This image has been floating around the Anti-Vaxxer circles. It contains the following four misleading statements:
1 – What would you think if an infectious disease specialist published a study showing that 81% of children who contracted pertussis (whooping cough) were fully vaccinated?
2 – And what if that infectious disease specialist told you the pertussis vaccine was effective about 50% in children in general but only 24% of the time in 8-12 year olds?
Dr. Witt’s study was published in March 2012 in Clinical Infectious Diseases
3 – What if the vaccine manufacturer admitted that it has never studied how long the vaccine lasts in children 4-6 years old?
4 – And what if the CDC said that a booster shot of that vaccine is not approved for 7-9 year olds?
Both of these statement [sic] were made to a reporter for Reuters in an article published April 2012.
The clear conclusion these four statements are attempting to convey is that vaccinations do not work. Insinuation aside, neither the articles they are referencing nor the data they present support such a conclusion. The blogger at SkewedDistribution does an excellent job of explaining the math which people fail to grasp:
Immanuel Pfeiffer Middle School has 1000 students enrolled. The students are vaccinated at the same rate as the rest of California (93%); therefore, 930 students are vaccinated and 70 are not. There is an outbreak of pertussis at IPMS, with 100 cases. Of these, 81% of the cases are vaccinated (n=81), and 19% are unvaccinated (n=19). The question, then, is what is the rate of pertussis in vaccinated vs. unvaccinated students?
The rate for vaccinated students is: 81/930=8.7%
The rate for unvaccinated students is 19/70=27.1%
I think it is instructive to use an analogy instead of just numbers:
Imagine a sample of 1000 adults. Of these adults, 93% or 930 adults at one point knew enough math to understand the above example and 70 never learned basic math. There is an outbreak of 100 cases of Math-itus (people who fail to understand some simple math) brought about by viewing some skewed data created by anti-vaxxers desperate for signs they are correct. Of these, 81 of the people at one point knew the math and are in denial while 19 people never knew the math in the first place. The question, then, is what is the rate of Math-itus to non-math-itus?
The rate for “vaccinated” students is: 81/930 = 8.7%
The rate for “unvaccinated” students is: 19/70 = 27.1%
If we stopped my above satire prior to the answers at the end, we could use it to claim:
1 – What would you think if a mathematician published a study showing that 81% of adults who contracted mathitus (fooled by numbers) knew math at one point?
2 – And what if that mathematician told you that math instruction was effective about 50% in when the people first learned it but only 24% of the time later in life?
The clear skewed conclusion implied from the above is that math instruction causes people to fail to understand math. So we should fight teaching math in schools!