This is an absolutely fascinating book for anyone interested in the way that science really works, bearing in mind the difficulties of having to base our models and theories on induction. Andrew Jaffe introduces the difficulties we face when trying to take a scientific view because largely we are dependent on induction: predicting the future from what has previously been observed. He explores what probability is, the two key ways of looking at it (frequentist and Bayesian) and how scientists use (or misuse it) to work out the implications of their experiments for hypotheses. This is then expanded into looking at the nature of scientific models and the philosophy of science before heading out to entropy, quantum randomness and attempting to achieve meaningful cosmology with its potential dearth of evidence.  The topic might sound a little dry, but in fact Jaffe does it with good humour and a very readable style. For example, he uses measuring his daughter's height by making marks on...

There's a stereotype of computer users: Mac users are creative and cool, while PC users are businesslike and unimaginative. Less well-known is that the world of statistics has an equivalent division. Bayesians are the Mac users of the stats world, where frequentists are the PC people. This book sets out to show why Bayesians are not just cool, but also mostly right. Tom Chivers does an excellent job of giving us some historical background, then dives into two key aspects of the use of statistics. These are in science, where the standard approach is frequentist and Bayes only creeps into a few specific applications, such as the accuracy of medical tests, and in decision theory where Bayes is dominant. If this all sounds very dry and unexciting, it's quite the reverse. I admit, I love probability and statistics, and I am something of a closet Bayesian*), but Chivers' light and entertaining style means that what could have been the mathematical equivalent of debating angels on...

This has probably been the hardest popular science book to review I've ever read, and because of this I'm going to give a relatively unusual structure to this write-up. The topic is fascinating. It's about the reality of making predictions - in general, and particularly about climate change. David Stainforth is very firmly of the opinion that climate change is an emergency that requires our action - but he is unusually honest it admitting that the problems of forecasting how climate change will proceed are so great because we face a whole pile of issues along the way. He highlights how predicting the way the climate will change is a 'one-shot bet' - we don't get to make a forecast time and time again, improving our technique. There will only be a single climate future. This isn't great because we are dealing with a very complex system, we are extrapolating into an unprecedented situation, and the chaotic, non-linear nature of the systems involved make predic...

This is one of my favourite kinds of book - it takes on the way statistics are presented to us, points out flaws and pitfalls, and gives clear guidance on how to do it better. The Chivers brothers' book isn't particularly new in doing this - for example, Michael Blastland and Andrew Dilnot did something similar in the excellent 2007 title The Tiger that Isn't - but it's good to have an up-to-date take on the subject, and How to Read Numbers gives us both some excellent new examples and highlights errors that are more common now. The relatively slim title (and that's a good thing) takes the reader through a whole host of things that can go wrong. So, for example, they explore the dangers of anecdotal evidence, tell of study samples that are too small or badly selected, explore the easily misunderstood meaning of 'statistical significance', consider confounders, effect size, absolute versus relative risk, rankings, cherry picking and more. This is all done i...

Many UK listeners will be familiar with the BBC's excellent  More or Less radio show, hosted by the Financial Times' 'undercover economist' Tim Harford. The programme takes on numbers in the news to explain them and, where necessary, show what's wrong with them, in a light but informative fashion. The only slight problem with the programme is that it does tend towards silly presentation styles (though the last couple of years these have been toned down). On his own, Tim Harford is perhaps less fun and more serious in style, but remains approachable on a subject that most of us ought to understand better. One of the most enjoyable things in the field is to shoot down misuse of stats. It's certainly an important thing to do, but Harford points out that only doing this, while entertaining, is potentially dangerous as it may lead to a total detachment from the usefulness of statistics. Instead, he suggests, we need to get better about thinking about the numbers we...

If there's one thing that's better than a juicy statistic, it's enjoying the process of pulling apart a dodgy one. It's why the radio programme More or Less is so excellent - so Paul Goodwin's book, subtitled 'surviving statistics in a post-truth world' was something I was really looking forward to - but for reasons I find it hard to put my finger on, it doesn't quite hit the spot. Goodwin, a maths professor at the University of Bath, starts with a series of chapters telling us what's wrong with many of the statistics we see everyday. And he makes good points. We discover the dangers of rankings and trying to summarise a complex distinction in a single measure. We see why proxies are poor (essentially, if you can't actually measure what you want to, using something else that might be an appropriate indicator, but often isn't). We explore why polls are problematic. And there's a bit on Bayesian statistics and how it still tends to be d...

How we see the world is not the way it really is. There have been several books based on this premise in the last few years, from Hans Rosling's impressive Factfulness to the distinctly fanciful The Case Against Reality by Donald Hoffman. In The Perils of Perception , Bobby Duffy takes an approach that is similar to Rosling's in surveying large numbers of people in different countries (in fact, one chapter of the book specifically references Rosling), but rather than concentrate as Rosling does on the specific topic of development, Duffy takes a much wider sweep of coverage of our perceptions of our world - and just like Rosling finds that most of us are way off on our appreciation of how things really are. Whether we're dealing with politics and immigration, finance, climate change, sex or crime, Duffy shows that the majority of people tend to get things wrong. (I think I've read too many of these books, as I tended, if anything, to err in the opposite dire...

Michael Blastland is co-author of one of my favourite titles on the use and misuse of numbers, The Tiger that Isn't - so I was excited to see this book and wasn't disappointed. Blastland opens with the story of a parthenogenic crustacean that seems to demonstrate that, despite having near-identical nature and nurture, a collection of the animals vary hugely in size, length of life and practically every other measure. This is used to introduce us to the idea that our science deals effectively with the easy bit, the 'half' that is accessible, but that in many circumstances there is a hidden half that comprises a whole range of very small factors which collectively can have a huge impact, but which are pretty much impossible to predict or account for. (I put 'half' in inverted commas as it might be fairer to say 'part' - there's no suggestion that this is exactly 50:50.) We go on to discover this hidden half turning up in all kinds of applica...

Statistics have a huge impact on us - we are bombarded with them in the news, they are essential to medical trials, fundamental science, some court cases and far more. Yet statistics is also a subject than many struggle to deal with (especially when the coupled subject of probability rears its head). Most of us just aren't equipped to understand what we're being told, or to question it when the statistics are dodgy. What David Spiegelhalter does here is provide a very thorough introductory grounding in statistics without making use of mathematical formulae*. And it's remarkable. What will probably surprise some who have some training in statistics, particularly if (like mine) it's on the old side, is that probability doesn't come into the book until page 205. Spiegelhalter argues that as probability is the hardest aspect for us to get an intuitive feel for, this makes a lot of sense - and I think he's right. That doesn't mean that he doesn't cover...

Without doubt a remarkable book. Hans Rosling (who died towards the end of writing Factfulness ), aided by his son and daughter-in-law, tells the remarkable story of the gap between our appreciation of the state of the world and the reality. Rosling, a doctor originally, illustrates some of the points he makes with personal experience, particularly examples where an incorrect assumption about facts he has made has led to potentially disastrous circumstances. But the core of the book makes use of a series of 12 multiple choice questions on the state of the world which, on the whole, we answer worse that choosing randomly - because almost universally we think the world is far worse than it really is. Although Rosling claims not to be an optimist, making it clear that he isn't saying everything is rosy - there's still a lot to improve - the fact is that most of our ideas of, for example, how bad world poverty is, education of girls, size of families and far more reflects w...