Sep 12 2013

The Undervaccinated and Motivated Numeracy

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.

8 responses so far

8 thoughts on “The Undervaccinated and Motivated Numeracy”

  1. BillyJoe7 says:

    There is also the slightly more complicated example of sex discrimination levelled at a particular university. Overall, compared with males, a much larger percentage of females who applied for admission to the university were refused admission. However, on further analysis, it was found that, for each course, compared with males, roughly the same percentage of females who applied for admission to that course were refused admission. How could this be explained? Well, apparently, females tended to apply for admission to courses that had a high refusal rate, whereas males tended to apply for admission to courses that had a low refusal rate.

  2. Great article. Shouldn’t the term be “motivated innumeracy”?

  3. Bruce Woodward says:

    This reminds me of that show Numb3rs that I think is cancelled now. My wife used to watch it all the time and I had to leave the room or be doing something that took my attention from it completely.

    The so called “smart” brother would throw around all kinds of fancy numbers and theories and heuristics that sometimes had absolutely no relation to the actual problem or were in fact HUGE oversimplifications made out to be super uber math(s) problems.

    This dude was a supposed genius but his ability to critically think was completely lacking… though I think that was more a result of bad writing than an intentional character flaw because his flawed techniques were the only way the bad guy was caught… ever.

    Terrible terrbile show. Being good at adding things in your head or even the ability to parse a logical statement in your head in super quick time does not mean you are able to analyse a piece of data and read the real story there.

  4. tmac57 says:

    To paraphrase Robert M. Price- Statistics can be used like a ventriloquist’s dummy.You can make them say whatever you want them to say.(Price’s example was about the bible).

    Some (maybe most) people who do this may be just falling into a common mental trap of confirmation bias,but I suspect that there are many intellectually dishonest actors out there that are merely exploiting the numbers to push their ideology,while fully realizing that they are intentionally misleading (lying to) their audience.

  5. oldmanjenkins says:

    An excellent book (in my opinion) regarding cognitive processing is Thinking Fast and Slow by Professor Daniel Kahneman. It has very good incite into how these cognitive discrepancies occur. In a sense, we are more biologically programmed to think certain ways than some are willing to admit.

  6. Old Man, I second that recommendation for basically anything by Kahneman, great stuff that lays out our mental shortcuts that we use all in the time in place of actual thinking.

  7. sonic says:

    What an well done paper. So clear. And not behind a pay wall.

  8. Steven

    “‘Motivated numeracy’ – losing basic math skills when ideologically motivated,” is a very gentle way to describe it.

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