Innumeracy
Most Americans, and most people, are functionally innumerate. What is “innumerate?” Well, if a basic lack of literacy makes you illiterate, then a basic lack of mathematic understanding makes you innumerate.
Of course the word “functional” is an important qualifier. For example, real illiteracy–an absolute inability to read–is extraordinarily rare in the United States, even in kids from the worst schools and educational background. That’s why we invented the term “functional illiteracy” (or “functionally illiterate”), because we needed to describe people who know their alphabet and can recognize a few words, but have trouble with much more than the headline on a news article, or who struggle filling out a driver’s license application. Similarly, most people can at least add and subtract reasonably well, so they’re not completely innumerate.
But if functional illiteracy is a problem, I think functional innumeracy may be a bigger one, because it’s more widespread in this society. It appears that most people cannot do math much past the arithmetic level, and tend to struggle even with that.
Now to be clear, I do not put myself up as a math expert; I barely got past basic algebra, which I’m not too good at. Nevertheless, one of the most important areas to staying even in contemporary society is an understanding of basic finances, which is really rather simple math in most ways, and many people struggle with that. Similarly, understanding a lot of social issues is very difficult if you do not understand basic, fundamental statistics. Don’t believe the old chestnut “there are lies, damned lies and statistics.” Most statistics, done properly, are not a lie at all, and can tell you enormous amounts about the world you live in. Furthermore, if you understand statistics, it will become very hard for someone to lie to you with statistics, because you can ask pertinent and simple questions that will help you determine if someone’s using a deceptive statistic.
Decades ago, it was generally believed that about 10% of the population is gay. What was that based on? A survey asking people if they’d ever had a sexual experience with anyone of the same sex. But that’s not a reasonable measure at all, for it leaves plenty of room for people who were just experimenting, who were pressured into something they really didn’t want to do, and so on. The simple pointed question of “How did you arrive at that figure?” would tend to help clarify what the statistic really means.
A recent survey of adults by Gallup shows that Americans tend to think that gay people are about 25% of the population. When asked how much of the population people think is gay, most people answer somewhere around that. Democrats exaggerate it a little more than Republicans, but generally, most people exaggerate the number by a factor of 5-10. A fully precise measurement of how many people are gay is hard to do since the definitions are somewhat fluid, but, a realistic figure of those who self-identify as gay puts them at around 3-4% of the population.
Now, from my perspective, the number of gay people in the world should be all but immaterial to their legal rights. They could be 80% of the population. They could be 1% of the population. It really shouldn’t be relevant. If anything, smaller numbers just means they’re probably in greater need of protection. But all of that aside, what disturbs me is the functional innumeracy of the answer.
If you think 25% of the population being gay is even close to the right number, that means you think about 1 in 4 people is gay. Now, I suppose if you’re living in a community like San Francisco, that number seems realistic. But otherwise, really? 1 in 4? Every 4th person you meet?
Maybe they were inclined to think, “well no, not in MY town, but you know, places like New York and California, it’s like that.” But that means you’d have to assume that in places like California, even more than 25% would have to be gay to make up for the fact that in other areas it’s less.
Of the people who answered Gallup’s survey, only 4% of the respondents got the essentially correct response, which is “less than 5%,” meaning, something like 1 out of 20 or 1 out of 25. Somewhere in that ballpark.
This isn’t the only area where people get numbers wildly wrong. Some years ago, Gallup did a similar survey that found that most people think there are far more blacks and hispanics in the United States than there actually are.
Similarly, a recent article in Rolling Stone attacks Fox News in very fearful terms. The author tosses out a lot of numbers that at first glance make this news network look like a behemoth, maybe the biggest influence on news that there is. Yet a close analysis of the numbers and a little critical thinking go a long way toward casting doubt on them and, therefore, casting doubt on other claims made by its author. For example, among the numbers tossed out is the assertion that “Fox News now reaches 100 million households,” which implies somehow that they have 100 million viewers. But this is ludicrous, and what the number self-evidently means is this:
Fox News is available on basic cable in most of the country.
Do some looking at the real numbers and you’ll find that, during prime time TV watching, Fox News on a good day has a bit under 2 million viewers, with the occasional spike during big events–and 2 million is considerably less than 1% of the US population.
I suppose that both Fox News and its fiercest critics would like you to believe they have 100 million viewers, but they don’t. Just for a comparison, liberal comedian Jon Stewart’s The Daily Show typically pulls in about as many viewers as your average Fox News show.
