This was, to anyone who knew anything about the coronavirus and the vaccines, not just improbable but effectively impossible. The simplest, most obvious explanation was that McAnulty had misspoken, saying “vaccinated” when he meant “unvaccinated.” And this was exactly what had happened. When he took questions a short while later, a reporter asked about his statement, and he said: “I think I misspoke before. Of the 43 people in intensive care units, 42 have not been vaccinated.”
But it was too late. Anti-vaxxers around the world flooded Facebook and Twitter with clips of McAnulty’s misstatement. The right-wing “news” site Gateway Pundit picked up and amplified the false information. These posts and tweets of course omitted the fact that McAnulty had quickly corrected himself, with some adding a lie by claiming that McAnulty had been speaking not just of ICU patients in New South Wales but of all the covid hospitalizations there. They trumpeted what he had said as evidence that the vaccines were “literally useless” at best and downright harmful at worst.
The speed and efficiency with which McAnulty’s misstatement traveled testify to the way anti-vaxxers and vaccine skeptics use social media to disseminate the message that the vaccines are unnecessary, ineffective and dangerous. But they also demonstrate how the successful spread of that message depends on an unfortunate fact: An awful lot of people just don’t do math. The message lands easily because of the general innumeracy — and specifically the ignorance of statistics — of the people consuming it. It takes only an elementary grasp of math to see that McAnulty’s initial statement was self-evidently unbelievable. At the time, most of New South Wales’s population was unvaccinated. So even if the vaccines were totally ineffective, meaning vaccinated and unvaccinated people were equally likely to be hospitalized, some unvaccinated people would have ended up in the hospital with covid. But tens of thousands of people happily believed otherwise without a second thought.
What’s often called motivated reasoning is at least partly to blame — people believed something that was mathematically nonsensical because they wanted to believe it. But too many people couldn’t recognize it as mathematically nonsensical. Americans are generally bad at math. A 2012 global study of the math skills of 16-to-65-year-olds found that American adults were less numerate than adults in most other developed countries. On a scale ranking skills from Level 1 to Level 5, with Level 5 the highest, 60 percent of Americans were at Level 2 or below, and almost 30 percent were at Level 1, which meant they struggled with even two-step calculations. That’s a serious problem when it comes to evaluating vaccine effectiveness, since doing so requires multiple steps: looking at what percentage of total covid hospitalizations or deaths are among the vaccinated, looking at what percentage of the population is vaccinated, and then adjusting for that and for age to calculate how much more likely an unvaccinated person is to be hospitalized or die.
Lots of people, of course, never get that far. They make simpler mistakes: thinking that if 30 percent of people testing positive are vaccinated, that means 30 percent of vaccinated people tested positive, or believing that if a vaccine is 95 percent effective against hospitalization, that means 5 percent of vaccinated people will end up in the hospital. And it isn’t just random people on Twitter who make these errors. CNN, in an article on how to fly safely, infamously suggested that a 90 percent effective vaccine would still mean that 10 percent of vaccinated fliers might catch the coronavirus. (What it really means is that a vaccinated person’s risk of being infected on the plane would be 90 percent lower than an unvaccinated person’s risk.)
Innumeracy, as the CNN example suggests, is not the province of any one group. And both sides in the information war over vaccines have used dubious statistics. But since the numbers show that vaccination offers excellent protection against hospitalization and death, covid skeptics and anti-vaxxers have become adept at exploiting people’s innumeracy to instill doubts.
Some of these tricks are straightforward. When Vermont, which has the highest vaccination rate of any state, saw coronavirus cases rise from a very low base in late summer to a few hundred a day, and saw hospitalizations climb into the double digits, vaccine skeptics didn’t say that Vermont still had some of the nation’s lowest case and hospitalization rates, or that its absolute numbers were still very small. Instead, they said Vermont’s cases were up “10,000%.” Saying “Vermont has 300 cases a day” wouldn’t have had quite the same effect, especially given that states like Florida were recording five times as many cases at the time. They also failed to mention that unvaccinated people in Vermont were far more likely to test positive for the coronavirus and to be hospitalized for it. The mere fact that Vermont’s cases were up was taken as evidence that the vaccines don’t work.
