08 December 2017

A Bradford Hill Christmas

The College of Policing research team helps us to examine whether Santa is the cause of our Christmas gifts - from a research and statistics perspective. 

​Despite the masses of evidence to the contrary, some trouble-makers still ask the question, "Does Santa Claus exist?" The likelihood is that these sceptics spent their childhood permanently on the naughty list and are still causing trouble today. But can science help us uncover the answer?

Sir Austin Bradford Hill was a statistician who worked mainly in public health and the spread of diseases. Along with Richard Doll he was one of the pioneers of randomised control trials, famously finding very strong evidence of the link between smoking and lung cancer in the early 1950s. If you want to read about the other wonderful things he did then here's the link to his Wikipedia entry.

In between saving the lives of millions of people Hill found time to outline a list of helpful criteria for judging whether an effect is causally related to the outcome. We've all heard the phrase "correlation does not imply causation" (we have, haven't we?), well these criteria help us determine when correlation might actually be related to causation. They are mainly used when we don't have access to good experimental data, which in our case might involve randomly assigning half the population to have a Christmas without Santa and seeing whether people still received presents. As an experiment is impractical, these seem like the perfect criteria for helping us determine the link between Santa and Christmas presents. Let's have a look at some of the Bradford Hill criteria.

Rule 1The effect has to come after the cause ("Temporality").
This is clearly the case. Santa arrives before Christmas, and departs immediately afterwards. No one ever gets Christmas presents before Santa appears, and Santa has never turned up on Boxing Day after everyone has had their presents looking a bit bemused and apologising for being late.

Rule 2: Consistency ("Reproducibility").
Is the effect observed in different times and places? No matter where you are in the world, Santa can always be found in the weeks preceding Christmas, from Helsinki to Bondi Beach, and for as long as people can remember. So Santa passes this test. If we could find places where people got presents on Christmas day and Santa wasn't there, then we might have evidence against the connection.

Rule 3: Strength of association (or effect size).
Apart from birthdays, people receive very few gifts per day over the course of a year. And yet on Christmas day, just after Santa has visited, they are suddenly in possession of dozens of toys, or unwanted novelty socks. Furthermore, young children, who tend to believe more in Father Christmas generally receive more presents than grumpy, middle aged men who are lucky to get a tie. This is all evidence of a strong "Santa effect".

Rule 4: Specificity.
Does the phenomena only happen at a specific place, time, or to certain people?  If it does then this is evidence of a causal connection.  Santa appears at Christmas along with the spontaneous appearance of millions of presents. Sightings of Santa in the summer are extremely rare, as are millions of presents stuffed into stockings. So we can conclude that he passes the specificity test as well.

Rule 5: Plausibility.
How realistic is the causal mechanism? Is there a more plausible reason? This is a tricky one. We have to choose between a hypersonic sleigh carrying thousands of tons of gifts, or a massive conspiracy where everyone buys presents for everyone else and pretends they are from Santa. However, we know that objects can travel at many times the speed of sound, and we also know that most people are VERY bad at keeping secrets. So the second option is highly unlikely, and we are left with the possibility of a very aerobatic reindeer powered sleigh, carrying an occupant who has access to extremely advanced technology.

All of this ignores the extra evidence for Santa's activities in such fly-on-the-wall documentaries as "Miracle on 34th Street", "Elf" and "Santa Claus Conquers the Martians".  

Using the Bradford Hill Criteria, coupled with other evidence, it is clear that  the case for Santa Claus being the cause of the presents you will find under the tree on Christmas morning is very strong. 

Merry Christmas! Don't forget to leave out a mince pie on Christmas Eve.

You can see the full set of "Bradford Hill" Criteria here: (https://en.wikipedia.org/wiki/Bradford_Hill_criteria)


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