The Whole Story
When every part disagrees with the total. A marketer reports that overall conversion rose 68%. Dr. Bayes asks about the two major traffic segments, and both declined.
Behind the joke.
This is Simpson's paradox. Branded conversion fell from 10% to 9% and non-branded from 2% to 1.5%, yet the overall rate rose because the traffic mix shifted toward branded visitors, who convert far more often. The total improved through a change in composition, not performance. When segments and the aggregate disagree, compare like with like within each segment before celebrating.
The transcript.
For readers who prefer dialogue without zooming in.
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Marketer: Overall conversion is up 68%!
Dr. Bayes: Extraordinary.
Dr. Bayes: And within your two major traffic segments?
Marketer: Both declined.
Dr. Bayes: Both?
Marketer: Yes.
Dr. Bayes: Extraordinary. Every part got worse and the whole got better.