How an anecdote becomes a statistic (based on 'research')

Everyone has heard about those astonishing facts whose source proves tricky to uncover.  “We only use 10% of our brain” is one example, usually followed by some encouragement to undertake a course in new ways of thinking.  There is no scientific basis for this supposed fact.

The same is true of statistics, when numbers are touted around supposedly supporting an argument (or perhaps prejudice) but whose origin proves elusive.  Here, for once, is a nice example where we can trace the story back to its source, and discover how tenuous it is. 

The Daily Telegraph reported on October 31^st 2011 (see here) that there are more Porsches in Greece than there are taxpayers declaring an income above 50,000 Euros per annum, “according to research by Professor Herakles Polemarchakis, former head of the Greek prime minister’s economic department”.   This suggests support for the assertion that tax evasion is widespread in Greece, that therefore the fiscal crisis is their own fault and hence that austerity measures can be justified.

The story is interesting for several reasons:

1.      A simple anecdote is preferred to statistical evidence,  

2.      For once, there is a reported source of the story, and

3.      There is some confusion about whether the story relates to all Porsches or the Cayenne model in particular (different news agencies have different versions).

The BBC followed up this story on the 16^th April 2012 (so the story had been going unchallenged for at least six months) with some fact checking, see here for details.  First they found that there were 311,428 people with incomes above 50,000 Euros in 2010.  Then they asked Porsche how many Cayennes they sold in Greece.  Their spokesman (after he finished laughing) said they had sold around 1,500 over the previous nine years. 

So what of Professor Polemarchakis’ research?  When asked, he replied that his remark was casual, based on what had been circulating in policy circles in Greece a few years back.  He said the only hard fact he was aware of was "the per capita number of Cayennes in [the Greek city of] Larissa was twice that of Cayennes in the OECD countries".

So it is that a casual observation becomes an anecdote which becomes evidence based on research.  However, it is one of those stories where one should immediately be suspicious of the “fact”.  A quick Google check shows Porsche’s European sales in 2011 were 42,084, so Greece is unlikely to take more than (at a guess) 10% of them, around 4,000 vehicles.  To have over 300,000 Porsches (never mind the Cayenne model only) in the country means they must have amassed them over 75 years…

Some good advice

Here is some good advice for budding statisticians from the economist John Kay:

http://www.johnkay.com/2011/08/24/sex-lies-and-pitfalls-of-overblown-statistics

His blog is more often about economic matters but is always worth reading.

Prices by Amazon

Ok, how come the price of my text book is £157.51 on Amazon?  Even I have to say "don't buy it!" at this price.  Instead, you can pay £43.06 at, er, Amazon here for the same product.  Obviously computers aren't yet perfect and I'd be interested to know how Amazon calculates the higher price.  (Prices correct when this blog was written.  These links won't last forever.)

I tend to think book prices are high but I look back at a text book I bought back in 1974, which seemed expensive at the time at £7.20.  The UK retail price index has risen since then by approximately nine times, so in today's money it would be about £64.80.  So it was fairly expensive but it was a hardback edition.  With improved manufacturing technology you would expect books to get relatively cheaper in price over time.

Why this blog?

It makes sense for my first post to explain why I am writing this blog.  Well, the first reason is commercial - it accompanies my text book and allows me to write supplementary material that fills out some of the topics covered in the book.  A physical text book has a number of constraints: there is a page limit for a start, it cannot be right up date with some of its examples and a text book requires a fairly formal writing style concentrating on the techniques of statistics.  A blog gets around some of these restrictions.  The limit to the amount of material depends more upon the time I can devote to it rather than a physical page limit.  I can post about up to date stories and research very easily.  And I can write in a more informal style and give some of the informal insights into the world of statistics.

The second reason for writing is that I believe there is a genuine value in educating people about statistics.  There is a huge amount of ignorance about the subject and few people are even moderately competent at it, never mind experts.  It is therefore very easy to misinterpret events and information, and there is certainly no shortage of bodies ready to supply misleading information.  I hope therefore that readers of the blog will learn at least a little about the subject and become aware of these issues.  Furthermore, I hope that people will come to actually like the subject and see that it is actually interesting and fun!  OK, maybe I'm being a little optimistic here.

In this blog I'll be commenting upon stories with a statistical slant appearing in the press and also upon interesting research that I come across.  The title of the blog comes from the saying "the plural of anecdote is statistics" which tells an important truth.  Psychologically, people are more often swayed by a powerful anecdote than by reams of dull statistics.  But those statistics are the summary of many anecdotes and hence generally give a more accurate account.  I will try to combine both in order to grab your attention and to illustrate something about statistics.

Here's a first attempt (it's in the book).  Some while back, The Guardian newspaper in the UK listed the '100 best schools' based on the fact that they each had 100% of their students pass a national exam.  Most of the schools in the list were small schools.  Does this prove that small schools are better than bigger schools?

Enjoy the blog.