(CNN) Researchers reject Fox News host Laura Ingraham’s misuse of their studies to support mask denialism.

Upfront: Laura Ingraham may be stupid, evil, or both, but this is a missed opportunity for CNN to explain the science in an accessible way. It could be done in three sentences with schoolyard vocabulary. Comments for CNN at the end.

The study in question: (Annals of Internal Medicine) Effectiveness of Adding a Mask Recommendation to Other Public Health Measures to Prevent SARS-CoV-2 Infection in Danish Mask Wearers. The study authors present conclusions valid to professional statisticians, yet fail to inform public health policy. The  implication that masks fail to protect the wearer is unjustified. How can this be?

Imagine you are a scientist investigating coin tosses. You use your funding to buy a single penny. You toss it six times; you get five heads.  The chance of this happening is 5%. The chance of five tails  is 5%.  Is 5% sheer random chance definitive? This is a demo of the Central Limit Theorem. Maybe you should drop your plan to write, “Random Variation of Coin Tosses With Implications for Gang Warfare”. The study is weak, lacking statistical power.

Instead of a binary outcome, the study observes:

• 5% chance mask use reduced any degree of COVID  infection, including asymptomatic by 46%. This is statistically weak. A study that measured reduction of severe infection could be much stronger.
• 5% chance mask use increased infection by 23%, which is absurd. This connects with weak statistical power.
• In case you haven’t noticed, the above is contradictory, a red flag.
• Severity of infection was not measured, only immune reaction, likely a limitation of sample size limited by budget.

Reduction of severe infection is crucial and unmeasured, which the authors acknowledge:

“Masks have been hypothesized to reduce inoculum size (34) and could increase the likelihood that infected mask users are asymptomatic, but this hypothesis has been challenged (35).”

There is a 5% chance of absurdity, that masks increase infection. The study authors are completely honest, acknowledging this with stated limitations:

“Inconclusive results, missing data, variable adherence, patient-reported findings on home tests, no blinding, and no assessment of whether masks could decrease disease transmission from mask wearers to others.”

Now for the journalism. Laura Ingraham is untouched by CNN as long as CNN’s scathing criticism is confined to the political domain. “Follow the leader” is a strong political meme that can’t be countered with “believe us not them”. Some significant minority of our society is amenable to reasoning with facts. Any political piece that goes beyond sheer tactics deserves a few nibbles of reason from the natural world, with companion schoolyard logic.