Intuitive statistical concepts and prejudice

As scientists, we are constantly met with the stubborn persistence of what we perceive as ‘bad’ statistical thinking from our politicians, journalists, landlords, and even friends and relatives. We may have forgotten that statistical thinking in the sciences is, actually, a skill which must be cultivated (see this article). In contrast, most people, if asked, will answer that they don’t know anything about statistics and don’t  make statistical or probabilistic judgements – but that’s complete rubbish! If you pay attention, we hear such pronouncements all the time, on TV (e.g., “X  hasn’t got a hit in  35 at-bats, he’s due for one now!”), at home (when your granny says disapprovingly “Men will always prefer a young leggy blonde to their loving wife”), or even at sea (“Red sky at morn, sailors take warn!”). I won’t go into detail about what you can find in the newspapers – it’s a bloodbath, especially with respect to headlines – just this morning I stumbled on a BBC Magazine article trying to explain the statistics behind the headline “UK pensioners poorer than Romanian ones“, which must have sent cold shivers down the spines of the British elderly.

But most often, we hear these kinds of statements in connection with other people, especially with groups of people. Take for instance the example of human height – a quantitative human trait that most people intuitively understand as a continuous variable with a ‘distribution’ and ‘extreme’ values (in contrast, for example to some cultural understandings of skin color, which can tend to be segmented). A recent conversation with a good friend went something like this: “Hey Carpathian, I read in Wikipedia that the Dutch are the tallest Europeans, but I know quite a few Dutch and they’re not very tall”– “That’s irrelevant – that statement refers to a comparison of mean statures for particular age groups across European countries” – “Oh so what’s the mean stature of Dutch people?” – “I don’t know – let’s look it up – it says here 1,81 m”  – “Wow, then, if the Dutch I know are only about 1,75m, there must be loads of Dutch people who are  - what – over 2,0 m tall!”

This conversation gave me some ideas about what might be causing the persistence of prejudice in our societies. Could it be that it is simply due to natural propensities toward systematic misunderstanding of some basic statistical concepts?  Some quick research into the question reveals that some work has been done on this – some from a psychology and cog-sci angle, but mostly from the mathematics-education perspective. This article and this follow-up article have particularly good summaries of the types of reasoning fallacies that are universally encountered in those studies (it seems that this book was an early synthetic study). Following Garfield et al., the above example with the different heights is a form of the ‘representativeness heuristic’,  a tendency to erroneously evaluate the likelihood of a sample in relation to one’s perception of the population, coupled with the ‘gambler’s fallacy’, the belief that chance is a self-correcting phenomenon, and with an association fallacy, which causes the subject to put greater weight on his own experience (hence the people one has seen or knows or is related to) . The gambler’s fallacy is a result of using the representativeness heuristic, since the subject believes that, in order to make up for a skewed sample, further samples are more likely to be skewed in the other direction. This error features in the TV sports reporter’s example as well, where a baseball player’s likelihood of getting a hit is evaluated in terms of a league average batting percentage and the idea that this particular individual’s score will ‘improve’ to match that number.

It doesn’t take much imagination to see where these natural tendencies might take us, especially when coupled with a few of the most common logical fallacies (which, judging by the amount of electronic space dedicated to them by Wikipedia, are themselves a force to be reckoned with). But the more interesting question is: what are the origins of these tendencies, and how can we explain them? Most classical theories of learning put a heavy emphasis on induction, which is itself a form of pattern-based statistical learning (see statistical learning infants (needs access to ScienceMag) and a more recent paper on word learning as Bayesian inference (needs access to Trends Cog Sci)). However, these attempts at explaining learning (and in particular, language learning) in terms of statistical concepts do not work  backwards – in other words, we still don’t know how people’s ideas of things like ‘mean’, ‘mode’, ‘spread’, etc. actually form.  Are the fallacies above the result of a lack of proper understanding of some of these concepts – or do errors arise from incorrect or illogical operations carried out with perfectly suitable concepts? Are these concepts in any way dependent on the kind of language of the subject – in a Sapir-Whorf-kind of folk-understanding of formal mathematical concepts?

In my view, a large-scale cross-cultural ethnographic project aimed at understanding the universal underpinnings of mathematical thinking would be a way to solve some of these problems. I think it doubtful that lab- or questionnaire-based approaches alone could get at the root of such questions, mainly because we may not know the diversity of behaviors with which we are dealing, but I am waiting to be proven wrong. Perhaps a combined experimental-ethnographic approach would bring the desired results – one example of such an endeavor is this one, where economists and anthropologists performed game-theoretic experiments in hunting-gathering and small-scale farming societies in various geographic settings, with quite impressive results.