So I came across an article, "40% of local Covid-19 cases are in the vaccinated. What does that say about the vaccines?", https://archive.is/Y8dx5. It states 40% of local cases are in the vaccinated but gives the following to support that this doesn't reflect poorly on the vaccine:
The state health department said that Wednesday’s study found “unvaccinated New Yorkers were 11 times more likely to be hospitalized and eight times more likely to be diagnosed with COVID-19 than those who were fully vaccinated.”
So, 40% of cases are in the vaccinated and Syracuse has a 60% vaccination rate. Let's do the math P(A|B) = P(B|A)P(A)/P(B). The probability of X is written P(X). The probability of X given Y is written P(X|Y). A is 'diagnosed with covid'. B is vaxxed. !B is not vaxxed. We don't know what P(A) is but that's okay, we will set it to x. P(A|B) = .4 * x / .6 and P(A|!B) = .6 * x / .4. The ratio of covid given not vaxxed to covid given vaxxed is P(A|!B)/P(A|B), (.6x/.4)/(.4x/.6) so .36/.16 or 9/4, 2.25. For the eight times statement to agree with with the reality the journalist has observed the vaccination rate would have to be 85% which would be an impossible number even if the vaccine was mandatory.
While I don't expect journalists to know bayes law I would expect them to at least find the numbers unlikely and maybe talk to a statistician instead of just spewing them out uncritically, but that would assume journalist was anything more than PR for the state.
They don't do anything. Journalists are the dumbest people around. Thanks for the numbers though.