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David Coggon (2nd edition; pp 120; £14.95) 2002. BMJ Books. ISBN 0 7279 1609 2
It is more difficult to write a good short book than a good long book! Textbooks of statistics tend to vary between easy introductions that never seem to tell you how to do the calculations and large ones that tell most of us too much. The desire, common among mathematicians, that we should understand the origins of all the methods, makes the bigger books hard going and, in practice, many research workers use computer software packages to do the analyses. How long must it be since anybody calculated a standard deviation for themselves using the “short cut formula”? Of course, unthinking application of packages is dangerous. Even when properly applied by experts, problems will arise: this year’s discovery of the errors in the Generalised Additive Models much used in air pollution work proves the point.
David Coggon is both a distinguished medical epidemiologist and a mathematician. He has provided a book that is easy to read and yet rigorous in the way in which concepts are developed. Very few formulae are included: the computer program approach is accepted. The rigour is most clearly seen in his analysis of bivariate data: 10 combinations (5 types of variable, arranged in pairs: 5!/2!(5–2)!) and in the chapters dealing with statistical modelling and with statistical power and sampling. This latter chapter has the clearest definition of statistical power, in terms of the probability of a type 2 error, that I have seen. A little more discussion of the relative importance of avoiding type 1 and type 2 errors would have been useful. Correlation coefficients are discussed in useful detail, though I could not find a definition of the much quoted statistic r2: the coefficient of determination.
Each of the nine short chapters ends with a set of questions. These are very well designed to test how well the reader has understood the chapter. Answers, rather more explanatory than usual in statistics books, are provided. Reading the questions and answers is a short cut to knowledge! Many years ago, School Algebra by Hall (568 pages), was the standard O level text: even more useful was Grenvilles Key to Hall’s School Algebra (699 pages) which took apart every problem set by Hall and explained how to solve them. Oh, for such a book on statistics: perhaps the author should write one!
In conclusion, David Coggon has written probably the best short introduction to practical statistics. All doctors interested in research should read it.