There is plenty of evidence that people can't analyze statistical information properly. Part of it is that people have trouble with doing even simple math, but a bigger problem is that people ask the wrong questions. Even smart people who are mathematically competent ask the wrong questions. In one experiment, described in this article, doctors get conditional probability problems wrong all the time. Here is the problem most doctors got wrong:
"The probability that [a] women has breast cancer is 0.8 percent. If a woman has breast cancer, the probability is 90 percent that she will have a positive mammogram. If a woman does not have breast cancer, the probability is 7 percent that she will still have a positive mammogram. Imagine a woman who has a positive mammogram. What is the probability that she actually has breast cancer?"
Not only do many people struggle with mathematical/logical thinking, it is also a fact that our brains vastly prefer stories to data, as Pulitzer prize winners and brain scans can attest. People feel a greater connection to, and feel more informed by, a single anecdote than solid data. Furthermore, it seems like forming stereotypes is a part of that storytelling process. As we assimilate new information, we use stories and judgment. There are so many stories in the news media where the data or studies presented are merely a hook to start opining upon. In my own field of education, two examples jump out. S.A.T. scores are declining? Tsk, tsk. Never mind that more students, ergo more marginal students, are taking the test, so of course averages will go down. The U.S. K-12 education system ranks poorly compared to other developed nations? For shame. It is a shame -- but most would-be reformers sidestep the real issue. Our system is segregated by race and income, and our suburban schools are doing well enough. Yet so many reformers talk about pay-for-performance for teachers or setting up charter schools or a voucher system and ignore desegregation as a necessary and perhaps even sufficient reform.
Perhaps the most frustrating statistical failing of all is when people fail to ask, What exactly is being counted? What is this variable? The researchers said they were measuring positive outlook, but they were really just counting how many people tweeted positive words. (And "I'm not happy" counts as positive words!) This doesn't require any math skills at all! Just critical thinking.
If people struggle so much with data, what hope is there for a rational populace? Dr. Deanna Kuhn has great evidence about how poorly people organize evidence and conduct simple inquiry. Most people looked for "evidence" that confirmed their initial theories, and the "arguments" they constructed were mostly retelling a story they believed illustrated their belief. (This is called scripting.) But she also found that simple, well-applied interventions could make a big difference on both counts. Dr. Kuhn found that students responded quite well to instruction that was specifically focused on critical thinking skills. The record club idea is one worth adapting with your students! I know from my experience as a debater and as a debate coach that the switch-sides, competitive nature of the activity teaches critical thinking skills rigorously. And I know from my experience that a high school statistics course can teach students all the critical concepts they need to correctly interpret conditional probability. But beyond that, learning to think statistically is very foundational to thinking critically about any evidence. Basic statistical concepts are just logic applied to reality.
I think that Identity Protective Cognition and statistical innumeracy are both real, and they are both the default state of the human brain. However, education can make a big difference. Sadly, our education system is mostly failing in these ways. That's the micro side, the analyzing evidence and arguments. What about the macro side? Do most people leave school with a grasp of the big picture, with a sense of how the major forces work in the world?
I read an article about public intellectuals on Wilson Quarterly, which hit a lot of correct notes. Part of the reason America lacks a set of true set of public intellectuals is our preference for pragmatic thinkers; our general anti-academic, anti-elitist sentiment; and our love of technological solutions -- no problem is insoluble once set upon by good old American ingenuity. But I think the most important reason we lack public intellectuals is that Americans do not especially value historical thinking. I am not going to make a hoary "those who don't remember the past are doomed to repeat it" kind of point. It is more complex than that. The problem is that Americans are especially good at distorting historical facts to fit current ideology. I'm sure that for many people, the Founding Fathers of their imagination have little to nothing to do with the reality. Americans like to think that the debate we're having now is the debate we have always been having. The idea that the past really is a strange, different place is forgotten.
I don't believe that Americans are especially aware of how concepts like "freedom" or "equality" have a long history of evolution, of how the concepts have changed over time and do not mean now what they meant two hundred years ago. People are not aware of the assumptions that are buried below the surface in our popular concepts or the difficulties that are papered over. The idea of "rights," such as a person's right to their property, can short-circuit other considerations and options. The trade-offs of any political economy become invisible or perhaps visible but inevitable. This is the work of philosophy (asking ourselves to state everything clearly and unpacking values and concepts), especially after the linguistic and historical turns, those movements to a constructivist and critical version of philosophy. This is important stuff to study, but I know that few kids besides debaters have an opportunity to do much thinking like this in high school. I can imagine a good college course on politics or public policy might, but I can also imagine many courses merely discuss different systems in an empirical way with little analysis of "justice." As a result of this lacuna in our collective education, American politics is dominated by blind hope. Nietzsche said we needed courage instead of hope, in the face of our many challenges. I am trying to be courageous about our education system, as well as our politics.