I don’t dispute that the study reveals some sort of bias against atheists, but I do find it amusing that 30-60% of people think that it’s possible that P(A)*P(B) > P(A), and that this doesn’t even warrant a mention in the article.
A similar question I’ve seen before: Which of these two scenarios is more likely?
Scenario A: Mexico declares war on the US.
Scenario B: US crackdowns on the source of drugs smuggled through Mexico force Mexican drug lords to form new alliances with Afghani poppy growers to stay in business. This results in the Mexican gangs being infiltrated by radical Islamic terrorists, who as part of the price for their opium poppies demand that the drug lords, together with a few key government officials they’d already blackmailed, shelter top lieutenants to Osama bin Laden. The US learns of this, and issues an ultimatum to the Mexican government to hand over the lieutenants, or face a cutoff of all trade with the US. In response to this ultimatum, the Mexican government, encouraged by the Islamic elements, declares war on the US.
A lot of people say that B is more likely, just because humans like to have a narrative.
I’m not sure that this was the case for the 60%. The phrasing was:
The wording is not sufficiently precise that we can be sure that (2) was interpreted as a subset of (1). In cultural context, the evil atheist in (2) could be interpreted as drawing a contrast with a “normal” teacher (1), who is assumed to be a principled god-fearing fellow.
I have seen that with “scientific-sounding answers” too.
Which is true?
Water expands when it freezes.
Water contracts when it freezes, because the cold reduces the distance between molecules, and as the temperature approaches 0 Kelvin, the protons in the nuclei and their electrons bind together and become closer and shrink the H2O molecules, folding them into a more compact array structure…
That’s not the same phenomenon that Chronos was describing. What he was describing was people choosing B as being more likely than A even though that is impossible; B is a subset of A so A has to be more likely than B. It demonstrates that people do not have an instinctive grasp of how probabilities work.
This is, first, an example of what’s called the conjunction fallacy. People are asked which is more likely - 1) The man is a teacher; or 2) The man is a teacher and has X religious beliefs. A significant proportion of people say that 2 is more likely. They say this regardless of what X is. It’s called the conjunction fallacy because what anyone who believes this is asserting that it’s more likely that A and B are simultaneously true than that just A is true. It’s obviously not true if you think slowly about it. The set of men who are teachers and who have X religious beliefs is a subset of the set of men who are teachers, so 1 has to be at least as likely as 2.
The conjunction fallacy is a pretty standard example of a modern logical fallacy, or perhaps it should be called a psychological fallacy. You can find a further description of how it works in Chapter 15 (“Linda: Less is More”) of Thinking, Fast and Slow by Daniel Kahneman. This is a book (almost the standard textbook, in fact) on how unconscious assumptions affect our thinking. I think that it would be useful for any regular on the SDMB to read this book, since what we’re doing here often involves carefully thinking through any question we’re asked to discover what biases there are in the question itself. While it’s possible to think of the conjunction fallacy as being about mathematics, it’s not clear that people who are good at math are less inclined toward this fallacy than those that aren’t good at math. The fallacy is about what people say when they don’t think carefully through something, not whether they would use math when they do think carefully about it.
Second, this shows that the set of people who are unconsciously prejudiced against atheists is larger than the set of people who are unconsciously prejudiced against theists. This bias interacts with the conjunction fallacy to make the proportion who answer this way when X is “atheist” more than when X is “theist”. So the results of the study in the link given in the OP aren’t surprising.
All true, but still the survey as reported has problems, doesn’t it? The survey can only measure bias in those who get the underlying probability problem wrong. Instead of being able to conclude that the surveyed population is biased, we know only that the subset of people who answered the question wrong are biased. Without additional controls, we don’t know whether there is a correcting bias toward atheists in those who answered correctly. It’s possible (but perhaps not likely) that the population as a whole is unbiased.
