So for the past several weeks, I’ve been in a Twitter argument with a libertarian who is also an anti-vaxxer. Recently, I showed him data from the CDC showing COVID cases by vaccination status. He took issue with the “Unvaccinated” group being defined as “An unvaccinated person had SARS-CoV-2 RNA antigen detected on a respiratory specimen and has not been verified to have received a COVID-19 vaccine.” His reasoning being that this definition implies that there are vaccinated people who didn’t have verification on them at the time they were diagnosed who are inflating the numbers.
I explained to him that if they are actually vaxxed, then their rates would be similar to the “verified” vaxxed people, and therefore driving the numbers of the “unvaxxed” down. I also explained that it is highly unlikely that it is a common thing for vaccinated people to go to the doctor or hospital with covid symptoms and NOT bring their vaccination card with them.
He asked if I would be fine with adding these people to the vaxxed group and I said, “Yes.” I gave him this example:
Group A:
100,000 “verified” vaccinated people
500 breakthrough cases
Results in a breakthrough case of 0.5%
Group B:
10,000 “unverified” vaccinated people
50 breakthrough cases
Results in a breakthrough case of 0.5%
Add Group B to Group A:
110,000 vaccinated people
550 breakthrough cases
Results in a breakthrough case of 0.5%
He said that isn’t the way fractions work, because I am “adding the denominators.” He said that in order to calculate this correctly, I would have to make Group B also be 500 breakthrough cases out of 100,000 people, and then when I add the two groups together, it would be 1,000 cases out of, still, 100,000 people, thus DOUBLING my rate.
Now, I struggled to understand how adding together the rates from two groups, each being the same rate, ends up DOUBLING the total rate. So I gave him a simpler example:
“There are two pizzas, each that started with 4 slices. Pizza A had 3/4ths of its slices eaten, and Pizza B had ½ of its slices eaten. What is the fraction of the total amount of slices eaten?”
Obviously, the answer is 5/8ths. You can get this by either hand-counting the slices, or solely by using fractions: Convert ½ to 2/4ths and adding it to 3/4ths, giving you 5/8ths. If you don’t add the denominator like he says you’re supposed to, you’d get 5/4ths, which doesn’t make sense.
Anyway, he refuses to answer the question, claiming it is a bogus comparison.
Is he right about anything? Did I get something wrong?
Thursday, Dec 9, 2021 · 4:07:05 PM +00:00
·
Awful Falafel Waffles ROFL
Update: I’ve finally realized a major part of his malfunction. He thinks that when a line graph showing Covid rates by vaccination status says “Per 100,000 population” on the Y axis, that it means “Out of 100,000 people, X vaccinated people got covid, and Y unvaccinated people got covid.” But what it REALLY means is, “Out of 100,000 vaccinated people, X got covid, and out of 100,000 unvaccinated people, Y got covid.”