Statistical Rules of Thumb

I guess that we all promulgate to students the standard rules of thumb that a sample of at least 30 justifies appeal to the central limit theorem, that np > 5 is satisfactory for a normal approximation to the binomial distribution, that expected frequencies of at least 5 should govern applications of χ2 goodness-of-fit tests and so on. van Belle has accumulated a whole book-full of such rules, some familiar, some obscure—at least to this reader—and mainly rather more substantial. The book is organized into eight chapters with about a dozen sections in each. It is the sections that give the rules. Each has a descriptive title, e.g. ‘Use at least twelve observations in constructing a confidence interval’, always followed by the same five subsections: ‘Introduction’—a general background description; ‘Rule of thumb’—the bare statement of the rule; ‘Illustration’—a hypothetical or genuine case-study; ‘Basis of the rule’—a description of the theoretical underpinning of the rule; ‘Discussion’; ‘Extensions’. The first chapter, entitled ‘The basics’, looks at fundamental issues in statistical modelling, hypo- thesis testing and estimation. Sample rules include the above one on confidence intervals, ‘Beware of linear models’, ‘Use p-values to determine sample size, confidence intervals to report results’ and ‘Be eclectic and ecumenical in inference’, this last one acknowledging that an applied statistician may use methods from each of Neyman–Pearson, likelihood and Bayesian approaches as appropriate. Chapter 2, on ‘Sample size’, includes rules such as ‘Calculating sample size using the coefficient of variation’, ‘Sample size calculation for the binomial distribution’ and ‘When unequal sample sizes matter; when they don't’. The third chapter on ‘Covariation’ covers rules such as ‘Do not correlate rates or ratios indiscriminately’ and ‘Pairing data is not always a good idea’. The next two chapters, on ‘Epidemiology’ and ‘Environmental studies’ respectively, are rather more specialized than the rest of the book and reflect the author's own long association with these areas. However, I found these sections interesting precisely because of my unfamiliarity with much of the material. Chapter 6 covers the design and analysis of experiments and clinical trials, and features much good advice for the practitioner, including pieces on ‘Blocking is the key to reducing variability’, ‘Distinguish between design structure and treatment structure’ and ‘Address multiple comparisons before starting the study’. The next chapter I particularly liked. It presents rules of thumb for communicating numerical information by using words, tables and graphs. Indeed, the first rule is to use text for a few numbers, tables for many numbers and graphs for complex relationships. In my current work environment, I cannot resist taking the opportunity to point colleagues—and students—to ‘Never use a pie chart’, ‘Stacked bargraphs are worse than bargraphs’ and ‘Three-dimensional bargraphs constitute mis- directed artistry’! The final chapter, on ‘Consulting’, is one that can usefully be read by anyone who is called on to give statistical or indeed any sort of ‘expert’ advice. The beginning practitioner in particular will find this chapter invaluable, with sections including ‘Structure a consultation session to have a beginning, a middle, and an end’, ‘Tailor advice to the level of the investigator’, ‘Ethics precedes, guides and follows consultation’ and ‘Listen to, and heed the advice of experts in the field’. I thoroughly recommend this book. It is well written and presented and, although it is true that many of the rules are formalized common sense that we would all apply, many have a less obvious technical justification and I would be surprised if any reader found no surprises. By its structure, it is the kind of book that one can happily dip into and find something of interest but it is also well indexed by topic and author and there is an excellent list of references. As the author acknowledges, you may look for a favourite rule and fail to find it or you may find a rule with which you would take issue. In both cases you are invited to contact the author. In any case I would urge you to visit the Web site (http://www.vanbelle.org) from where you can download Chapter 2 as a taster as well as consult the growing ‘Rule of the month’ list and the disturbingly lengthy list of corrections, to which I am about to make some additions!