Also, it seems to me that it would have better to use a value-neutral question as a control instead of atheist vs theist. Wouldn’t it be better, for instance, to ask in the non-athiest version of the question whether it is more likely that the serial killer be a teacher, or be a teacher and right-handed? Doing so would eliminate the question of whether this is measuring a bias against atheists, or a bias toward the religious. I don’t think those are entirely complementary questions – there’s a whole third class of people I would put in the “don’t know or don’t care” camp, so a bias toward the religious is not necessarily a bias against atheists specifically.
Of course, that’s just commentary on the reporting. Having been too lazy to look up the actual paper, it’s entirely possible that it includes controls for this kind of thing.
I take no position on whether the entire study is flawed and whether the article that was linked to about the study was an accurate description of it. I haven’t read the original paper, so I can’t say anything about its scientific accuracy. I was only trying to explain the concept of the conjunction fallacy (as did others in this thread, although without using the name “conjunction fallacy”). I only mentioned the contrast between atheists and theists because the study used that distinction, and I take no position about whether that’s a useful way to do the study.
You’re all wrong. Unless this questionnaire said Math Test at the top then most of the people taking it thought they were being asked if a teacher was a sociopath was he more likely to be atheist/religious or not. The point of the thing was to find out what people’s preconceived notions were.
I don’t agree that it’s a math issue. It’s a matter of how to interpret the question.
I think most people, when seeing an open-ended A and a more detailed B, assume that A means that the detail in B is not true. Meaning if A is “… is a teacher” and B is “… is a teacher and an atheist”, they assume that A means “… is a teacher and not an atheist”.
It’s not like all survey questions are phrased flawlessly. My own experience with surveys is that I frequently find myself wondering if I should answer the question as literally phrased or based on what I think they probably really mean. So I think that many people are assuming that the question in this case really meant “… and not an atheist” and are responding accordingly.
I would guess if the question made clear that A meant “… is a teacher, whether an atheist or not” that very few people would make this mistake.
I agree with Mr. Phipps. Unless I had been told that the study was intended to measure of the understanding of statistics (not just mathematics), my assumption would be to be that it was just a poorly worded question.
You see that all the time. Many survey-takers try to give the answers they feel are intended, and not literal interpretation of the question. I think this is, as Mr Phipps points out, they have been subjected to so many poorly-worded questions that they tend to ignore the literal interpretation, since that interpretation is often viewed as being wrong.
I also automatically interpreted the statements such that B was not a subset of A. I had to put my “scientists ask trick questions” filter on to see the problem. (Said filter is because I hear about so many studies that seem to be about one thing but are really another. In wonder how bad that affects results.)
Of course, there is still a problem with people being more likely to assume the bad person is an atheist. In fact, it explains why the two numbers almost add up to 100%, as 1B and 2A are seen as equivalent.
No, they are language challenged. For the astute reason given below:
As a lawyer with a father and brother who are both mathematicians, my experience is that the latter can have a misguided and partial understanding of language. They tend to view language (at least in the context of problem setting) as if it’s computer code or mathematical notation. But everyday language has heaps of rules that are so ingrained that we have no conscious awareness of their existence.
My father recites the following as an example of people not thinking logically:
*“A man looks at a farmer’s field containing a herd of magnificent horses, although one has a leg missing. He offers the farmer $20 for every horse with three legs in the field. The farmer, knowing he has only one horse with a missing leg, gladly takes the money. The man then takes the whole herd of horses, pointing out that all the horses have three legs. All but one have more than that, but they all have three.” *
The man is simply wrong. There is an unstated but completely understood rule of economy of language. You don’t use qualifiers about a thing unless you have to. Consequently, absent other words of clarification, use of a qualifier strongly implies that you are not referring to things that do not fit that qualifer, else why would you use the qualifer?
The assumption made in the paper referenced by the OP (assuming it has been reported correctly) about what their question means is wrong. Juxtaposing “teachers” against “teachers who are atheists” without other modifiers strongly implies the former group does not include the latter.
And I agree with this:
Even those answering the question who realised the ambiguity are left with a dilemma? Do you assume you know what the questioner meant, even though that’s not precisely what they said? Or do you go with the literal interpretation?
Happens all too often in the setting of math problems.