hesela.devSimpson's paradox
Simpson's paradox is a change or reversal in an association when subgroup results are combined or separated.
Combining strata can change the comparison because the groups being compared contribute different proportions to those strata. Conditioning is not automatically the right interpretation: Simpson's 1951 examples emphasize that the meaning of the classifications matters. [1]
In Hesela's invented drive-exposure example, cohort A has higher AFR in both age bands (2% versus 1%, and 6% versus 5%) but lower pooled AFR (2.4% versus 4.6%). A supplies 90% of its exposure in the younger band; B supplies 90% in the older band. These are fixed arithmetic inputs, not evidence about a vendor. Shared 50/50 exposure weights give 4% for A and 3% for B. [2]
Keep failures, drive-days, age boundaries and reference weights visible. An aggregate describes its own composition; standardization changes the comparison target and does not establish causation or remove unmeasured differences. [2]