample variance n-1 unbiased proof; mean squared error variance estimators. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).