Standard deviations

Gary Smith

Why I looked at this book

One often hears of statistical anomalies and paradoxes. Do left handers really die several years younger than right handers? (The answer is No). Then there's Simpson's paradox - A looks to be better than B, but looking more closely B always seems to do better than A. I'm hoping that this book will give plenty of examples of these sort of statistical anomalies.

First impressions

The sample discusses the case of Paul the Octopus, who predicted the results of games in the 2010 World Cup, and explains why things aren't quite what they seem. In other cases surprising results have turned out to be due to people fudging the data. It's a lively read and I'm looking forward to the rest of the book

Main review

The book didn't disappoint in that it continued to be a lively read, but in a way it was too easy to read. I was hoping for more counterintuitive examples that left me thinking 'How can things possibly be like that?' The closest this book gets to this is the problem 'You meet a woman with two children, at least one of which is a girl. What is the probability that the other is a boy'. Smith gives persuasive arguments that the answer is 1/2 although many people think it's 2/3. But he doesn't discuss why there is this disagreement, so I'll do so here:

It depends how you know that at least one child is a girl. If you specifically asked 'Is at least one of your children a girl' then the answer is 2/3. If you came by this information in the normal sort of way (for instance the woman shows you a picture of one of her children - so it could equally well have been a boy) then the answer is 1/2. One sees why Smith's answer is more plausible when you get to modifications of the problem. Would you ever specifically ask 'Is at least one of your children a girl who was born on a Tuesday?'?. But I would have liked more discussion of the problem.

What the book does highlight is stuff that gets published which really shouldn't have. For instance two academics published a paper comparing real prices of shares with nominal prices, but they didn't seem to realise that all they were doing was looking at the movement of the price index. Now this is usually inflation, but in the later part of the 19th Century the USA experienced a period of deflation, (which formed the backdrop for The Wizard of Oz) with the CPI getting back to it's 1864 level by about 1910 - So the lines diverged then converged again. After 1910 the lines diverged, but the authors seem to think they ought to converge again, and (incorrectly) claim that this might mean a large movement of share prices.

This book is full of such examples, making you realise how much is published without significant checking of what is claimed. As such it may help you from making such errors yourself, and it's certainly an entertaining read, so I can wholeheartedly recommend it.