Dumbing Down

In the once great Britain politicians are now pretty dumb.

Royal Statistical Society did a survey of UK Members of Parliament, asking them if a coin is tossed twice what is the probability of getting two heads.

You know the answer I am sure. It is 25%. The probability of the first head is 0.5, the probability of the second is 0.5. The tosses are independent so multiply. Simple.

But MPs are not as smart as you. Only 40% of MPs got the answer right. But if you break that down by party, 53% of Conservative MPs got the right answer. But only 23% of Labour. Some MPs said the answer was one in three. They probably thought that a head then a tail was the same as a tail then a head.

But then I don’t think anyone since Lenin has thought Marxists are smart. And no one thought Lenin was smart, but they didn’t dare tell anyone.

The assumption of independence is crucial. A large numbers of the MPs gave the answer 50%. That would be correct if the second toss was guaranteed to be the same as the first. That would be perfect correlation.

The paediatrician Sir Roy Meadow was often called upon as an expert witness for the prosecution in trials of parents accused of child murder.

In the sad case of Sally Clark who lost two babies, at 8 weeks and 11 weeks, Professor Meadow said the chance of the deaths being due to cot death or Sudden Infant Death Syndrome was 73 million to one. Sally Clark was found guilty of murder.

Meadow seems to have come to his conclusion by squaring the one-in-8,543 chance of a child in a middle-class family falling victim to a cot death that he had read in an article. That probability for a single incidence of cot death is incorrect. But then assuming independence and squaring is irresponsible. There could well be environmental or genetic factors which make the probability of two such deaths far more likely.

The President of the Royal Statistical Society published an open letter outlining the professor’s errors (there were more than just the assumption of independence). Sally Clark’s conviction was overturned.

This was not the only case that Roy Meadow had been involved in. Many were similarly reopened. Eventually Professor Sir Roy Meadow was banned from expert witness work.