Statistics · Maths EE idea · Ambitious
Where does the chi-squared test come from?
A research question to start from
Why does the chi-squared statistic follow approximately a chi-squared distribution, and how small can expected frequencies be before the test fails?
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 study of a test's foundations and limits rather than a use of it.
Mathematics you would need
- Normal approximation to binomial
- Sums of squared normals
- Degrees of freedom
- Simulation of test size
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
- Derive the one-degree-of-freedom case from the normal approximation.
- Explain the general case and degrees of freedom.
- Simulate the true significance level for small expected counts.
Scope and difficulty
Ambitious. Ambitious.
Pitfalls
- Using the test on a dataset instead.
- Quoting rules (expected ≥ 5) without testing them.
Where to start reading
Search a library catalogue or a university's open lecture notes for: chi-squared statistic derivation normal approximation; small expected frequencies test size. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).