Although things like gay people, minorities, political news networks, and so on are hotbutton issues, we can distract ourselves too much by looking at those specific issues. What things like this really tell us is that a lot of us are functionally innumerate: we don’t take the time to stop and understand numbers that get tossed at us. And that, I think, has long-term negative ramifications for society as a whole, including our political discourse.
Blogging pioneer Dean Esmay writes for Dean’s World, covering an eclectic variety of topics, political and non-. This guest posting is cross-posted there.
18 Responses to “Innumeracy”
@deanismay
“Don’t believe the old chestnut “there are lies, damned lies and statistics.””
How about; There are people who use statistics and people who are used by statistics! Or Statistics don’t lie people lie!
SEE ALSO
Innumeracy : Mathematical Illiteracy and Its Consequences … John Allen Paulos
Excellent post. I get really frustrated when I talk to certain people and have to just basically throw up my hands and walk away because they are innumerate. Thanks for putting a word to it for me. Schools really should focus more on math and stats for kids as a lack of this knowledge leaves us more vulnerable to manipulation just like illiteracy does.
PS – “a similar survey that found that most people think there are far more blacks and hispanics in the United States than there actually are. ” – See Superdestoyer
DavidMtem: I like the phrase, “Figures don’t lie, but liars figure.”
Although I don’t think every bad statistic is a lie. I think innumeracy accounts for a lot of them. And 3 out of 4 dentists surveyed agree!
What Rolling Stone wrote was:
Mr. Esmay rightly acknowledged that the number self-evidently means that Fox News is available on basic cable in most of the country… But that’s all it means. It was the closing point to the preceding paragraph.
But, Mr. Esmay calling the RS article an “attack” on Fox News in “fearful terms” and his inference to the 100 million households comment “tossed out” and “ludicrous” only tells us of Mr. Esmay extremely partisan take on this issue.
Here’s one of the reasons that Fox News reaches 100,000,000 households:
Is it curious as to why Mr. Esmay missed this? Or did he simply choose to ignore it as it might toss a monkey wrench into his theory as to how Rolling Stone is “Innumeracy” deficient.
Entertaining article Mr Esmay, Thanks.
As my ability to edit “timed out” I will highlight again:
Well, too many people interested not in learning what numbers tell us about the issues. Instead they are more interested in finding something to support their position. You see this in the global warming debate where people are sometimes quick to accept things that sound really good without stopping to think them through.
On statistics, I agree that statistics themselves don’t lie. But how much they tell you depends on the details on some brush over those details to push the conclusions they want.
Absolutely David, It’s a crime that there are so many people that still refuse to listen to what actual climate scientists are saying.
SteveK: Nothing you quote has any relevance to anything I wrote that I can see. But we can let others read it all and decide for themselves.
@DEAN ESMAY
I was quoting what you wrote and pointing out the partisan attack position you had taken against the Rolling Stone article. Now you want to breeze past your own words and claim what I said wasn’t relevant.
O.K… If you can’t see the relevance I’m a bit surprised, but you’re correct, others can read what you wrote and decide for themselves.
PS – Had you left your attack on the Rolling Stone article on Ailes and Fox News out of your post I tend to agree with you your thoughts on Innumeracy.
Your selective quotes and misrepresentation of what the Rolling Stone article said shows that people can try to mislead (lie to?) people with “Numeracy,” too.
I would not have said “5% or less” to the question of how many people are gay. Roughly 3-5% self-identify as gay, but there’s also the absolute fact that it’s a question about which many will lie, and will almost always lie in one direction. Best estimates say that the number of people who have alternate sexualities — which includes those who identify as gay, lesbian, queer, bisexual, transgender, and even includes groups like asexuals and intersex people, as well as those who have not honestly disclosed their sexuality — is closer to 10%. 3% is a number used by those who assume that if you’re not living as an out, gay, cis person, you are a straight person. This is obviously incorrect.
I also think statistics are probably harder than you’re giving them credit for. Statistics that are perfectly valid can make people believe that evolution is highly improbable, whereas a slightly different analysis makes evolution all but inevitable.
