Archive | October, 2013

Demonstrating that we really are very bad at dealing with numbers ?

29 Oct

Math

In the next couple of weeks I’ll start to teach my students about Tversky & Kahneman’s work on heuristics and biases. As a warm-up to that I this week ran through a few examples of cognitive biases. I’m not sure why this came as a surprise, but I realised just how compelling examples of cognitive biases are, particularly those illustrating numerical biases.

My favourite is over thirty years old, but stills seems to engage today’s student:

Disease X is found in 1 in 1000 people

There is a test for disease X that is 100% accurate at detecting the disease where it is present

The disease has a 5% false positive rate? That is in 5% of cases where the disease is not present the test will say that it is present

If you select a person at random and test them for the disease and receive a positive result what is the chance that this person actually has the disease ?

When presented with this question the vast majority of people say that there is a 95% chance that the randomly selected person has the disease. What is really intriguing is that if you step students through the simple arithmetic of this problem they have little trouble appreciating the correct answer i.e.

Imagine testing one thousand people, one of those will have the disease and thus 999 will not have the disease. The test of the one person with the disease will yield a positive result. The tests of the remaining 999 will yield 50 positive results (5% of 999). That’s 51 positive tests from 1000, even though we know that only one person actually have the disease . 1 out of 51 represents means that the chance of a randomly selected person having the disease is actually 1.96% ! For those interested in the psychology behind this, the problem is a demonstration of something called base-rate neglect. Put simply, people ignore how often the disease actually occurs.

This can be a little easier to see in a simple diagram:

exp

The huge discrepancy between their response and the actually answer seems to have a big impact on students, and hopefully makes them aware of consciously reviews responses to statistical questions. These type of problem seem like an excellent way of illustrating to students that we are naturally not disposed to deal well will statistics, and so I’m going to throw a few more in over the next few weeks. There is a second version of this problem which is equally powerful, and I’m going to use it next week to see if the students have retained the concept from the DIsease X problem :

“A cab was involved in a hit and run accident at night. Two cab companies, the Green and the Blue, operate in the city. 85% of the cabs in the city are Green and 15% are Blue.
A witness identified the cab as Blue. The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the two colors 80% of the time and failed 20% of the time.
What is the probability that the cab involved in the accident was Blue rather than Green knowing that this witness identified it as Blue?”

Do tight belts give you throat cancer ?

23 Oct

belt_2689094b

On 1st October the Daily Telegraph reported that wearing tight belts increased your risk of throat cancer. Unlike much popular science reporting this looked like a very straight report of a study, in that it explains the methodology of the study , details where it was published and even quotes one of the authors.

The story gets interesting for teaching purposes it you actually go to the original journal article, as it makes no reference to throat cancer ! What the study actually reports is a link between wearing tight belts and developing acid reflux, equally importantly it was only a very small study (24 participants) that ran for only a few days. It appears that the link to cancer came from an interview with one of the lead authors where he mentioned to small increase in cancer risk that acid reflux caused.

This story seems useful in both encouraging students to read original sources, but also makes a good point about how scientists communicate about science. A scientist talking to another scientist about a tiny increase in cancer risk, will come away with the idea that it isn’t much to worry about. One suspects that a member of the public (or worse, a journalist) would come away from such a conservation just with the phrase ‘CANCER RISK’.

Does no one in public life have a grasp of science ???

15 Oct

gove

The UK press this week has seen a lot of reporting of the views of a Dominic Cummings, a ‘special advisor’ to Michael Gove the Education Secretary. Amongst Cummings views was that 70% of a child’s intelligence is inherited, and thus teaching was not the big influence people think it is. If, for the moment, you ignore the smell of eugenics hanging around this statement it just demonstrates a complete lack of understanding of the basic science.

I’m no genetics expert, but the first thing that occurred to me when I read this story was the concept of a ‘environmental multiplier’. This is an idea I first came across in Jim Flynn’s work, and simply says that environmental factors can have a multiplying effect of relatively small genetic advantages. Imagine an eight year old male child who is 20% taller than other children his age in his class. This is undoubtedly a genetic advantage. Now put that child in a suburb of either London or Chicago, and ask yourself which is more likely to result in a world-class basketball player. Clearly the child in Chicago is more likely to grow up to be a world-class basketball player, but no because of his genetic advantage alone but because of the multiplying influence of his environment. THe Harvard Psychologist Steven Pinker precisely summed up this idea when he said than money and recipes run in families, but that doesn’t mean they are genetic !

Now, this alone isn’t that interesting a story, in that we have a ‘special advisor’ to government who either doesn’t understand, or is deliberately misinterpreting science for political ends. But, a follow-up to this story today is particularly illuminating.

toynbee

In Polly Toynbee’s column in todays Guardian she does the right thing about Dominic Cummings ‘70%’ idea, and asks a geneticist if it makes any sense. However, the story runs under the headline ‘…wealth is considerably more heritable than genes’. I understand the Polly Toynbee will not have had any input into the headline of her column, but it is unbelievably depressing that a Guardian sub-editor could write such a clearly ridiculous headline, and that headline could work its way right through the system and get published. Just for a moment try to imaging how anything could be more heritable than genes !!!

All of this adds to my conviction that it is vital that the general public are educated about the basics of science. On a more cheerful note I’m also quite proud of the fact that by the end of my rational thinking course my students will clearly know more about science than the average Guardian sub-editor.

What do I need to add to my rational thinking course ?

13 Oct

My own department is current working on a rewrite of our undergraduate programme and as a result my current rational thinking course will change from being taught over one semester to being taught across a whole year, i.e. The amount of teaching time I have will double. I’ve written before about my ideas for a rational thinking syllabus, but a doubling of the length of the course means that I’m going to need additional material.

For the last few weeks I’ve been thinking about the idea of ‘context’ in relation to rational thinking. I’ve already included the idea of ‘historical context’ in my rational thinking syllabus but it now seems to me that ‘context’ is a much broader idea than the strictly ‘historical’, for example can a decision be truly rational unless it takes into account the social and political context in which it is made ? One of the most obvious examples of this is the frequent debate in the UK about how various drugs should be classified by the criminal justice system. Essentially, a ‘rational’ review of the evidence, without consideration of ‘context’, leads to the conclusion that alcohol should be treated at least as seriously as some drugs that are currently illegal in the UK. However, as soon as you factor ‘context’ into the situation the decision becomes much less clear cut. For example, historical ‘context (i.e. The USA’s prohibition of alcohol) suggest that any ban would lead to a growth in organised crime.

Equally, social context seems important for quality decision making. For example, my own students’ evaluation of research conducted in the USA can often be biased by their assumption that they have a good understanding of American society. This assumption seems to be borne out frequent exposure to America television and film. However, as soon as one delves into American society in any depth one finds clear differences with norms in Europe on topics as diverse as gun control and abortion.

All of this leads me to an idea that has been circulating my own institution for a few months, without finds a good home. The idea of ‘cultural capital’ has been around since the early 70’s, encompasses non-financial assessed that enable social mobility. If one discounts ‘education’ from this concept, you are still left with too major ideas and appreciation of the arts and an understanding of the ‘context’ ideas that I’ve been talking about.  So over the next few months I’m going to be thinking about how I can best integrate ‘context’ into my existing syllabus.

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