It’s a Friday afternoon for me…and I was just about to log off and go home. I haven’t posted in a wee while and thought I’d have a quick peek at the set of ‘posts I’ve written but didn’t publish’ and I found a short one that amused me.

I wrote it at the peak of COVID-itus and, given some dramatic protests going on at that time, I chose to keep my powder dry.

But, bugger that…here it is (better late than never):

I’ve seen a repeating misunderstanding (e.g. within social media¹) of the mathematics re. the relationship between vaccinated people and those being treated in hospital with COVID.

Some people are incorrectly concluding that, if a high % of those people being treated in hospital with COVID are vaccinated² then this shows that you are more likely to end up in hospital with COVID if you get vaccinated!

I’ve also seen some tortuous back-and-forth social media threads trying to ‘argue’ about this.

So, taking us away from the emotive world of COVID, I put forward (what I hope is) a simple example to explain what’s going on…

Example³

Let’s suppose that:

• 100 cars are driving along at night with their lights on and 6 of these are involved in an accident; whilst
• 4 cars are driving along at night without their lights on and 2 of these are involved in an accident.

If we only look at ‘cars involved in accidents’, we can see that 6 of the 8 (or 75%) had their lights on. Which, with just this information, may look like you should turn your lights off!

However, if we look at the complete picture, we can see that there is a 6% chance of having an accident if you have your lights on (6 out of 100) and a 50% chance if you don’t (2 out of 4).

i.e. Turn your lights on.

Now, replace:

• ‘Cars driving at night’ with ‘people in a community’;
• ‘Lights on or off’ with ‘whether vaccinated or not’; and
• ‘Involved in an accident’ with ‘ending up in hospital with COVID’.

Footnotes:
1. Regarding the source of the misunderstanding: Some health authorities may not have been as clear in their communications as perhaps they could have been…which will have fuelled the social media.

2. The countries with high vaccination rates will likely be in this situation.

3. Please note that I’ve completely made up the figures that I’ve used in the example and this is deliberate. The point of the post is just to expose the mathematical error. There will be a set of COVID vaccinated/ unvaccinated ratios and equivalent ‘accidents’ (e.g. people in hospital with COVID) that can be substituted in.

Also, please assume that all 104 cars are driving on the same nights, in the same geographic location! (i.e. the same community)