SteveK: While I don’t care much about Fox News–it used to be my favorite news network, but that was years ago and I now consider much of its content to be trash, especially the odious likes of Glenn Beck, Bill O’Reilly, and the execrable Sean Hannity–the Rolling Stone piece is pretty openly biased, calling Fox News an unfair and unbalanced network and likening it to the Soviet and Maoist propaganda machines in its very opening lines. Such assertions should call for a lot of evidence, but in fact it doesn’t give us much of that beyond a lot of out-of-context numbers and some questionable assertions. I picked one example. There are others.
For another example, what is the significance to the fact that Rupert Murdoch paid a few million dollars ($25 million is chump change) to get cable companies to carry his feed when the network started? It’s normal in the cable industry for a new channel to want to get on the basic cable lineup to pay for the privilege, but somehow Rolling Stone got all the way through its piece without managing to mention that. To pick another example, they managed to get through the entire piece without ever once mentioning just how many daily viewers Fox News has–and that’s probably because if they had, they would have had to admit that Fox News has less than 2 million viewers a day most of the time.
Nor did they manage to do a simple contrast, as I did, where I pointed out that Jon Stewart has better ratings than the entire Fox News channel on a regular basis.
There are factual errors in the piece that a little due diligence would have also found, such as its completely false-to-fact assertion that Fox News was the first network to call Florida for George W. Bush in 2000–which is the exact opposite of the truth, it was in fact the very LAST network to do so. But even more astonishingly, it claims that Fox News somehow tilted to the election to George Bush by reporting on the fact that the vote count in Florida was questionable, as if somehow, after the polls had closed, Fox News could possibly tilt the results one way or the other by simply reporting that Florida now looked too close to call.
This factually-challenged piece is filled with out of context numbers and questionable assertions of fact like this. The glaring problems with some of their numbers should alert the numerate reader to question the entire piece. Again, I picked one example, but anyone practicing journalistic due diligence can find others.
The Rolling Stone piece is opinion journalism. Which Rolling Stone has every right to publish, but let’s call it what it is. And, among the many cheap tactics of opinion journalism it uses is out-of-context numbers, which is gratifying red meat to partisans who share its fear and loathing of Fox News, but should render more objective readers suspicious as to whether or not Rolling Stone is being completely honest with its readers.
Once again, I believe that simply looking hard at numbers people present to us and thinking through what those numbers actually mean would do a lot to sharpen our political discourse and lead us to more honest discussions.
Cousin John’s calls tipped election tally
I was watching all the news coverage on election night in 2000, flipping back and forth through them all. Fox News was the very last to call Florida for Bush. In any case, even if it had been the first (which it was not) it is silly to assert that by simply reporting that the election count in Florida was under question, Fox News could tilt the results. George Bush having a cousin who worked for one of the networks who gave him some inside polling numbers after the polls closed would not change that.
How Bush’s man at Fox News worked to shape the outcome of the US election
Don Quijote: All of this, even if it were true (both of your sources are questionable: The Guardian? World Socialist?) continues to miss the central point, which is, what the heck difference would it make? Is the suggestion that somehow, by calling the election for Bush, Fox News forced all the other news networks to do the same in a matter of minutes? Or that somehow, by reporting this, Fox News influenced the outcome of the vote?
I’m sorry, but regardless of your feelings on the outcome of 2000, this is all pretty irrelevant.
We need to look carefully at the sources we look to, the facts they claim to present, and the conclusions we draw. And especially in the areas of presenting numbers, we all need to do a better job of engaging our critical faculties.
And with that, I’ll let the rest of you have the last word.
Mr. Esmay – great article, although the comment thread is drifting away from the innumeracy topic. The term “innumeracy” is a good one, although the problem goes beyond an inadequate understanding of math to include also a general lack of understanding of statistics. To go a step further, there is also a lack of understanding and skepticism of polls and studies in general.
There are many bad studies and bad polls out there. Many people not only lack the knowledge to understand that but also lack any desire to gain that knowledge. As is pointed out above, many people are really interested in finding something that supports the positions they already hold. This is just as much of a problem on the right as it is the left.
I’ve taken courses on how to evaluate a study, and what they recommended was looking at the methods section of the study even before looking at the results. I confess that is as hard for me to do as anyone else, but the point is that ideally you start out as skeptical and force the study to prove you wrong. You then go on look at the numbers, confidence intervals, p-values, etc. The discussion section of the study should include possible flaws and confounding variables.
In the media, methods are generally ignored and are difficult to find, and often any attempt to find them are met with hostility and suspicion of your motives. This is the opposite of the way people should approach statistics.
The Guardian is rather far from a questionable source.