Your point 3 is incorrect. The analysis fails to show that the data observed can be distinguished from data drawn randomly from a Poisson distribution of mean 2.
The double negative here and concept of "distinguishing from" is important. In particular, this result does not rule out being underpowered by which we'd mean to say that given infinite tragic observations we may be able to make a case to distinguish the data from the random distribution, but since we only had a little that effect was buried.
Again, you cannot even say things like "are likely not" and "should expect" because those are epistemologically reversed from what we can state. What we can say, in parallel, is
- We do not have evidence here suggesting that mass shootings are copycat crimes (if we buy that copycat crimes would lead to non-Poisson distribution of mass shootings).
- We have not been able to show it flawed to predict 10 mass shootings over the next 5 years.
It's definitely a pain in the ass to rework all your statements this way, but it's also necessary for them to mean anything resembling truth. Statistics is a fickle beast, especially frequentist methods interpreted predictively. This song and dance, however, is required to make the general process of using statistical tests trustworthy enough over time.
The double negative here and concept of "distinguishing from" is important. In particular, this result does not rule out being underpowered by which we'd mean to say that given infinite tragic observations we may be able to make a case to distinguish the data from the random distribution, but since we only had a little that effect was buried.
Again, you cannot even say things like "are likely not" and "should expect" because those are epistemologically reversed from what we can state. What we can say, in parallel, is
It's definitely a pain in the ass to rework all your statements this way, but it's also necessary for them to mean anything resembling truth. Statistics is a fickle beast, especially frequentist methods interpreted predictively. This song and dance, however, is required to make the general process of using statistical tests trustworthy enough over time.