It will probably come as no surprise that not being vaccinated, or being undervaccinated (missing a schedule routine vaccine) is associated with a higher risk of being infected with the disease that the vaccines are meant to prevent. This is just another way of saying that vaccines work – they reduce the risk of infection.

Often anti-vaccinationists deliberately look at such data wrong, however, in order to create a false impression. They will cite data showing that the majority of the infected are vaccinated, implying that the vaccines do not work. This argument is not valid, however. If, for example, 95% of a population is vaccinated, but 2% of them are non-responders and get the illness, while 5% are unvaccinated and 20% of them get the illness, the vaccinated will outnumber the unvaccinated among those infected – even though ten times as many unvaccinated as vaccinated get sick.

This represents what researchers are now calling “motivated numeracy” – losing basic math skills when ideologically motivated.

Essentially the researchers found that when data is presented, even in a very simple form, people can make sense of that data by relying on simple, and invalid, heuristics or they can make the mental effort to more thoughtfully analyse the data. There are two factors that determine which strategy they will take (lazy or thoughtful) – their baseline numeracy, and their ideological motivation.

The researcher found, in fact, that highly numerate people will revert to relying upon simple and wrong heuristics when those heuristics lead to the answer that supports their preexisting biases.

They used gun control and crime as their example, but it also applies to vaccines and infection. A heuristic is a simple mental short cut that may work sometimes, but is not strictly true. In my example, the heuristic would be – which group has more infections (vaccinated or unvaccinated). The correct analysis, rather, is what percentage of vaccinated and unvaccinated populations get sick, or – what is the relative risk.

Even the most intelligent and math literate subjects in the study had no problem losing their math skills and relying on obviously wrong heuristics when it suited their ideology, and this effect was equal for liberals and conservatives.  I suspect what happened was that people instinctively look at the numbers with a simple heuristic. If that provides an answer congruent to their beliefs, they stop there. If that provides an answer incongruent to their beliefs, then they take a closer look at the data (if they are able).

This is one form of confirmation bias – accepting data without question when it says what we want, but analyzing to death anything we don’t like.

Getting back to vaccines – what do we find when we properly look at the data? There are many studies showing that vaccines provide protection and reduce relative risk. The latest one comes from JAMA Pediatrics. They looked at cases of whooping cough and compared them to controls. They found that 47% of children with whooping cough were undervaccinated, while only 22% of controls were. That’s a clear association.

The motivated numeracy study, however, suggests that merely educating people to make them more math literate is not sufficient to prevent misreading data. Perhaps you have to also give them critical thinking skills.