"The numbers have no way of speaking for themselves. We speak for them. We imbue them with meaning." - Nate Silver, The Signal and the Noise.
We've been seeing many charts relating to Covid-19 and most of the time do not touch about the statistics behind them as they might not be relevant for the laymen? This post covers two chart examples and what they mean from the statistical perspective.
Top: About 75% got at least one dose (as shown), which means 25% are not vaccinated at all and that among 7 randomly chosen persons, we would expect about 2 persons totally not vaccinated, but now we're seeing 6. Next, we can do hypothesis testing to see that this difference in proportion is statistically significant i.e. the difference is not due to random chance and can be attributed to the vaccination. Which is indeed the case. (This doesn't mean that it is 3 times more likely to require oxygen support/ ICU if one is unvaccinated.)
Bottom: The risk of requiring oxygen support/ ICU is 2/(546+369) = 0.219% for those vaccinated with at least one dose, and the risk of that for those not vaccinated at all is 8/295 = 2.71%, 12.4 times that of those vaccinated with at least one dose. The relative risk is computed as (12.4-1)*100% = 1140%.
