Deceptive numbers (1)

We typically view numbers as objective and precise but numbers can also deceive. I have collected a few interesting examples for the readers of da-boss to ponder on.

First an anecdote. An old guide at a natural history museum with an imposing T. Rex on display is asked by a visitor about the age of the skeleton. He replies: “It is 65 million and 38 years old.” The visitor is stunned. “How do you know that?”. The guide responds: “On my first day at work I asked a scientist the same question and he said 65 million years. That was 38 years ago”. 65 000 000 + 38 = 65 000 038 so why is this a nonsensical answer? Because 65 million years was just a rough estimate, with an accuracy of say +/- 1 million years. Using the same dating convention the skeleton is still “65 million” years old. The 38 years which have passed since the guide started work at the museum are dwarfed into insignificance by the error of the original estimate.

Not a bad start but let us move on to more serious issues. Like the year 2000 Bush vs Gore Florida election. There are some errors which affect the results of public elections. For example badly laid out ballot papers, faulty vote counting machines, human errors (and fraud) during manual recounts, judicial interference effectively changing the pool of “eligible” votes etc. As a result of these systemic problems the accuracy of any election is of the order of 0.25-0.5%. So the 2000 Florida election was a DRAW! The 300 or so vote advantage to Bush is like the 38 years in the previous example – it has no practical, real-life meaning. The election legislation in the US has a procedure for dealing with draws – coin toss – and it should have been used in 2000.

There is also deceptive use of statistics in the courtrooms. One chilling example was the case of a British woman accused of murder after her two children died of what was diagnosed as SIDS (Sudden Infant Death Syndrome). The prosecution presented statistics that SIDS affects one in 8500 children in the UK. This, according to the prosecutor, meant that two SIDS cases in one family had an estimated probability of 1-to-8500*8500 = 1-to-72 million. This is a tiny probability and based on this evidence the woman was convicted of murder. Outraged, the British Statistical Society wrote a letter to the judiciary and the conviction was overturned on appeal. Why is the 1-to-72 million number dodgy? Because the two SIDS cases were not independent events. From what we know SIDS has a risk profile tied to genetics, environmental conditions etc. It is obvious that a second child born to the same parents and living in the same house as the first victim had a much higher than average chance of dying of SIDS. Similarly, the fact burglaries are relatively rare does not mean that one person is unlikely to commit three or five. If they stole once they are a burglar and burglars usually steal more than once. This is where the “cockroach theory” kicks in – “where there is one there is more”.

Deceptive numbers (2)


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