One of the ways to lie with statistics, is to compare where the rate is small. I noticed an example yesterday. The numbers are these and apparently from the CDC. The headline is “The unvaccinated are 11 times more likely to have a serious case of Covid-19 than are the vaccinated
There are two messages there.
The headline does not provide any useful information unless you know the rate of serious cases among the vaccinated. It turns out that is 1.2 per 100,000. A very good result for vaccines.
The unvaccinated therefore are 11 times greater at 13.2 times per 100,000. While 11 times greater is meaningful, it is not meaningful by itself. Why? Because 13.2 times per 100,000 is one in 7,576, or 0.013%. Even that is not very helpful. Look at the other way. If 1 in 7,576 is the the group harmed then 7,575 in 7,576 is not. That is 99.987%. have no problem as opposed to 99.99988% among the vaccinated,
Unvaccinated are okay in 99.987% cases while the vaccinated are at 99.99988%, is not a very compelling headline.
The statistics above claimed they come from the CDC, but realistically they should be investigated further. Skeptical is a good position to hold regarding any statistic. Sometimes you can see through the numbers.
What could have happened to make the ones here reasonable?
Only three things I can see:
If anyone cared, they could assess the reasons and know more. If you dig deep enough you can usually discover not only the what happened, but also the why it happened.
Comparing statistics where the rate of occurrence is tiny must be examined in detail.
When statistics are presented with no context you can still come to some conclusions that supply insight.
The raw statistics would be nice to have but I can’t find them. The CDC is a inscrutable.
Never use statistical evidence to make medical decisions. There is risk using data covering large populations with varying conditions to assess how risk applies to you. Try to fit your situation to data relating to others like yourself not the population taken as a whole.
Learn to undo the carefully painted statistical picture. Looking from the other side usually provides insight. It is a good habit to have.
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