It is estimated that, in a typical large UK hospital, pulmonary haemorrhage deaths for new born babies is rare - it occurs between 1 to 3 times per 2000 births. The largest hospitals in the UK deliver about 690 births per month. What's the probability of seeing a cluster of 4 of these deaths in the same hospital in a single month? Using standard statistical assumptions (all explained and demonstrated in the 3-minute video below) the probability is about 0.7%, i.e. 1 in a 142 chance. So it is quite rare. But rare events happen all the time; in this case what we really need to ask is something like: how likely are we to see such a (monthly) cluster in a single hospital in the whole of the UK in over a year? The answer (assuming about 20 similar hospitals) is about 81%. In other words it would actually be surprising if we did not see such a cluster somewhere in the UK at least once a year. But what if we observed not 4, but 8 such deaths in one hospital in one month?

In this case the probability it happens in one hospital in one month is 0.00026% (1 in 385,000 chance). The probability it happens somewhere in the UK in a year is about 0.063%, (1 in 1,600 chance). So it is a genuinely unlikely 'event' which may well have a causal (non-random) explanation.

The video uses AgenaRisk software for calculations. The model can be downloaded here and run using the free trial version of AgenaRisk.

Did this event actually happen or was this presented as an illustrated example?