According to a recent article, two hairstylists in Missouri interacted with a total of 140 clients and six co-workers before learning that they had tested positive for COVID-19. However, none of the 146 people they were around caught the virus. Among other precautions, the salon where the two stylists work required both the customers and its employees to wear masks.
While this is just one incident, it provides strong statistical evidence that masks are effective at preventing the spread of COVID-19. If we assume that each time a stylist interacted with a co-worker or a client there was the same probability p that they would spread the virus, and if we assume that these events are independent, it results in the graph below.
The x-axis is the effectiveness of masks, as measured by the probability that a mask prevents infection during any particular encounter. The y-axis is the probability that 146 such encounters results in no spread of COVID-19. The key takeaway from this graph is that masks are at least 97% effective. If they were any less effective, the odds of the hairstylists not transmitting the virus to at least one of the 146 people would be less than 1%. The average effectiveness of masks as indicated by this curve is between 98% and 99%.
Some local leaders are mandating mask requirements. Unfortunately, Rutherford County, Tennessee, where my family and I live, is not among them. This has to change if we want to slow the spread of COVID-19. We need widespread requirements for mask wearing in public spaces.
The salon unwittingly ran an experiment on mask effectivity.
This is solid evidence that needs to be shared. Great work, Christian.
Thanks, Doug.
Good work as always, this will go in the list on Pearl Trees under “academic” evidence
Amazing what simple HS Stats can tell us
Thanks, Glen.
Does your conclusion here depend on the assumption that if both the client and the stylist had NOT been wearing a mask, 100% of clients would have been infected? And also that masks are the only factor that prevented infection? (Side note: only 46 out of 146 people were actually tested; the rest chose to quarantine without tests). I’m honestly not trying to be ugly or argumentative. And I do wear a mask when indoors in a public place. I’m a medical health professional (optometrist) who will admit that my best subject was not biostatistics. I’m just trying to think critically and scientifically about the whole mask issue.
Thanks for the question. No, the results do not depend on the likelihood of transmission without masks.
That is also a good point. I am assuming that the other 100 did not catch the virus,
Changing the 146 to 46 does not change the results much, though. It makes only a percentage point or so difference.
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