Similarly, when vaccine skeptics focus on countries that have had (or have) high case rates despite also having high vaccination rates, like Israel and Britain, and compare them unfavorably with the United States, they never mention that these other countries test far more than the United States does. That means that those countries identify many more infections than the United States does, and that their larger per capita caseloads are largely an artifact of testing. This summer, for instance, Southern states with low rates of vaccination had much higher positive test rates than Israel did, suggesting that their coronavirus infection rate was much higher as well. But because they were testing so much less, the states’ case counts looked better. And so the most common social media refrain from vaccine skeptics in July and August was “What about Israel?,” not “What about Tennessee and Mississippi?”
The most important place where innumeracy has helped foster vaccine skepticism is in the debate over vaccine effectiveness against severe illness and death. Vaccinated people can, and do, get severely ill and die of covid. So skeptics regularly point to the absolute number of deaths from breakthrough cases, or the share of total covid deaths accounted for by vaccinated people, as proof that the vaccines are failing.
The problems with this “analysis” are straightforward. First, if you’re trying to determine the effectiveness of vaccines, you need to know more than the percentage of hospitalizations and deaths that vaccinated people account for. You also need to factor in the percentage of people who have been vaccinated, and adjust accordingly to determine the mortality and hospitalization rates for vaccinated and unvaccinated people.
Second, to get a true picture of vaccine effectiveness, you also have to adjust for age. There are two basic facts about covid and vaccines: Since the pandemic began, seniors have accounted for most covid deaths and severe illness; and seniors are the most vaccinated group, while most unvaccinated people are young. As a result, naive comparisons of the covid mortality and hospitalization rates for vaccinated and unvaccinated people understate vaccine effectiveness, since so many unvaccinated people are young and therefore less likely to be hospitalized with covid or to die of it.
To correctly measure vaccine effectiveness, then, you need to compare the mortality and hospitalization rates for vaccinated and unvaccinated people of the same age. And when you do this, it becomes clear how risky being unvaccinated is. In Oklahoma, for instance, the state says around 17 percent of seniors are not fully vaccinated. But those 17 percent account for 70 percent of all senior hospitalizations in the state over the past month. That means unvaccinated seniors in Oklahoma are 11 times more likely to be hospitalized for covid than vaccinated seniors are.
The math behind that “11 times” number isn’t complicated. But it isn’t obvious, either, and it does take a willingness to do it yourself, which lots of people understandably can’t or don’t want to do. As a result, simply presenting big numbers without context — a 10,000 percent increase; 3o percent of hospitalizations — ends up being an effective technique for making vaccines look bad. And while there are lots of people on social media debunking fake stats and providing more rigorous statistical analysis, if you don’t trust them, there’s no reason you’ll trust their math.
Public health authorities have often made this situation worse by the way they collect (or don’t collect) data and present it. The Centers for Disease Control and Prevention’s state vaccination numbers, for instance, sometimes conflict with the numbers provided by state departments of health, and it’s not clear why. While some states — among them Oklahoma and Connecticut — do a good job of presenting data on cases, severe illness and death among the vaccinated and unvaccinated, plenty of other states do much less. Go to Florida’s covid-19 website, and you will search in vain for the daily numbers of reported cases and tests. And the state offers no data at all on hospitalizations and deaths by vaccination status.
Public health officials have also hurt their credibility by oscillating between making statistically dubious claims about vaccine effectiveness — Anthony Fauci’s saying that coronavirus surges like the ones we saw last year were unlikely once the vaccination rate reached 50 percent in a community, for example — and making scary, dubious claims about the risks of the delta variant to the vaccinated. There is no quick fix for innumeracy. But public health officials can help mitigate the problem by being rigorous in their messaging and careful to present data in a clear, comparative way. (Connecticut’s weekly covid reports, for instance, show not just the absolute numbers but also the relative risk of infection and hospitalization for unvaccinated people in an easy-to-understand format.) If they don’t, their mistakes will be weaponized by anti-vaxxers to spread fear, uncertainty and doubt.