Comment by getnormality
8 hours ago
From a life spent on count statistics, one thing I think is interesting is how definitively you can reject perfect randomness from a very small sample like this.
The expected event count from 17,000 people exposed to a month of constant uniform event risk with an annual hazard rate of 20 per 100,000 per year is 0.28. The p-value for observing a count of 5 from a (Poissonian) mean of 0.28 is 1 in 100,000. So it's pretty unlikely by perfect random chance.
The other thing you see in a life spent in count statistics is a lot of statistically extreme events that turn out to have no deep or predictive significance.
You hinted at this in your last sentence, so I assume you're aware, but I feel like spelling it out anyways:
There's many slices of ~10-20k people you can divide the US (military) in, many of them overlapping.
What is the chance that in some year at least one of the slices will say "Hey, we had excess suicides!" - much higher.