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Sampling 3rd dose after two weeks would be statistically insignificant and not enough time to record stats from sickness.

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I dont understand, why would that be "statiatically insignificant"? for what analysis?

I replied to the last paragraph of parent poster. If you study the few people getting dose 3 two weeks after, you're not going to learn anything about effectiveness of dose 3.

If I understand what you're saying, that's not what was done, at least here in Israel.

After the 3rd vaccine, afaik, they compared the rates of hospitalizations of people do did vs. didn't yet get the 3rd vaccine, as compared to what happened the week before. They saw a drop in 3rd-vaccinated, and only in 3rd-vaccinated, implying that it did have an effect. And this wasn't a small population (I don't know exact numbers but I assume several 10s/100s of thousands).

This is the initial report that was published after two weeks: https://www.reuters.com/business/healthcare-pharmaceuticals/...

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