Statistics · Maths EE idea · Accessible
When combining data reverses the result
A research question to start from
Under what conditions can a trend in every group reverse when the groups are combined, and how can this be predicted algebraically?
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
An algebraic characterisation of a paradox, with real examples you analyse.
Mathematics you would need
- Weighted averages
- Inequalities between fractions
- Contingency tables
- Vectors (geometric view)
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
- Construct examples from scratch.
- Derive conditions for reversal.
- Show the vector picture and analyse a published example.
Scope and difficulty
Accessible. Accessible.
Pitfalls
- Collecting examples without theory.
- Confusing correlation and causation in the discussion.
Where to start reading
Search a library catalogue or a university's open lecture notes for: Simpson's paradox conditions weighted average vector interpretation. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).