The reason improving every hospital can worsen the statistics

A report shows that every individual unit in an organisation improved its rate over the year. The combined figure for the organisation declined. No number was falsified and no calculation was wrong. This is a structural property of averages, and it has overturned published conclusions in medicine, education and employment law.

What everyone sees

A single headline rate, presented as the summary of everything beneath it. The instinct is that a summary inherits the direction of its parts — if every component improved, the total must have improved. It is a reasonable instinct and it is not true.

What is actually happening

Aggregating groups of different sizes and different baselines can reverse the direction of an effect. This is Simpson’s paradox. If the units that improved also took on a much larger share of the harder cases, the combined rate can fall while every separate rate rises. The classic public example is the 1973 Berkeley admissions data, where an apparent bias at university level disappeared — and partly reversed — once department-level applications were examined.

Why it stays hidden

Because the aggregate is the number that gets published. Disaggregation costs effort, requires the underlying data, and frequently produces a less quotable answer. A reversal is only visible to somebody who asks what the grouping was, and the grouping is usually the least documented decision in the whole analysis.