# Why don’t most people understand simple statistics?

Mark Liberman has an excellent post examining the general public’s understanding of basic statistical concepts such as means, variances, and distributions. Here’s a taste:

Until about a hundred years ago, our language and culture lacked the words and ideas needed to deal with the evaluation and comparison of sampled properties of groups. Even today, only a minuscule proportion of the U.S. population understands even the simplest form of these concepts and terms. Out of the roughly 300 million Americans, I doubt that as many as 500 thousand grasp these ideas to any practical extent, and 50,000 might be a better estimate. The rest of the population is surprisingly uninterested in learning, and even actively resists the intermittent attempts to teach them, despite the fact that in their frequent dealings with social and biomedical scientists they have a practical need to evaluate and compare the numerical properties of representative samples.

Liberman points out that the relevant concepts are fairly recent. The inability (or unwillingness) of the average Joe to “get it” manifests itself in the coverage of science in the popular press. For example, rather than adequately describing the relative risk of some factor on having some disease, syndrome, or other phenotype, most journalists simply tell you that some group of people are more likely to have the phenotype.

1. #1 Candice
October 7, 2007

Yet another reason I’m glad to have had the teachers I did growing up. I was not only taught these concepts in math class, but they were given attention in my (combined!) English and social science classes — during our critical thinking unit, somewhere in between lessons about bias detection and logical fallacies. I can’t imagine reading a newspaper without these skills. Without being able to interpret things on my own, I guess I’d have no choice but to take anything I read at face value. Kind of helps me understand why appeals to authority can be so persuasive.

2. #2 agnostic
October 7, 2007

We need to know what IQ level is necessary to grasp which statistical ideas. As a guide, it’s typically assumed that the average college graduate has an IQ that’s 1 SD above the pop mean. Then we can compare the fraction of the pop that’s capable of getting the ideas to whatever the observed or estimated fraction is for those who really do get it.

If we don’t do this elementary exercise, we’ll be lost. Let’s go with “you have to be smart enough to graduate college” to get what’s going on. That means roughly 1/6 of the pop is capable of getting the ideas. Liebermans suggests that 1/600, or only 1% of those capable, actually do get it.

That could be — unless you major in something that requires numbers, you won’t know squat. And even a lot of those whose major only requires basic stats (say, many social sciences), usually emphasize basic statistical inference. In reality, for most of these cases, that means knowing which test to run on your software program, and seeing if the p-values are acceptable.

Most of the thinking has been off-loaded to the computer — which is good in a way, since it allows more people to run statistical tests. But it also means that a smaller fraction of those capable of understanding statistics actually will. For comparison, we learn in 8th or 9th grade that x^a * x^b = x^(a+b), and we store that as a fact for recall later. But, though it’s elementary to explain using the definition of what x^a means, most people aren’t thinking that way, so they couldn’t explain it.

So there’s a trade-off: greater knowledge about how the world works requires “getting” less of what produced that knowledge — except the mathematicians, who are always griping that those outside of their tribe know how to do something but don’t get why that process works. I’m in favor of greater knowledge about how the world works, even if it means people read the newspaper more moronically, unless it resulted in a huge mismanagement of public funds. And clearly those who aren’t forgetting simple statistics due to learning more advanced things are not excused — reporters, for instance.

3. #3 Scott Simmons
October 7, 2007

I’m not sure that these very basic concepts are ones that require the mathematical ability of a potential college graduate to grasp, though. Is it at all possible that if discussion of this were more pervasive in our culture, and were included in elementary mathematical education, much more than even 1/6th of the population could cope with some of these ideas?

4. #4 Dale Hoyt
October 7, 2007

For many years I attempted to teach Biology and Genetics students the rudiments of statistics, with, alas, only limited success. The notions of population, sample, variance, hypothesis testing, etc. require more time and practice than can be devoted to them in such courses. Most students in the life sciences are math-phobic and few take statistics courses until they reach graduate school. Even among professional biologists publishing in journals like Science and Nature you can find examples of statistical ignorance. Is it any wonder that the average man on the street doesn’t understand them either? Practical statistics needs to be incorporated into high school math courses and, possibly, earlier. But I’d remain doubtful that even then the average person would understand enough to be critical of what they read in the papers.

5. #5 agnostic
October 7, 2007

You definitely need a certain level of intelligence to “get” statistics, or any math, or anything academic. Most people don’t realize this because they only associate with fellow smarties.

Think of all the math you’re forced to learn through high school. How much does the average person — not the average SB reader — remember in adulthood? Basically, nothing. So throwing statistics into the mix wouldn’t change things that much. It might for those who are preparing to go to college, but they already offer AP Statistics and usually a lower level stats class.

Most nerds are under the vainglorious impression that “if only the key ideas in my field had a big enough megaphone to make themselves heard, society would be improved.” Not really — the average person doesn’t care about academics. Even most of the capable ones want a career that doesn’t involve academic stuff — PR or journalism, say — so they’re going to forget your pet idea anyway.

6. #6 Alex Whiteside
October 8, 2007

While mathematics is needed to perform statistical analysis, I really doubt that it’s completely essential in understanding the results. Huff’s classic “How to Lie with Statistics” demonstrates that you can arm people against most of the statistical dodges we get in politics and advertising, without involving any actual calculation. We can educate people on disease without giving them microbiology lectures, why should stats be any different?

7. #7 Abbie
October 8, 2007

I may confuse mean, median, and mode, but I know not to ever play the lottery. Is that good enough?

8. #8 Jim Thomerson
October 8, 2007

I was told that the book “How to Lie With Statistics” was a required test for the General Education Statistics Course at my university. Sounds good to me. It is an excellent book. As to the lottery, if you do not buy a ticket, your chance of winning is 0. If you do buy a ticket, your chance of winning is slightly larger than 0. If you can afford a ticket, it is a matter of making a small investment with a very small chance of a large return. I don’t buy lottery tickets because it doesn’t interest me to do so.

In the news, talking about Po’folks, Democrats tend to use arithmetic means while Republicans prefer medians. Not sure either party knows what a mode is.

9. #9 Lorne
October 11, 2007

A good easy read for helping the average person to understand stats is http://www.struckbylightning.ca/

10. #10 Jim Thomerson
October 13, 2007

One aspect is that most folks have no idea that many things are distributed in a somewhat normal fashion; a lot of examples clustered around the mean, and a few examples way out on the tails of the distribution. Folks who do not understand this say things like, “My uncle Joe smoked three packs a day since he was six years old and died in a car wreck at age 94. Therefore the statement that smoking cigaretts increases the chance of dying with lung cancer is false.”