Birth defects and developmental anomalies occur at a known non-zero baseline rate in every population — real combined major-anomaly rates are on the order of a few per 1,000 births, varying by defect category. Because the true count in any one town is a small random draw, not a fixed number, some towns will show more cases than average purely by chance, exactly the way some coin-flip runs land on more heads than others. When a community near a factory, power line or "sighting" site notices an above-average count, it is tempting to conclude the site caused it. This simulator tests that instinct directly.
Each grid cell is an independent region with the same births and the same baseline rate. Its actual case count is drawn from a Poisson distribution — the standard model for counting rare, independent events over a fixed population:
expected (λ) = births × rate / 1000
P(observed = k) = e^(−λ) · λ^k / k!
p-value = P(X ≥ observed) = 1 − Σ (k=0 → observed−1) e^(−λ)λ^k/k!
The simulator then does what a worried community actually does: it looks across every region and highlights the single worst one as "the claimed cluster," then computes how surprising that count would be if it came from the baseline rate alone. The raw p-value routinely looks dramatic (p < 0.05) even though nothing but chance produced it — because you scanned N regions and kept only the extreme. The Bonferroni-corrected p-value (raw p × number of regions scanned, capped at 1) accounts for that multiple-comparisons trap; watch it climb back toward "unremarkable" as you add more regions to the scan.
- Births per region — population size under study; bigger populations shrink relative statistical noise (expected count scales with births).
- Baseline rate — the population-wide anomaly rate per 1,000 births that every region shares under the null hypothesis.
- Claimed-cluster size — how many adjoining cells get pooled into "the cluster" before comparing observed to expected; smaller pooled areas have higher relative variance, so tiny "cluster" zones are the easiest to mistake for a signal.
This is the same statistical trap as cherry-picked report clusters in UFO-sighting data — a general "pick the extreme, then act surprised" illusion — except here the null model is a specific, measurable epidemiological baseline rate rather than a generic random process.