When facing Z scores of 5 and 7 indicating that the unvaccinated care rate is significantly lower than the vaccinated case rate, the precautionary principle has a lot to say about whether to continue vaccination while we await understanding of the cause of this difference. 
For a null hypothesis is that there is no difference in case rates between vaccinated and unvaccinated, the probability of observing a difference like this is 1 in 8110. This is monthly data so that's once in 675 years
The hypothesis everyone is hoping for is that the case rate for vaccinated is less than the case rate for unvaccinated. That requires us to use a single tailed test. The probability of seeing Z=7 on a single tailed test is 1 in 16,207 or once every 1350 years
What this tells us is that there is a SIGNIFICANTLY LOWER CASE RATE FOR UNVACCINATED.
What this does not tell us is WHY.
Two obvious theories present themselves:
1. Vaccination makes you more susceptible
2. Unvaccinated less likely to get tested
Also
3. Both can be true
What this does not tell us is WHY.
Two obvious theories present themselves:
1. Vaccination makes you more susceptible
2. Unvaccinated less likely to get tested
Also
3. Both can be true
What we need now, or even better yesterday, is to design some experiments that can differentiate these two theories, run those experiments and see what the data says.
Or we can ignore the scientific method and blindly follow a new religion of "The science"
Society, your choice
Or we can ignore the scientific method and blindly follow a new religion of "The science"
Society, your choice
FYI for reference on Z scores. if you have a single tailed test, the basic standard for publication is a P<0.05 (i.e. 1 in 20 odds of happening by chance) which is a Z score greater than 1.65. Four of the age cohorts meet this criteria
Even a Z score of 3.77 is a ONE in TWELVE THOUSAND chance for the single tailed test. Three of the age cohorts are at least this... so what we have is three one in twelve thousand chance occurances all in the same data set... the reported rates are almost certainly lower... why?
WHY are unvaccinated cases reporting lower than vaccinated cases in Israel last month? Given vaccinated people had been lead to believe they're less likely to catch (which is why restrictions were reduced for them) one would think they'd be less likely to present for testing
One could argue that the unvaccinated at this stage are more refusniks and might be reluctant to get tested, but my experience of Israeli people would suggest that they are conscientious principled people. I do not believe the subset who are unvaccinated would skip testing
So the question is... what experiments can we design that would probe the very real differences in case reporting rates between the vaccinated and unvaccinated. Occam says that absence additional data we should use vaccination status as simplest explanation that fits observations
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