And on, and on, and on. Oh yeah there was also this fun one:
“But it’s here now and it’s spreading and it’s gonna increase. … We are looking at a winter of severe illness and death for the unvaccinated – for themselves, their families and the hospitals they’ll soon overwhelm. But there’s good news: If you’re vaccinated and you have your booster shot, you’re protected from severe illness and death,” the President added.
Donald Trump is the last person you should take medical advice from. He was criticized nonstop by medical professionals, scientists and even scientific journals for saying all kinds of crazy things, and this is the least of it. My 12 years of postsecondary education have not prepared me to articulate exactly how stupid this person is. It's indescribable.
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Link 2
That study has a confidence interval that is not reported in the news article. CNN is not a great authority for health advice. It's okay to watch/read it, but then it's incumbent upon you to verify the technical details. They get science stuff wrong all the time, and so do all other non-specialist news organizations.
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Link 3
Despite the super misleading name, this is a pro-industry lobbying organization. This website is not where you go to find health advice. Notwithstanding, the web page says the data shows 100% effectiveness (n = approx 30,000) against "severe covid" (which is defined in very precise terms), but again this will have a confidence interval which is not reported here.
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Link 4 / Biden quote
"you’re protected from severe illness and death" is accurate. No mention of 100%.
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Link 5 / last quote
Also seems accurate, at a glance. No mention of 100%.
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Bottom line: politicians are not who you need to listen to for medical advice (yes that sucks, and yes they should do better). Also you can't blame scientists, doctors and public health experts for your own misunderstanding, for the fact that you get your information from dubious places, and for your inability to grasp nuance. Also, public health messaging is insanely difficult even in the best of conditions: even when the message is 100% accurate there will be second-hand reports that get it wrong, and people who understand the complete opposite of what is said. You need to understand this if you want to hope to understand what's happening.
Go to nature.com or science.org if you want science news.