Statistical thinking

800px-Rodin's_The_Thinker
This is how you think statistically

Did you know that over the course of your lifetime you will eat eight spiders in your sleep when they crawl into your open mouth? I hope you didn’t because it is nonsense but widely thought to be true. However, it is useful as a tool to illustrate statistical thinking. If we were trying to answer this question, how would it be done and how much confidence would you have in the answer? Whenever I hear any scientific claim being made I try to imagine what sort of study design would allow me to make it.

spider_pizza_by_luthien3-d33bg6n

So, for the spider question you would probably want a large sample of people from a variety of backgrounds to take part. You then would want to somehow film them sleeping (as self-report isn’t going to work here if people are supposed to be eating them in their sleep). Now if the figure of 8 over a lifetime were correct, and an average lifetime lasts say, 80 years, then we would expect one spider to be sleep-eaten per decade. So unless the study ran for a decade (filming every night) then most participants wouldn’t even contribute one arachnid consumption to the total. Such a long study seems practically impossible. An alternative would be to get an even larger group of people and film them over a shorter number of nights. Again, this seems unfeasible.

This of course doesn’t take into account all of the confounding factors (whether you sleep on your back, side or front, mouth size, geographic location). And this doesn’t even address the question of why anyone would be so interested in this study that they would stump up the millions it would require for it to be done properly. So, if that is what would be required to produce reliable evidence on this burning issue, and we think it is unlikely to have happened, we must concede that either a much less preferable design was used or that it was entirely made up. This is part of how i critically appraise any evidence i hear about and I find it extremely helpful.

The ability to critically appraise evidence is more crucial now than ever. We live in an information age and are constantly being fed information from all corners. We need some way to protect ourselves from being mislead.

That is why I was impressed recently when my dad showed me last year’s Leaving Certificate (the Irish equivalent of A levels) exam question in Maths. The whole thing is available here but this is the bit that I liked most

Que 7 table

(iii) A commentator states that “The changes reflected in the data from 2006 to 2011 make it more difficult to balance the Government’s income and expenditure”

Do you agree with this statement? Give two reasons for your answer based on your calculations above.

This is exactly the type of question that mathematics and statistics can provide the tools to answer. These skills allow people to interrogate press releases, and government statistics, and manufacturer’s claims, and scientific findings and are crucial to allow people to make informed decisions. We are constantly bombarded with claims and counter claims from politicians and academics and adverts and journalists. Maths and stats lets people make up their own minds. Statistical thinking is one of the most important components of that.

 

 

 

Photo credit-Rodin’s the Thinker: By Drflet (Own work) [CC BY-SA 3.0 (http://creativecommons.org /licenses/by-sa/3.0)], via Wikimedia Commons

Photo credit-Spider pizza: By Luthien3 (Own work) [CC BY-SA 3.0 (http://creativecommons.org /licenses/by-sa/3.0)], via Deviantart

 

 

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