The most-analysed dataset is still misread
Everyone knows the Titanic headline. Far fewer have looked at what happens when you stratify class and sex jointly instead of marginally.
“Women and children first” is the summary of the Titanic dataset that everyone arrives with. It is also broadly correct, which is what makes the dataset such a good teaching case — the failure modes show up in the supporting claims, not the headline.
Marginal reading invents an effect
Look at survival by class and you get a clean monotonic story: first class fared best, third worst. Look at survival by sex and you get an enormous effect. Both are true marginally.
The trap is treating them as two independent findings and then adding them together in the write-up. Class and sex are not independent in this table, and the joint distribution is where the actual structure is. Once stratified, a large part of what looked like an independent class effect is redistributed — class matters enormously, but mostly as a modifier of the sex effect rather than alongside it.
Small cells, loud claims
Stratifying is what exposes the second problem. A two-way split turns a 1,309-row table into cells, and some of those cells are small. The confidence intervals on them are wide enough that several frequently repeated sub-claims about specific class-and-sex combinations are not distinguishable from each other.
They still get stated as fact, because a cell in a heatmap looks equally authoritative whether it holds four hundred people or eleven.
Why it generalises
Nothing about this is specific to 1912. Substitute channel for class and segment for sex and it is the same reporting failure that shows up in a marketing readout: two marginal breakdowns, presented as independent drivers, with no interval on either, and a recommendation that depends entirely on a cell nobody checked the size of.
The transferable habit is small: before writing the sentence, look at the joint table and look at the cell counts. The full working is in the case study.