A trend present in every subgroup can reverse or vanish when the subgroups are aggregated.
Berkeley's 1973 graduate admissions data showed an aggregate disadvantage for women. Department-level analysis found few statistically significant differences and about as many departments favouring women as men; pooled properly, the data showed a small significant bias in favour of women. The aggregate pattern arose largely because women applied more often to harder-to-enter departments.
In practice
- A drug that does better than the alternative in men and better in women can look worse overall, if the trial enrolled them in different proportions.
- A company's overall pay gap can be large while every role pays equally, because the roles are not equally staffed — and the aggregate figure is the one that matters politically.
- Standing
- Compare Lord's paradox, where two correct analyses of the same data disagree, and the Will Rogers phenomenon, where reclassification alone moves both averages.
- Subject
- Science & Epistemology
- Essay
- Paradoxes in the data, and sayings about knowing