Why Should I Care About... Statistics?

Roast Potatoes
Image credit: benjglbbs/Flickr

The Food Standards Agency has recently launched a campaign called Go for Gold. The premise of the campaign is that certain chemicals (acrylamides) produced in toast, roast potatoes and other starchy foods when they are blackened in cooking has an association with increased cancer risk. Sir David Spiegelhalter, Cambridge University’s Winton Professor of the Public Understanding of Risk, has commented in an opinion piece on the University of Cambridge ‘s research website to say “there is no good evidence of harm from humans consuming acrylamide in their diet: Cancer Research UK say that ‘at the moment, there is no strong evidence linking acrylamide and cancer.’”

“Remember that each study is testing an association with a long list of cancers, so using the standard criteria for statistical significance, we would expect 1 in 20 of these associations to be positive by chance alone”. This is part of an ongoing problem of misrepresentation of statistics within the media and even the legal system.

An idea that I first came across in 1st year undergrad maths for Natural Scientists, Bayes’ Theorem, is another example of how statistics may be misrepresented. The theorem itself is fairly easily presented: P(A|B)=P(A)P(B|A)/P(B), here P(A) is the probability of A occurring, P(B) is the probability of B occurring, and P(B|A) and P(A|B) are the probability of B given A and vice versa. What this can allow you to do is calculate the probability of an event occurring given some knowledge about the system before the event took place.

For example (taken from Wikipedia) given a made up population with 1 % of people having cancer (P(cancer)), the probability of being 65 years old in the total population is 0.2 % (P(65yo)), and the probability of someone diagnosed with cancer being 65 (P(65yo|cancer)) being 0.5 %, we get the probability of a 65 year old having cancer (P(cancer|65)) as P(cancer) times P(65yo|cancer) divided by P(65yo), which comes out as 2.5 %. Although a block of text isn’t the best forum to show even simple maths hopefully this convoluted example shows that although the appropriate statistic for the likelihood of a 65 having cancer might be 0.5 % at first glance, it is actually 2.5 %.

While this might seem a tedious made up example, the appropriate application of statistics helped the appeal for Sally Clark, a solicitor who had her two sons die from sudden infant death syndrome [SIDS]. The chance of having a single child die of SIDS in the circumstances facing her children was given as the prosecution as one in 8500, and they then squared that to get the chance of two children dying in the circumstances, which was stated as one in around 72 million. Despite the statistic of one in 8500 likely being incorrect in the first place, the two deaths were likely connected and so squaring the probability as one would for two independent identical occurrences was also incorrect, and the appropriate likelihood estimate was much lower.

The point of all this is that although statistics are sometimes confusing or boring, their proper understanding is important to all aspects of life, from murder trials to whether or not you decide to eat browned toast.

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