Using Numbers Again

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.

  1. Vaccinations work very well thank you.
  2. The unvaccinated are taking needless risks

How context matters

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:

  1. Older people are most at risk and would skew the statistic if at risk. We can estimate that most all old people are vaccinated and vaccinations protect them. Unvaccinated older people could be the problem demographic.
  2. Many of the unvaccinated have already had the disease, have natural antibodies, and strong immune response.
  3. Other unvaccinated persons have stimulated their immune system with Vitamin D, Vitamin C, Zinc, and exercise.

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.

The takeaway

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.

I help people have more retirement income and larger, more liquid estates.

Call in Canada 705-927-4770, or email

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

%d bloggers like this: